# HG changeset patch
# User Alpar Juttner <alpar@cs.elte.hu>
# Date 1240315699 -3600
# Node ID 0ba8dfce725936da00a99430fb96aa971f5ecb8c
# Parent f63e87b9748ef2b2150ead29795b5c914c275fab# Parent 16d7255a6849b843f36037539abe07bb9bf1a8b0
Merge
diff -r f63e87b9748e -r 0ba8dfce7259 doc/groups.dox
--- a/doc/groups.dox Tue Apr 21 10:34:49 2009 +0100
+++ b/doc/groups.dox Tue Apr 21 13:08:19 2009 +0100
@@ -435,9 +435,10 @@
@ingroup algs
\brief Algorithms for finding matchings in graphs and bipartite graphs.
-This group contains algorithm objects and functions to calculate
+This group contains the algorithms for calculating
matchings in graphs and bipartite graphs. The general matching problem is
-finding a subset of the arcs which does not shares common endpoints.
+finding a subset of the edges for which each node has at most one incident
+edge.
There are several different algorithms for calculate matchings in
graphs. The matching problems in bipartite graphs are generally
diff -r f63e87b9748e -r 0ba8dfce7259 lemon/Makefile.am
--- a/lemon/Makefile.am Tue Apr 21 10:34:49 2009 +0100
+++ b/lemon/Makefile.am Tue Apr 21 13:08:19 2009 +0100
@@ -89,8 +89,8 @@
lemon/lp_skeleton.h \
lemon/list_graph.h \
lemon/maps.h \
+ lemon/matching.h \
lemon/math.h \
- lemon/max_matching.h \
lemon/min_cost_arborescence.h \
lemon/nauty_reader.h \
lemon/path.h \
diff -r f63e87b9748e -r 0ba8dfce7259 lemon/euler.h
--- a/lemon/euler.h Tue Apr 21 10:34:49 2009 +0100
+++ b/lemon/euler.h Tue Apr 21 13:08:19 2009 +0100
@@ -26,33 +26,31 @@
/// \ingroup graph_properties
/// \file
-/// \brief Euler tour
+/// \brief Euler tour iterators and a function for checking the \e Eulerian
+/// property.
///
-///This file provides an Euler tour iterator and ways to check
-///if a digraph is euler.
-
+///This file provides Euler tour iterators and a function to check
+///if a (di)graph is \e Eulerian.
namespace lemon {
- ///Euler iterator for digraphs.
+ ///Euler tour iterator for digraphs.
- /// \ingroup graph_properties
- ///This iterator converts to the \c Arc type of the digraph and using
- ///operator ++, it provides an Euler tour of a \e directed
- ///graph (if there exists).
+ /// \ingroup graph_prop
+ ///This iterator provides an Euler tour (Eulerian circuit) of a \e directed
+ ///graph (if there exists) and it converts to the \c Arc type of the digraph.
///
- ///For example
- ///if the given digraph is Euler (i.e it has only one nontrivial component
- ///and the in-degree is equal to the out-degree for all nodes),
- ///the following code will put the arcs of \c g
- ///to the vector \c et according to an
- ///Euler tour of \c g.
+ ///For example, if the given digraph has an Euler tour (i.e it has only one
+ ///non-trivial component and the in-degree is equal to the out-degree
+ ///for all nodes), then the following code will put the arcs of \c g
+ ///to the vector \c et according to an Euler tour of \c g.
///\code
/// std::vector<ListDigraph::Arc> et;
- /// for(DiEulerIt<ListDigraph> e(g),e!=INVALID;++e)
+ /// for(DiEulerIt<ListDigraph> e(g); e!=INVALID; ++e)
/// et.push_back(e);
///\endcode
- ///If \c g is not Euler then the resulted tour will not be full or closed.
+ ///If \c g has no Euler tour, then the resulted walk will not be closed
+ ///or not contain all arcs.
///\sa EulerIt
template<typename GR>
class DiEulerIt
@@ -65,53 +63,65 @@
typedef typename GR::InArcIt InArcIt;
const GR &g;
- typename GR::template NodeMap<OutArcIt> nedge;
+ typename GR::template NodeMap<OutArcIt> narc;
std::list<Arc> euler;
public:
///Constructor
+ ///Constructor.
///\param gr A digraph.
- ///\param start The starting point of the tour. If it is not given
- /// the tour will start from the first node.
+ ///\param start The starting point of the tour. If it is not given,
+ ///the tour will start from the first node that has an outgoing arc.
DiEulerIt(const GR &gr, typename GR::Node start = INVALID)
- : g(gr), nedge(g)
+ : g(gr), narc(g)
{
- if(start==INVALID) start=NodeIt(g);
- for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n);
- while(nedge[start]!=INVALID) {
- euler.push_back(nedge[start]);
- Node next=g.target(nedge[start]);
- ++nedge[start];
- start=next;
+ if (start==INVALID) {
+ NodeIt n(g);
+ while (n!=INVALID && OutArcIt(g,n)==INVALID) ++n;
+ start=n;
+ }
+ if (start!=INVALID) {
+ for (NodeIt n(g); n!=INVALID; ++n) narc[n]=OutArcIt(g,n);
+ while (narc[start]!=INVALID) {
+ euler.push_back(narc[start]);
+ Node next=g.target(narc[start]);
+ ++narc[start];
+ start=next;
+ }
}
}
- ///Arc Conversion
+ ///Arc conversion
operator Arc() { return euler.empty()?INVALID:euler.front(); }
+ ///Compare with \c INVALID
bool operator==(Invalid) { return euler.empty(); }
+ ///Compare with \c INVALID
bool operator!=(Invalid) { return !euler.empty(); }
///Next arc of the tour
+
+ ///Next arc of the tour
+ ///
DiEulerIt &operator++() {
Node s=g.target(euler.front());
euler.pop_front();
- //This produces a warning.Strange.
- //std::list<Arc>::iterator next=euler.begin();
typename std::list<Arc>::iterator next=euler.begin();
- while(nedge[s]!=INVALID) {
- euler.insert(next,nedge[s]);
- Node n=g.target(nedge[s]);
- ++nedge[s];
+ while(narc[s]!=INVALID) {
+ euler.insert(next,narc[s]);
+ Node n=g.target(narc[s]);
+ ++narc[s];
s=n;
}
return *this;
}
///Postfix incrementation
+ /// Postfix incrementation.
+ ///
///\warning This incrementation
- ///returns an \c Arc, not an \ref DiEulerIt, as one may
+ ///returns an \c Arc, not a \ref DiEulerIt, as one may
///expect.
Arc operator++(int)
{
@@ -121,30 +131,28 @@
}
};
- ///Euler iterator for graphs.
+ ///Euler tour iterator for graphs.
/// \ingroup graph_properties
- ///This iterator converts to the \c Arc (or \c Edge)
- ///type of the digraph and using
- ///operator ++, it provides an Euler tour of an undirected
- ///digraph (if there exists).
+ ///This iterator provides an Euler tour (Eulerian circuit) of an
+ ///\e undirected graph (if there exists) and it converts to the \c Arc
+ ///and \c Edge types of the graph.
///
- ///For example
- ///if the given digraph if Euler (i.e it has only one nontrivial component
- ///and the degree of each node is even),
+ ///For example, if the given graph has an Euler tour (i.e it has only one
+ ///non-trivial component and the degree of each node is even),
///the following code will print the arc IDs according to an
///Euler tour of \c g.
///\code
- /// for(EulerIt<ListGraph> e(g),e!=INVALID;++e) {
+ /// for(EulerIt<ListGraph> e(g); e!=INVALID; ++e) {
/// std::cout << g.id(Edge(e)) << std::eol;
/// }
///\endcode
- ///Although the iterator provides an Euler tour of an graph,
- ///it still returns Arcs in order to indicate the direction of the tour.
- ///(But Arc will convert to Edges, of course).
+ ///Although this iterator is for undirected graphs, it still returns
+ ///arcs in order to indicate the direction of the tour.
+ ///(But arcs convert to edges, of course.)
///
- ///If \c g is not Euler then the resulted tour will not be full or closed.
- ///\sa EulerIt
+ ///If \c g has no Euler tour, then the resulted walk will not be closed
+ ///or not contain all edges.
template<typename GR>
class EulerIt
{
@@ -157,7 +165,7 @@
typedef typename GR::InArcIt InArcIt;
const GR &g;
- typename GR::template NodeMap<OutArcIt> nedge;
+ typename GR::template NodeMap<OutArcIt> narc;
typename GR::template EdgeMap<bool> visited;
std::list<Arc> euler;
@@ -165,47 +173,56 @@
///Constructor
- ///\param gr An graph.
- ///\param start The starting point of the tour. If it is not given
- /// the tour will start from the first node.
+ ///Constructor.
+ ///\param gr A graph.
+ ///\param start The starting point of the tour. If it is not given,
+ ///the tour will start from the first node that has an incident edge.
EulerIt(const GR &gr, typename GR::Node start = INVALID)
- : g(gr), nedge(g), visited(g, false)
+ : g(gr), narc(g), visited(g, false)
{
- if(start==INVALID) start=NodeIt(g);
- for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n);
- while(nedge[start]!=INVALID) {
- euler.push_back(nedge[start]);
- visited[nedge[start]]=true;
- Node next=g.target(nedge[start]);
- ++nedge[start];
- start=next;
- while(nedge[start]!=INVALID && visited[nedge[start]]) ++nedge[start];
+ if (start==INVALID) {
+ NodeIt n(g);
+ while (n!=INVALID && OutArcIt(g,n)==INVALID) ++n;
+ start=n;
+ }
+ if (start!=INVALID) {
+ for (NodeIt n(g); n!=INVALID; ++n) narc[n]=OutArcIt(g,n);
+ while(narc[start]!=INVALID) {
+ euler.push_back(narc[start]);
+ visited[narc[start]]=true;
+ Node next=g.target(narc[start]);
+ ++narc[start];
+ start=next;
+ while(narc[start]!=INVALID && visited[narc[start]]) ++narc[start];
+ }
}
}
- ///Arc Conversion
+ ///Arc conversion
operator Arc() const { return euler.empty()?INVALID:euler.front(); }
- ///Arc Conversion
+ ///Edge conversion
operator Edge() const { return euler.empty()?INVALID:euler.front(); }
- ///\e
+ ///Compare with \c INVALID
bool operator==(Invalid) const { return euler.empty(); }
- ///\e
+ ///Compare with \c INVALID
bool operator!=(Invalid) const { return !euler.empty(); }
///Next arc of the tour
+
+ ///Next arc of the tour
+ ///
EulerIt &operator++() {
Node s=g.target(euler.front());
euler.pop_front();
typename std::list<Arc>::iterator next=euler.begin();
-
- while(nedge[s]!=INVALID) {
- while(nedge[s]!=INVALID && visited[nedge[s]]) ++nedge[s];
- if(nedge[s]==INVALID) break;
+ while(narc[s]!=INVALID) {
+ while(narc[s]!=INVALID && visited[narc[s]]) ++narc[s];
+ if(narc[s]==INVALID) break;
else {
- euler.insert(next,nedge[s]);
- visited[nedge[s]]=true;
- Node n=g.target(nedge[s]);
- ++nedge[s];
+ euler.insert(next,narc[s]);
+ visited[narc[s]]=true;
+ Node n=g.target(narc[s]);
+ ++narc[s];
s=n;
}
}
@@ -214,9 +231,10 @@
///Postfix incrementation
- ///\warning This incrementation
- ///returns an \c Arc, not an \ref EulerIt, as one may
- ///expect.
+ /// Postfix incrementation.
+ ///
+ ///\warning This incrementation returns an \c Arc (which converts to
+ ///an \c Edge), not an \ref EulerIt, as one may expect.
Arc operator++(int)
{
Arc e=*this;
@@ -226,18 +244,23 @@
};
- ///Checks if the graph is Eulerian
+ ///Check if the given graph is \e Eulerian
/// \ingroup graph_properties
- ///Checks if the graph is Eulerian. It works for both directed and undirected
- ///graphs.
- ///\note By definition, a digraph is called \e Eulerian if
- ///and only if it is connected and the number of its incoming and outgoing
+ ///This function checks if the given graph is \e Eulerian.
+ ///It works for both directed and undirected graphs.
+ ///
+ ///By definition, a digraph is called \e Eulerian if
+ ///and only if it is connected and the number of incoming and outgoing
///arcs are the same for each node.
///Similarly, an undirected graph is called \e Eulerian if
- ///and only if it is connected and the number of incident arcs is even
- ///for each node. <em>Therefore, there are digraphs which are not Eulerian,
- ///but still have an Euler tour</em>.
+ ///and only if it is connected and the number of incident edges is even
+ ///for each node.
+ ///
+ ///\note There are (di)graphs that are not Eulerian, but still have an
+ /// Euler tour, since they may contain isolated nodes.
+ ///
+ ///\sa DiEulerIt, EulerIt
template<typename GR>
#ifdef DOXYGEN
bool
@@ -256,7 +279,7 @@
{
for(typename GR::NodeIt n(g);n!=INVALID;++n)
if(countInArcs(g,n)!=countOutArcs(g,n)) return false;
- return connected(Undirector<const GR>(g));
+ return connected(undirector(g));
}
}
diff -r f63e87b9748e -r 0ba8dfce7259 lemon/matching.h
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/matching.h Tue Apr 21 13:08:19 2009 +0100
@@ -0,0 +1,3244 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2009
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef LEMON_MAX_MATCHING_H
+#define LEMON_MAX_MATCHING_H
+
+#include <vector>
+#include <queue>
+#include <set>
+#include <limits>
+
+#include <lemon/core.h>
+#include <lemon/unionfind.h>
+#include <lemon/bin_heap.h>
+#include <lemon/maps.h>
+
+///\ingroup matching
+///\file
+///\brief Maximum matching algorithms in general graphs.
+
+namespace lemon {
+
+ /// \ingroup matching
+ ///
+ /// \brief Maximum cardinality matching in general graphs
+ ///
+ /// This class implements Edmonds' alternating forest matching algorithm
+ /// for finding a maximum cardinality matching in a general undirected graph.
+ /// It can be started from an arbitrary initial matching
+ /// (the default is the empty one).
+ ///
+ /// The dual solution of the problem is a map of the nodes to
+ /// \ref MaxMatching::Status "Status", having values \c EVEN (or \c D),
+ /// \c ODD (or \c A) and \c MATCHED (or \c C) defining the Gallai-Edmonds
+ /// decomposition of the graph. The nodes in \c EVEN/D induce a subgraph
+ /// with factor-critical components, the nodes in \c ODD/A form the
+ /// canonical barrier, and the nodes in \c MATCHED/C induce a graph having
+ /// a perfect matching. The number of the factor-critical components
+ /// minus the number of barrier nodes is a lower bound on the
+ /// unmatched nodes, and the matching is optimal if and only if this bound is
+ /// tight. This decomposition can be obtained using \ref status() or
+ /// \ref statusMap() after running the algorithm.
+ ///
+ /// \tparam GR The undirected graph type the algorithm runs on.
+ template <typename GR>
+ class MaxMatching {
+ public:
+
+ /// The graph type of the algorithm
+ typedef GR Graph;
+ /// The type of the matching map
+ typedef typename Graph::template NodeMap<typename Graph::Arc>
+ MatchingMap;
+
+ ///\brief Status constants for Gallai-Edmonds decomposition.
+ ///
+ ///These constants are used for indicating the Gallai-Edmonds
+ ///decomposition of a graph. The nodes with status \c EVEN (or \c D)
+ ///induce a subgraph with factor-critical components, the nodes with
+ ///status \c ODD (or \c A) form the canonical barrier, and the nodes
+ ///with status \c MATCHED (or \c C) induce a subgraph having a
+ ///perfect matching.
+ enum Status {
+ EVEN = 1, ///< = 1. (\c D is an alias for \c EVEN.)
+ D = 1,
+ MATCHED = 0, ///< = 0. (\c C is an alias for \c MATCHED.)
+ C = 0,
+ ODD = -1, ///< = -1. (\c A is an alias for \c ODD.)
+ A = -1,
+ UNMATCHED = -2 ///< = -2.
+ };
+
+ /// The type of the status map
+ typedef typename Graph::template NodeMap<Status> StatusMap;
+
+ private:
+
+ TEMPLATE_GRAPH_TYPEDEFS(Graph);
+
+ typedef UnionFindEnum<IntNodeMap> BlossomSet;
+ typedef ExtendFindEnum<IntNodeMap> TreeSet;
+ typedef RangeMap<Node> NodeIntMap;
+ typedef MatchingMap EarMap;
+ typedef std::vector<Node> NodeQueue;
+
+ const Graph& _graph;
+ MatchingMap* _matching;
+ StatusMap* _status;
+
+ EarMap* _ear;
+
+ IntNodeMap* _blossom_set_index;
+ BlossomSet* _blossom_set;
+ NodeIntMap* _blossom_rep;
+
+ IntNodeMap* _tree_set_index;
+ TreeSet* _tree_set;
+
+ NodeQueue _node_queue;
+ int _process, _postpone, _last;
+
+ int _node_num;
+
+ private:
+
+ void createStructures() {
+ _node_num = countNodes(_graph);
+ if (!_matching) {
+ _matching = new MatchingMap(_graph);
+ }
+ if (!_status) {
+ _status = new StatusMap(_graph);
+ }
+ if (!_ear) {
+ _ear = new EarMap(_graph);
+ }
+ if (!_blossom_set) {
+ _blossom_set_index = new IntNodeMap(_graph);
+ _blossom_set = new BlossomSet(*_blossom_set_index);
+ }
+ if (!_blossom_rep) {
+ _blossom_rep = new NodeIntMap(_node_num);
+ }
+ if (!_tree_set) {
+ _tree_set_index = new IntNodeMap(_graph);
+ _tree_set = new TreeSet(*_tree_set_index);
+ }
+ _node_queue.resize(_node_num);
+ }
+
+ void destroyStructures() {
+ if (_matching) {
+ delete _matching;
+ }
+ if (_status) {
+ delete _status;
+ }
+ if (_ear) {
+ delete _ear;
+ }
+ if (_blossom_set) {
+ delete _blossom_set;
+ delete _blossom_set_index;
+ }
+ if (_blossom_rep) {
+ delete _blossom_rep;
+ }
+ if (_tree_set) {
+ delete _tree_set_index;
+ delete _tree_set;
+ }
+ }
+
+ void processDense(const Node& n) {
+ _process = _postpone = _last = 0;
+ _node_queue[_last++] = n;
+
+ while (_process != _last) {
+ Node u = _node_queue[_process++];
+ for (OutArcIt a(_graph, u); a != INVALID; ++a) {
+ Node v = _graph.target(a);
+ if ((*_status)[v] == MATCHED) {
+ extendOnArc(a);
+ } else if ((*_status)[v] == UNMATCHED) {
+ augmentOnArc(a);
+ return;
+ }
+ }
+ }
+
+ while (_postpone != _last) {
+ Node u = _node_queue[_postpone++];
+
+ for (OutArcIt a(_graph, u); a != INVALID ; ++a) {
+ Node v = _graph.target(a);
+
+ if ((*_status)[v] == EVEN) {
+ if (_blossom_set->find(u) != _blossom_set->find(v)) {
+ shrinkOnEdge(a);
+ }
+ }
+
+ while (_process != _last) {
+ Node w = _node_queue[_process++];
+ for (OutArcIt b(_graph, w); b != INVALID; ++b) {
+ Node x = _graph.target(b);
+ if ((*_status)[x] == MATCHED) {
+ extendOnArc(b);
+ } else if ((*_status)[x] == UNMATCHED) {
+ augmentOnArc(b);
+ return;
+ }
+ }
+ }
+ }
+ }
+ }
+
+ void processSparse(const Node& n) {
+ _process = _last = 0;
+ _node_queue[_last++] = n;
+ while (_process != _last) {
+ Node u = _node_queue[_process++];
+ for (OutArcIt a(_graph, u); a != INVALID; ++a) {
+ Node v = _graph.target(a);
+
+ if ((*_status)[v] == EVEN) {
+ if (_blossom_set->find(u) != _blossom_set->find(v)) {
+ shrinkOnEdge(a);
+ }
+ } else if ((*_status)[v] == MATCHED) {
+ extendOnArc(a);
+ } else if ((*_status)[v] == UNMATCHED) {
+ augmentOnArc(a);
+ return;
+ }
+ }
+ }
+ }
+
+ void shrinkOnEdge(const Edge& e) {
+ Node nca = INVALID;
+
+ {
+ std::set<Node> left_set, right_set;
+
+ Node left = (*_blossom_rep)[_blossom_set->find(_graph.u(e))];
+ left_set.insert(left);
+
+ Node right = (*_blossom_rep)[_blossom_set->find(_graph.v(e))];
+ right_set.insert(right);
+
+ while (true) {
+ if ((*_matching)[left] == INVALID) break;
+ left = _graph.target((*_matching)[left]);
+ left = (*_blossom_rep)[_blossom_set->
+ find(_graph.target((*_ear)[left]))];
+ if (right_set.find(left) != right_set.end()) {
+ nca = left;
+ break;
+ }
+ left_set.insert(left);
+
+ if ((*_matching)[right] == INVALID) break;
+ right = _graph.target((*_matching)[right]);
+ right = (*_blossom_rep)[_blossom_set->
+ find(_graph.target((*_ear)[right]))];
+ if (left_set.find(right) != left_set.end()) {
+ nca = right;
+ break;
+ }
+ right_set.insert(right);
+ }
+
+ if (nca == INVALID) {
+ if ((*_matching)[left] == INVALID) {
+ nca = right;
+ while (left_set.find(nca) == left_set.end()) {
+ nca = _graph.target((*_matching)[nca]);
+ nca =(*_blossom_rep)[_blossom_set->
+ find(_graph.target((*_ear)[nca]))];
+ }
+ } else {
+ nca = left;
+ while (right_set.find(nca) == right_set.end()) {
+ nca = _graph.target((*_matching)[nca]);
+ nca = (*_blossom_rep)[_blossom_set->
+ find(_graph.target((*_ear)[nca]))];
+ }
+ }
+ }
+ }
+
+ {
+
+ Node node = _graph.u(e);
+ Arc arc = _graph.direct(e, true);
+ Node base = (*_blossom_rep)[_blossom_set->find(node)];
+
+ while (base != nca) {
+ (*_ear)[node] = arc;
+
+ Node n = node;
+ while (n != base) {
+ n = _graph.target((*_matching)[n]);
+ Arc a = (*_ear)[n];
+ n = _graph.target(a);
+ (*_ear)[n] = _graph.oppositeArc(a);
+ }
+ node = _graph.target((*_matching)[base]);
+ _tree_set->erase(base);
+ _tree_set->erase(node);
+ _blossom_set->insert(node, _blossom_set->find(base));
+ (*_status)[node] = EVEN;
+ _node_queue[_last++] = node;
+ arc = _graph.oppositeArc((*_ear)[node]);
+ node = _graph.target((*_ear)[node]);
+ base = (*_blossom_rep)[_blossom_set->find(node)];
+ _blossom_set->join(_graph.target(arc), base);
+ }
+ }
+
+ (*_blossom_rep)[_blossom_set->find(nca)] = nca;
+
+ {
+
+ Node node = _graph.v(e);
+ Arc arc = _graph.direct(e, false);
+ Node base = (*_blossom_rep)[_blossom_set->find(node)];
+
+ while (base != nca) {
+ (*_ear)[node] = arc;
+
+ Node n = node;
+ while (n != base) {
+ n = _graph.target((*_matching)[n]);
+ Arc a = (*_ear)[n];
+ n = _graph.target(a);
+ (*_ear)[n] = _graph.oppositeArc(a);
+ }
+ node = _graph.target((*_matching)[base]);
+ _tree_set->erase(base);
+ _tree_set->erase(node);
+ _blossom_set->insert(node, _blossom_set->find(base));
+ (*_status)[node] = EVEN;
+ _node_queue[_last++] = node;
+ arc = _graph.oppositeArc((*_ear)[node]);
+ node = _graph.target((*_ear)[node]);
+ base = (*_blossom_rep)[_blossom_set->find(node)];
+ _blossom_set->join(_graph.target(arc), base);
+ }
+ }
+
+ (*_blossom_rep)[_blossom_set->find(nca)] = nca;
+ }
+
+ void extendOnArc(const Arc& a) {
+ Node base = _graph.source(a);
+ Node odd = _graph.target(a);
+
+ (*_ear)[odd] = _graph.oppositeArc(a);
+ Node even = _graph.target((*_matching)[odd]);
+ (*_blossom_rep)[_blossom_set->insert(even)] = even;
+ (*_status)[odd] = ODD;
+ (*_status)[even] = EVEN;
+ int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(base)]);
+ _tree_set->insert(odd, tree);
+ _tree_set->insert(even, tree);
+ _node_queue[_last++] = even;
+
+ }
+
+ void augmentOnArc(const Arc& a) {
+ Node even = _graph.source(a);
+ Node odd = _graph.target(a);
+
+ int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(even)]);
+
+ (*_matching)[odd] = _graph.oppositeArc(a);
+ (*_status)[odd] = MATCHED;
+
+ Arc arc = (*_matching)[even];
+ (*_matching)[even] = a;
+
+ while (arc != INVALID) {
+ odd = _graph.target(arc);
+ arc = (*_ear)[odd];
+ even = _graph.target(arc);
+ (*_matching)[odd] = arc;
+ arc = (*_matching)[even];
+ (*_matching)[even] = _graph.oppositeArc((*_matching)[odd]);
+ }
+
+ for (typename TreeSet::ItemIt it(*_tree_set, tree);
+ it != INVALID; ++it) {
+ if ((*_status)[it] == ODD) {
+ (*_status)[it] = MATCHED;
+ } else {
+ int blossom = _blossom_set->find(it);
+ for (typename BlossomSet::ItemIt jt(*_blossom_set, blossom);
+ jt != INVALID; ++jt) {
+ (*_status)[jt] = MATCHED;
+ }
+ _blossom_set->eraseClass(blossom);
+ }
+ }
+ _tree_set->eraseClass(tree);
+
+ }
+
+ public:
+
+ /// \brief Constructor
+ ///
+ /// Constructor.
+ MaxMatching(const Graph& graph)
+ : _graph(graph), _matching(0), _status(0), _ear(0),
+ _blossom_set_index(0), _blossom_set(0), _blossom_rep(0),
+ _tree_set_index(0), _tree_set(0) {}
+
+ ~MaxMatching() {
+ destroyStructures();
+ }
+
+ /// \name Execution Control
+ /// The simplest way to execute the algorithm is to use the
+ /// \c run() member function.\n
+ /// If you need better control on the execution, you have to call
+ /// one of the functions \ref init(), \ref greedyInit() or
+ /// \ref matchingInit() first, then you can start the algorithm with
+ /// \ref startSparse() or \ref startDense().
+
+ ///@{
+
+ /// \brief Set the initial matching to the empty matching.
+ ///
+ /// This function sets the initial matching to the empty matching.
+ void init() {
+ createStructures();
+ for(NodeIt n(_graph); n != INVALID; ++n) {
+ (*_matching)[n] = INVALID;
+ (*_status)[n] = UNMATCHED;
+ }
+ }
+
+ /// \brief Find an initial matching in a greedy way.
+ ///
+ /// This function finds an initial matching in a greedy way.
+ void greedyInit() {
+ createStructures();
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ (*_matching)[n] = INVALID;
+ (*_status)[n] = UNMATCHED;
+ }
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ if ((*_matching)[n] == INVALID) {
+ for (OutArcIt a(_graph, n); a != INVALID ; ++a) {
+ Node v = _graph.target(a);
+ if ((*_matching)[v] == INVALID && v != n) {
+ (*_matching)[n] = a;
+ (*_status)[n] = MATCHED;
+ (*_matching)[v] = _graph.oppositeArc(a);
+ (*_status)[v] = MATCHED;
+ break;
+ }
+ }
+ }
+ }
+ }
+
+
+ /// \brief Initialize the matching from a map.
+ ///
+ /// This function initializes the matching from a \c bool valued edge
+ /// map. This map should have the property that there are no two incident
+ /// edges with \c true value, i.e. it really contains a matching.
+ /// \return \c true if the map contains a matching.
+ template <typename MatchingMap>
+ bool matchingInit(const MatchingMap& matching) {
+ createStructures();
+
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ (*_matching)[n] = INVALID;
+ (*_status)[n] = UNMATCHED;
+ }
+ for(EdgeIt e(_graph); e!=INVALID; ++e) {
+ if (matching[e]) {
+
+ Node u = _graph.u(e);
+ if ((*_matching)[u] != INVALID) return false;
+ (*_matching)[u] = _graph.direct(e, true);
+ (*_status)[u] = MATCHED;
+
+ Node v = _graph.v(e);
+ if ((*_matching)[v] != INVALID) return false;
+ (*_matching)[v] = _graph.direct(e, false);
+ (*_status)[v] = MATCHED;
+ }
+ }
+ return true;
+ }
+
+ /// \brief Start Edmonds' algorithm
+ ///
+ /// This function runs the original Edmonds' algorithm.
+ ///
+ /// \pre \ref Init(), \ref greedyInit() or \ref matchingInit() must be
+ /// called before using this function.
+ void startSparse() {
+ for(NodeIt n(_graph); n != INVALID; ++n) {
+ if ((*_status)[n] == UNMATCHED) {
+ (*_blossom_rep)[_blossom_set->insert(n)] = n;
+ _tree_set->insert(n);
+ (*_status)[n] = EVEN;
+ processSparse(n);
+ }
+ }
+ }
+
+ /// \brief Start Edmonds' algorithm with a heuristic improvement
+ /// for dense graphs
+ ///
+ /// This function runs Edmonds' algorithm with a heuristic of postponing
+ /// shrinks, therefore resulting in a faster algorithm for dense graphs.
+ ///
+ /// \pre \ref Init(), \ref greedyInit() or \ref matchingInit() must be
+ /// called before using this function.
+ void startDense() {
+ for(NodeIt n(_graph); n != INVALID; ++n) {
+ if ((*_status)[n] == UNMATCHED) {
+ (*_blossom_rep)[_blossom_set->insert(n)] = n;
+ _tree_set->insert(n);
+ (*_status)[n] = EVEN;
+ processDense(n);
+ }
+ }
+ }
+
+
+ /// \brief Run Edmonds' algorithm
+ ///
+ /// This function runs Edmonds' algorithm. An additional heuristic of
+ /// postponing shrinks is used for relatively dense graphs
+ /// (for which <tt>m>=2*n</tt> holds).
+ void run() {
+ if (countEdges(_graph) < 2 * countNodes(_graph)) {
+ greedyInit();
+ startSparse();
+ } else {
+ init();
+ startDense();
+ }
+ }
+
+ /// @}
+
+ /// \name Primal Solution
+ /// Functions to get the primal solution, i.e. the maximum matching.
+
+ /// @{
+
+ /// \brief Return the size (cardinality) of the matching.
+ ///
+ /// This function returns the size (cardinality) of the current matching.
+ /// After run() it returns the size of the maximum matching in the graph.
+ int matchingSize() const {
+ int size = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ if ((*_matching)[n] != INVALID) {
+ ++size;
+ }
+ }
+ return size / 2;
+ }
+
+ /// \brief Return \c true if the given edge is in the matching.
+ ///
+ /// This function returns \c true if the given edge is in the current
+ /// matching.
+ bool matching(const Edge& edge) const {
+ return edge == (*_matching)[_graph.u(edge)];
+ }
+
+ /// \brief Return the matching arc (or edge) incident to the given node.
+ ///
+ /// This function returns the matching arc (or edge) incident to the
+ /// given node in the current matching or \c INVALID if the node is
+ /// not covered by the matching.
+ Arc matching(const Node& n) const {
+ return (*_matching)[n];
+ }
+
+ /// \brief Return a const reference to the matching map.
+ ///
+ /// This function returns a const reference to a node map that stores
+ /// the matching arc (or edge) incident to each node.
+ const MatchingMap& matchingMap() const {
+ return *_matching;
+ }
+
+ /// \brief Return the mate of the given node.
+ ///
+ /// This function returns the mate of the given node in the current
+ /// matching or \c INVALID if the node is not covered by the matching.
+ Node mate(const Node& n) const {
+ return (*_matching)[n] != INVALID ?
+ _graph.target((*_matching)[n]) : INVALID;
+ }
+
+ /// @}
+
+ /// \name Dual Solution
+ /// Functions to get the dual solution, i.e. the Gallai-Edmonds
+ /// decomposition.
+
+ /// @{
+
+ /// \brief Return the status of the given node in the Edmonds-Gallai
+ /// decomposition.
+ ///
+ /// This function returns the \ref Status "status" of the given node
+ /// in the Edmonds-Gallai decomposition.
+ Status status(const Node& n) const {
+ return (*_status)[n];
+ }
+
+ /// \brief Return a const reference to the status map, which stores
+ /// the Edmonds-Gallai decomposition.
+ ///
+ /// This function returns a const reference to a node map that stores the
+ /// \ref Status "status" of each node in the Edmonds-Gallai decomposition.
+ const StatusMap& statusMap() const {
+ return *_status;
+ }
+
+ /// \brief Return \c true if the given node is in the barrier.
+ ///
+ /// This function returns \c true if the given node is in the barrier.
+ bool barrier(const Node& n) const {
+ return (*_status)[n] == ODD;
+ }
+
+ /// @}
+
+ };
+
+ /// \ingroup matching
+ ///
+ /// \brief Weighted matching in general graphs
+ ///
+ /// This class provides an efficient implementation of Edmond's
+ /// maximum weighted matching algorithm. The implementation is based
+ /// on extensive use of priority queues and provides
+ /// \f$O(nm\log n)\f$ time complexity.
+ ///
+ /// The maximum weighted matching problem is to find a subset of the
+ /// edges in an undirected graph with maximum overall weight for which
+ /// each node has at most one incident edge.
+ /// It can be formulated with the following linear program.
+ /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]
+ /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
+ \quad \forall B\in\mathcal{O}\f] */
+ /// \f[x_e \ge 0\quad \forall e\in E\f]
+ /// \f[\max \sum_{e\in E}x_ew_e\f]
+ /// where \f$\delta(X)\f$ is the set of edges incident to a node in
+ /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
+ /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
+ /// subsets of the nodes.
+ ///
+ /// The algorithm calculates an optimal matching and a proof of the
+ /// optimality. The solution of the dual problem can be used to check
+ /// the result of the algorithm. The dual linear problem is the
+ /// following.
+ /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}
+ z_B \ge w_{uv} \quad \forall uv\in E\f] */
+ /// \f[y_u \ge 0 \quad \forall u \in V\f]
+ /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
+ /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
+ \frac{\vert B \vert - 1}{2}z_B\f] */
+ ///
+ /// The algorithm can be executed with the run() function.
+ /// After it the matching (the primal solution) and the dual solution
+ /// can be obtained using the query functions and the
+ /// \ref MaxWeightedMatching::BlossomIt "BlossomIt" nested class,
+ /// which is able to iterate on the nodes of a blossom.
+ /// If the value type is integer, then the dual solution is multiplied
+ /// by \ref MaxWeightedMatching::dualScale "4".
+ ///
+ /// \tparam GR The undirected graph type the algorithm runs on.
+ /// \tparam WM The type edge weight map. The default type is
+ /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".
+#ifdef DOXYGEN
+ template <typename GR, typename WM>
+#else
+ template <typename GR,
+ typename WM = typename GR::template EdgeMap<int> >
+#endif
+ class MaxWeightedMatching {
+ public:
+
+ /// The graph type of the algorithm
+ typedef GR Graph;
+ /// The type of the edge weight map
+ typedef WM WeightMap;
+ /// The value type of the edge weights
+ typedef typename WeightMap::Value Value;
+
+ /// The type of the matching map
+ typedef typename Graph::template NodeMap<typename Graph::Arc>
+ MatchingMap;
+
+ /// \brief Scaling factor for dual solution
+ ///
+ /// Scaling factor for dual solution. It is equal to 4 or 1
+ /// according to the value type.
+ static const int dualScale =
+ std::numeric_limits<Value>::is_integer ? 4 : 1;
+
+ private:
+
+ TEMPLATE_GRAPH_TYPEDEFS(Graph);
+
+ typedef typename Graph::template NodeMap<Value> NodePotential;
+ typedef std::vector<Node> BlossomNodeList;
+
+ struct BlossomVariable {
+ int begin, end;
+ Value value;
+
+ BlossomVariable(int _begin, int _end, Value _value)
+ : begin(_begin), end(_end), value(_value) {}
+
+ };
+
+ typedef std::vector<BlossomVariable> BlossomPotential;
+
+ const Graph& _graph;
+ const WeightMap& _weight;
+
+ MatchingMap* _matching;
+
+ NodePotential* _node_potential;
+
+ BlossomPotential _blossom_potential;
+ BlossomNodeList _blossom_node_list;
+
+ int _node_num;
+ int _blossom_num;
+
+ typedef RangeMap<int> IntIntMap;
+
+ enum Status {
+ EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2
+ };
+
+ typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
+ struct BlossomData {
+ int tree;
+ Status status;
+ Arc pred, next;
+ Value pot, offset;
+ Node base;
+ };
+
+ IntNodeMap *_blossom_index;
+ BlossomSet *_blossom_set;
+ RangeMap<BlossomData>* _blossom_data;
+
+ IntNodeMap *_node_index;
+ IntArcMap *_node_heap_index;
+
+ struct NodeData {
+
+ NodeData(IntArcMap& node_heap_index)
+ : heap(node_heap_index) {}
+
+ int blossom;
+ Value pot;
+ BinHeap<Value, IntArcMap> heap;
+ std::map<int, Arc> heap_index;
+
+ int tree;
+ };
+
+ RangeMap<NodeData>* _node_data;
+
+ typedef ExtendFindEnum<IntIntMap> TreeSet;
+
+ IntIntMap *_tree_set_index;
+ TreeSet *_tree_set;
+
+ IntNodeMap *_delta1_index;
+ BinHeap<Value, IntNodeMap> *_delta1;
+
+ IntIntMap *_delta2_index;
+ BinHeap<Value, IntIntMap> *_delta2;
+
+ IntEdgeMap *_delta3_index;
+ BinHeap<Value, IntEdgeMap> *_delta3;
+
+ IntIntMap *_delta4_index;
+ BinHeap<Value, IntIntMap> *_delta4;
+
+ Value _delta_sum;
+
+ void createStructures() {
+ _node_num = countNodes(_graph);
+ _blossom_num = _node_num * 3 / 2;
+
+ if (!_matching) {
+ _matching = new MatchingMap(_graph);
+ }
+ if (!_node_potential) {
+ _node_potential = new NodePotential(_graph);
+ }
+ if (!_blossom_set) {
+ _blossom_index = new IntNodeMap(_graph);
+ _blossom_set = new BlossomSet(*_blossom_index);
+ _blossom_data = new RangeMap<BlossomData>(_blossom_num);
+ }
+
+ if (!_node_index) {
+ _node_index = new IntNodeMap(_graph);
+ _node_heap_index = new IntArcMap(_graph);
+ _node_data = new RangeMap<NodeData>(_node_num,
+ NodeData(*_node_heap_index));
+ }
+
+ if (!_tree_set) {
+ _tree_set_index = new IntIntMap(_blossom_num);
+ _tree_set = new TreeSet(*_tree_set_index);
+ }
+ if (!_delta1) {
+ _delta1_index = new IntNodeMap(_graph);
+ _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index);
+ }
+ if (!_delta2) {
+ _delta2_index = new IntIntMap(_blossom_num);
+ _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
+ }
+ if (!_delta3) {
+ _delta3_index = new IntEdgeMap(_graph);
+ _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
+ }
+ if (!_delta4) {
+ _delta4_index = new IntIntMap(_blossom_num);
+ _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
+ }
+ }
+
+ void destroyStructures() {
+ _node_num = countNodes(_graph);
+ _blossom_num = _node_num * 3 / 2;
+
+ if (_matching) {
+ delete _matching;
+ }
+ if (_node_potential) {
+ delete _node_potential;
+ }
+ if (_blossom_set) {
+ delete _blossom_index;
+ delete _blossom_set;
+ delete _blossom_data;
+ }
+
+ if (_node_index) {
+ delete _node_index;
+ delete _node_heap_index;
+ delete _node_data;
+ }
+
+ if (_tree_set) {
+ delete _tree_set_index;
+ delete _tree_set;
+ }
+ if (_delta1) {
+ delete _delta1_index;
+ delete _delta1;
+ }
+ if (_delta2) {
+ delete _delta2_index;
+ delete _delta2;
+ }
+ if (_delta3) {
+ delete _delta3_index;
+ delete _delta3;
+ }
+ if (_delta4) {
+ delete _delta4_index;
+ delete _delta4;
+ }
+ }
+
+ void matchedToEven(int blossom, int tree) {
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+
+ if (!_blossom_set->trivial(blossom)) {
+ (*_blossom_data)[blossom].pot -=
+ 2 * (_delta_sum - (*_blossom_data)[blossom].offset);
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+
+ _blossom_set->increase(n, std::numeric_limits<Value>::max());
+ int ni = (*_node_index)[n];
+
+ (*_node_data)[ni].heap.clear();
+ (*_node_data)[ni].heap_index.clear();
+
+ (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
+
+ _delta1->push(n, (*_node_data)[ni].pot);
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if ((*_blossom_data)[vb].status == EVEN) {
+ if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
+ _delta3->push(e, rw / 2);
+ }
+ } else if ((*_blossom_data)[vb].status == UNMATCHED) {
+ if (_delta3->state(e) != _delta3->IN_HEAP) {
+ _delta3->push(e, rw);
+ }
+ } else {
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[vi].heap_index.find(tree);
+
+ if (it != (*_node_data)[vi].heap_index.end()) {
+ if ((*_node_data)[vi].heap[it->second] > rw) {
+ (*_node_data)[vi].heap.replace(it->second, e);
+ (*_node_data)[vi].heap.decrease(e, rw);
+ it->second = e;
+ }
+ } else {
+ (*_node_data)[vi].heap.push(e, rw);
+ (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
+ }
+
+ if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
+ _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
+
+ if ((*_blossom_data)[vb].status == MATCHED) {
+ if (_delta2->state(vb) != _delta2->IN_HEAP) {
+ _delta2->push(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset){
+ _delta2->decrease(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ }
+ }
+ }
+ }
+ }
+ }
+ (*_blossom_data)[blossom].offset = 0;
+ }
+
+ void matchedToOdd(int blossom) {
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+ (*_blossom_data)[blossom].offset += _delta_sum;
+ if (!_blossom_set->trivial(blossom)) {
+ _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
+ (*_blossom_data)[blossom].offset);
+ }
+ }
+
+ void evenToMatched(int blossom, int tree) {
+ if (!_blossom_set->trivial(blossom)) {
+ (*_blossom_data)[blossom].pot += 2 * _delta_sum;
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+ int ni = (*_node_index)[n];
+ (*_node_data)[ni].pot -= _delta_sum;
+
+ _delta1->erase(n);
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if (vb == blossom) {
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+ } else if ((*_blossom_data)[vb].status == EVEN) {
+
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+
+ int vt = _tree_set->find(vb);
+
+ if (vt != tree) {
+
+ Arc r = _graph.oppositeArc(e);
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[ni].heap_index.find(vt);
+
+ if (it != (*_node_data)[ni].heap_index.end()) {
+ if ((*_node_data)[ni].heap[it->second] > rw) {
+ (*_node_data)[ni].heap.replace(it->second, r);
+ (*_node_data)[ni].heap.decrease(r, rw);
+ it->second = r;
+ }
+ } else {
+ (*_node_data)[ni].heap.push(r, rw);
+ (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
+ }
+
+ if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
+ _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
+
+ if (_delta2->state(blossom) != _delta2->IN_HEAP) {
+ _delta2->push(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ } else if ((*_delta2)[blossom] >
+ _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset){
+ _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ }
+ }
+ }
+
+ } else if ((*_blossom_data)[vb].status == UNMATCHED) {
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+ } else {
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[vi].heap_index.find(tree);
+
+ if (it != (*_node_data)[vi].heap_index.end()) {
+ (*_node_data)[vi].heap.erase(it->second);
+ (*_node_data)[vi].heap_index.erase(it);
+ if ((*_node_data)[vi].heap.empty()) {
+ _blossom_set->increase(v, std::numeric_limits<Value>::max());
+ } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
+ _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
+ }
+
+ if ((*_blossom_data)[vb].status == MATCHED) {
+ if (_blossom_set->classPrio(vb) ==
+ std::numeric_limits<Value>::max()) {
+ _delta2->erase(vb);
+ } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset) {
+ _delta2->increase(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+
+ void oddToMatched(int blossom) {
+ (*_blossom_data)[blossom].offset -= _delta_sum;
+
+ if (_blossom_set->classPrio(blossom) !=
+ std::numeric_limits<Value>::max()) {
+ _delta2->push(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ }
+
+ if (!_blossom_set->trivial(blossom)) {
+ _delta4->erase(blossom);
+ }
+ }
+
+ void oddToEven(int blossom, int tree) {
+ if (!_blossom_set->trivial(blossom)) {
+ _delta4->erase(blossom);
+ (*_blossom_data)[blossom].pot -=
+ 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+ int ni = (*_node_index)[n];
+
+ _blossom_set->increase(n, std::numeric_limits<Value>::max());
+
+ (*_node_data)[ni].heap.clear();
+ (*_node_data)[ni].heap_index.clear();
+ (*_node_data)[ni].pot +=
+ 2 * _delta_sum - (*_blossom_data)[blossom].offset;
+
+ _delta1->push(n, (*_node_data)[ni].pot);
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if ((*_blossom_data)[vb].status == EVEN) {
+ if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
+ _delta3->push(e, rw / 2);
+ }
+ } else if ((*_blossom_data)[vb].status == UNMATCHED) {
+ if (_delta3->state(e) != _delta3->IN_HEAP) {
+ _delta3->push(e, rw);
+ }
+ } else {
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[vi].heap_index.find(tree);
+
+ if (it != (*_node_data)[vi].heap_index.end()) {
+ if ((*_node_data)[vi].heap[it->second] > rw) {
+ (*_node_data)[vi].heap.replace(it->second, e);
+ (*_node_data)[vi].heap.decrease(e, rw);
+ it->second = e;
+ }
+ } else {
+ (*_node_data)[vi].heap.push(e, rw);
+ (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
+ }
+
+ if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
+ _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
+
+ if ((*_blossom_data)[vb].status == MATCHED) {
+ if (_delta2->state(vb) != _delta2->IN_HEAP) {
+ _delta2->push(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset) {
+ _delta2->decrease(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ }
+ }
+ }
+ }
+ }
+ }
+ (*_blossom_data)[blossom].offset = 0;
+ }
+
+
+ void matchedToUnmatched(int blossom) {
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+ int ni = (*_node_index)[n];
+
+ _blossom_set->increase(n, std::numeric_limits<Value>::max());
+
+ (*_node_data)[ni].heap.clear();
+ (*_node_data)[ni].heap_index.clear();
+
+ for (OutArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.target(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if ((*_blossom_data)[vb].status == EVEN) {
+ if (_delta3->state(e) != _delta3->IN_HEAP) {
+ _delta3->push(e, rw);
+ }
+ }
+ }
+ }
+ }
+
+ void unmatchedToMatched(int blossom) {
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+ int ni = (*_node_index)[n];
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if (vb == blossom) {
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+ } else if ((*_blossom_data)[vb].status == EVEN) {
+
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+
+ int vt = _tree_set->find(vb);
+
+ Arc r = _graph.oppositeArc(e);
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[ni].heap_index.find(vt);
+
+ if (it != (*_node_data)[ni].heap_index.end()) {
+ if ((*_node_data)[ni].heap[it->second] > rw) {
+ (*_node_data)[ni].heap.replace(it->second, r);
+ (*_node_data)[ni].heap.decrease(r, rw);
+ it->second = r;
+ }
+ } else {
+ (*_node_data)[ni].heap.push(r, rw);
+ (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
+ }
+
+ if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
+ _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
+
+ if (_delta2->state(blossom) != _delta2->IN_HEAP) {
+ _delta2->push(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ } else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)-
+ (*_blossom_data)[blossom].offset){
+ _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ }
+ }
+
+ } else if ((*_blossom_data)[vb].status == UNMATCHED) {
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+ }
+ }
+ }
+ }
+
+ void alternatePath(int even, int tree) {
+ int odd;
+
+ evenToMatched(even, tree);
+ (*_blossom_data)[even].status = MATCHED;
+
+ while ((*_blossom_data)[even].pred != INVALID) {
+ odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
+ (*_blossom_data)[odd].status = MATCHED;
+ oddToMatched(odd);
+ (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
+
+ even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
+ (*_blossom_data)[even].status = MATCHED;
+ evenToMatched(even, tree);
+ (*_blossom_data)[even].next =
+ _graph.oppositeArc((*_blossom_data)[odd].pred);
+ }
+
+ }
+
+ void destroyTree(int tree) {
+ for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
+ if ((*_blossom_data)[b].status == EVEN) {
+ (*_blossom_data)[b].status = MATCHED;
+ evenToMatched(b, tree);
+ } else if ((*_blossom_data)[b].status == ODD) {
+ (*_blossom_data)[b].status = MATCHED;
+ oddToMatched(b);
+ }
+ }
+ _tree_set->eraseClass(tree);
+ }
+
+
+ void unmatchNode(const Node& node) {
+ int blossom = _blossom_set->find(node);
+ int tree = _tree_set->find(blossom);
+
+ alternatePath(blossom, tree);
+ destroyTree(tree);
+
+ (*_blossom_data)[blossom].status = UNMATCHED;
+ (*_blossom_data)[blossom].base = node;
+ matchedToUnmatched(blossom);
+ }
+
+
+ void augmentOnEdge(const Edge& edge) {
+
+ int left = _blossom_set->find(_graph.u(edge));
+ int right = _blossom_set->find(_graph.v(edge));
+
+ if ((*_blossom_data)[left].status == EVEN) {
+ int left_tree = _tree_set->find(left);
+ alternatePath(left, left_tree);
+ destroyTree(left_tree);
+ } else {
+ (*_blossom_data)[left].status = MATCHED;
+ unmatchedToMatched(left);
+ }
+
+ if ((*_blossom_data)[right].status == EVEN) {
+ int right_tree = _tree_set->find(right);
+ alternatePath(right, right_tree);
+ destroyTree(right_tree);
+ } else {
+ (*_blossom_data)[right].status = MATCHED;
+ unmatchedToMatched(right);
+ }
+
+ (*_blossom_data)[left].next = _graph.direct(edge, true);
+ (*_blossom_data)[right].next = _graph.direct(edge, false);
+ }
+
+ void extendOnArc(const Arc& arc) {
+ int base = _blossom_set->find(_graph.target(arc));
+ int tree = _tree_set->find(base);
+
+ int odd = _blossom_set->find(_graph.source(arc));
+ _tree_set->insert(odd, tree);
+ (*_blossom_data)[odd].status = ODD;
+ matchedToOdd(odd);
+ (*_blossom_data)[odd].pred = arc;
+
+ int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
+ (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
+ _tree_set->insert(even, tree);
+ (*_blossom_data)[even].status = EVEN;
+ matchedToEven(even, tree);
+ }
+
+ void shrinkOnEdge(const Edge& edge, int tree) {
+ int nca = -1;
+ std::vector<int> left_path, right_path;
+
+ {
+ std::set<int> left_set, right_set;
+ int left = _blossom_set->find(_graph.u(edge));
+ left_path.push_back(left);
+ left_set.insert(left);
+
+ int right = _blossom_set->find(_graph.v(edge));
+ right_path.push_back(right);
+ right_set.insert(right);
+
+ while (true) {
+
+ if ((*_blossom_data)[left].pred == INVALID) break;
+
+ left =
+ _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
+ left_path.push_back(left);
+ left =
+ _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
+ left_path.push_back(left);
+
+ left_set.insert(left);
+
+ if (right_set.find(left) != right_set.end()) {
+ nca = left;
+ break;
+ }
+
+ if ((*_blossom_data)[right].pred == INVALID) break;
+
+ right =
+ _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
+ right_path.push_back(right);
+ right =
+ _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
+ right_path.push_back(right);
+
+ right_set.insert(right);
+
+ if (left_set.find(right) != left_set.end()) {
+ nca = right;
+ break;
+ }
+
+ }
+
+ if (nca == -1) {
+ if ((*_blossom_data)[left].pred == INVALID) {
+ nca = right;
+ while (left_set.find(nca) == left_set.end()) {
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ right_path.push_back(nca);
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ right_path.push_back(nca);
+ }
+ } else {
+ nca = left;
+ while (right_set.find(nca) == right_set.end()) {
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ left_path.push_back(nca);
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ left_path.push_back(nca);
+ }
+ }
+ }
+ }
+
+ std::vector<int> subblossoms;
+ Arc prev;
+
+ prev = _graph.direct(edge, true);
+ for (int i = 0; left_path[i] != nca; i += 2) {
+ subblossoms.push_back(left_path[i]);
+ (*_blossom_data)[left_path[i]].next = prev;
+ _tree_set->erase(left_path[i]);
+
+ subblossoms.push_back(left_path[i + 1]);
+ (*_blossom_data)[left_path[i + 1]].status = EVEN;
+ oddToEven(left_path[i + 1], tree);
+ _tree_set->erase(left_path[i + 1]);
+ prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
+ }
+
+ int k = 0;
+ while (right_path[k] != nca) ++k;
+
+ subblossoms.push_back(nca);
+ (*_blossom_data)[nca].next = prev;
+
+ for (int i = k - 2; i >= 0; i -= 2) {
+ subblossoms.push_back(right_path[i + 1]);
+ (*_blossom_data)[right_path[i + 1]].status = EVEN;
+ oddToEven(right_path[i + 1], tree);
+ _tree_set->erase(right_path[i + 1]);
+
+ (*_blossom_data)[right_path[i + 1]].next =
+ (*_blossom_data)[right_path[i + 1]].pred;
+
+ subblossoms.push_back(right_path[i]);
+ _tree_set->erase(right_path[i]);
+ }
+
+ int surface =
+ _blossom_set->join(subblossoms.begin(), subblossoms.end());
+
+ for (int i = 0; i < int(subblossoms.size()); ++i) {
+ if (!_blossom_set->trivial(subblossoms[i])) {
+ (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
+ }
+ (*_blossom_data)[subblossoms[i]].status = MATCHED;
+ }
+
+ (*_blossom_data)[surface].pot = -2 * _delta_sum;
+ (*_blossom_data)[surface].offset = 0;
+ (*_blossom_data)[surface].status = EVEN;
+ (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
+ (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
+
+ _tree_set->insert(surface, tree);
+ _tree_set->erase(nca);
+ }
+
+ void splitBlossom(int blossom) {
+ Arc next = (*_blossom_data)[blossom].next;
+ Arc pred = (*_blossom_data)[blossom].pred;
+
+ int tree = _tree_set->find(blossom);
+
+ (*_blossom_data)[blossom].status = MATCHED;
+ oddToMatched(blossom);
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+
+ std::vector<int> subblossoms;
+ _blossom_set->split(blossom, std::back_inserter(subblossoms));
+
+ Value offset = (*_blossom_data)[blossom].offset;
+ int b = _blossom_set->find(_graph.source(pred));
+ int d = _blossom_set->find(_graph.source(next));
+
+ int ib = -1, id = -1;
+ for (int i = 0; i < int(subblossoms.size()); ++i) {
+ if (subblossoms[i] == b) ib = i;
+ if (subblossoms[i] == d) id = i;
+
+ (*_blossom_data)[subblossoms[i]].offset = offset;
+ if (!_blossom_set->trivial(subblossoms[i])) {
+ (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
+ }
+ if (_blossom_set->classPrio(subblossoms[i]) !=
+ std::numeric_limits<Value>::max()) {
+ _delta2->push(subblossoms[i],
+ _blossom_set->classPrio(subblossoms[i]) -
+ (*_blossom_data)[subblossoms[i]].offset);
+ }
+ }
+
+ if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
+ for (int i = (id + 1) % subblossoms.size();
+ i != ib; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ (*_blossom_data)[sb].next =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+ }
+
+ for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ int ub = subblossoms[(i + 2) % subblossoms.size()];
+
+ (*_blossom_data)[sb].status = ODD;
+ matchedToOdd(sb);
+ _tree_set->insert(sb, tree);
+ (*_blossom_data)[sb].pred = pred;
+ (*_blossom_data)[sb].next =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+
+ pred = (*_blossom_data)[ub].next;
+
+ (*_blossom_data)[tb].status = EVEN;
+ matchedToEven(tb, tree);
+ _tree_set->insert(tb, tree);
+ (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
+ }
+
+ (*_blossom_data)[subblossoms[id]].status = ODD;
+ matchedToOdd(subblossoms[id]);
+ _tree_set->insert(subblossoms[id], tree);
+ (*_blossom_data)[subblossoms[id]].next = next;
+ (*_blossom_data)[subblossoms[id]].pred = pred;
+
+ } else {
+
+ for (int i = (ib + 1) % subblossoms.size();
+ i != id; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ (*_blossom_data)[sb].next =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+ }
+
+ for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ int ub = subblossoms[(i + 2) % subblossoms.size()];
+
+ (*_blossom_data)[sb].status = ODD;
+ matchedToOdd(sb);
+ _tree_set->insert(sb, tree);
+ (*_blossom_data)[sb].next = next;
+ (*_blossom_data)[sb].pred =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+
+ (*_blossom_data)[tb].status = EVEN;
+ matchedToEven(tb, tree);
+ _tree_set->insert(tb, tree);
+ (*_blossom_data)[tb].pred =
+ (*_blossom_data)[tb].next =
+ _graph.oppositeArc((*_blossom_data)[ub].next);
+ next = (*_blossom_data)[ub].next;
+ }
+
+ (*_blossom_data)[subblossoms[ib]].status = ODD;
+ matchedToOdd(subblossoms[ib]);
+ _tree_set->insert(subblossoms[ib], tree);
+ (*_blossom_data)[subblossoms[ib]].next = next;
+ (*_blossom_data)[subblossoms[ib]].pred = pred;
+ }
+ _tree_set->erase(blossom);
+ }
+
+ void extractBlossom(int blossom, const Node& base, const Arc& matching) {
+ if (_blossom_set->trivial(blossom)) {
+ int bi = (*_node_index)[base];
+ Value pot = (*_node_data)[bi].pot;
+
+ (*_matching)[base] = matching;
+ _blossom_node_list.push_back(base);
+ (*_node_potential)[base] = pot;
+ } else {
+
+ Value pot = (*_blossom_data)[blossom].pot;
+ int bn = _blossom_node_list.size();
+
+ std::vector<int> subblossoms;
+ _blossom_set->split(blossom, std::back_inserter(subblossoms));
+ int b = _blossom_set->find(base);
+ int ib = -1;
+ for (int i = 0; i < int(subblossoms.size()); ++i) {
+ if (subblossoms[i] == b) { ib = i; break; }
+ }
+
+ for (int i = 1; i < int(subblossoms.size()); i += 2) {
+ int sb = subblossoms[(ib + i) % subblossoms.size()];
+ int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
+
+ Arc m = (*_blossom_data)[tb].next;
+ extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
+ extractBlossom(tb, _graph.source(m), m);
+ }
+ extractBlossom(subblossoms[ib], base, matching);
+
+ int en = _blossom_node_list.size();
+
+ _blossom_potential.push_back(BlossomVariable(bn, en, pot));
+ }
+ }
+
+ void extractMatching() {
+ std::vector<int> blossoms;
+ for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
+ blossoms.push_back(c);
+ }
+
+ for (int i = 0; i < int(blossoms.size()); ++i) {
+ if ((*_blossom_data)[blossoms[i]].status == MATCHED) {
+
+ Value offset = (*_blossom_data)[blossoms[i]].offset;
+ (*_blossom_data)[blossoms[i]].pot += 2 * offset;
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
+ n != INVALID; ++n) {
+ (*_node_data)[(*_node_index)[n]].pot -= offset;
+ }
+
+ Arc matching = (*_blossom_data)[blossoms[i]].next;
+ Node base = _graph.source(matching);
+ extractBlossom(blossoms[i], base, matching);
+ } else {
+ Node base = (*_blossom_data)[blossoms[i]].base;
+ extractBlossom(blossoms[i], base, INVALID);
+ }
+ }
+ }
+
+ public:
+
+ /// \brief Constructor
+ ///
+ /// Constructor.
+ MaxWeightedMatching(const Graph& graph, const WeightMap& weight)
+ : _graph(graph), _weight(weight), _matching(0),
+ _node_potential(0), _blossom_potential(), _blossom_node_list(),
+ _node_num(0), _blossom_num(0),
+
+ _blossom_index(0), _blossom_set(0), _blossom_data(0),
+ _node_index(0), _node_heap_index(0), _node_data(0),
+ _tree_set_index(0), _tree_set(0),
+
+ _delta1_index(0), _delta1(0),
+ _delta2_index(0), _delta2(0),
+ _delta3_index(0), _delta3(0),
+ _delta4_index(0), _delta4(0),
+
+ _delta_sum() {}
+
+ ~MaxWeightedMatching() {
+ destroyStructures();
+ }
+
+ /// \name Execution Control
+ /// The simplest way to execute the algorithm is to use the
+ /// \ref run() member function.
+
+ ///@{
+
+ /// \brief Initialize the algorithm
+ ///
+ /// This function initializes the algorithm.
+ void init() {
+ createStructures();
+
+ for (ArcIt e(_graph); e != INVALID; ++e) {
+ (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
+ }
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ (*_delta1_index)[n] = _delta1->PRE_HEAP;
+ }
+ for (EdgeIt e(_graph); e != INVALID; ++e) {
+ (*_delta3_index)[e] = _delta3->PRE_HEAP;
+ }
+ for (int i = 0; i < _blossom_num; ++i) {
+ (*_delta2_index)[i] = _delta2->PRE_HEAP;
+ (*_delta4_index)[i] = _delta4->PRE_HEAP;
+ }
+
+ int index = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ Value max = 0;
+ for (OutArcIt e(_graph, n); e != INVALID; ++e) {
+ if (_graph.target(e) == n) continue;
+ if ((dualScale * _weight[e]) / 2 > max) {
+ max = (dualScale * _weight[e]) / 2;
+ }
+ }
+ (*_node_index)[n] = index;
+ (*_node_data)[index].pot = max;
+ _delta1->push(n, max);
+ int blossom =
+ _blossom_set->insert(n, std::numeric_limits<Value>::max());
+
+ _tree_set->insert(blossom);
+
+ (*_blossom_data)[blossom].status = EVEN;
+ (*_blossom_data)[blossom].pred = INVALID;
+ (*_blossom_data)[blossom].next = INVALID;
+ (*_blossom_data)[blossom].pot = 0;
+ (*_blossom_data)[blossom].offset = 0;
+ ++index;
+ }
+ for (EdgeIt e(_graph); e != INVALID; ++e) {
+ int si = (*_node_index)[_graph.u(e)];
+ int ti = (*_node_index)[_graph.v(e)];
+ if (_graph.u(e) != _graph.v(e)) {
+ _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
+ dualScale * _weight[e]) / 2);
+ }
+ }
+ }
+
+ /// \brief Start the algorithm
+ ///
+ /// This function starts the algorithm.
+ ///
+ /// \pre \ref init() must be called before using this function.
+ void start() {
+ enum OpType {
+ D1, D2, D3, D4
+ };
+
+ int unmatched = _node_num;
+ while (unmatched > 0) {
+ Value d1 = !_delta1->empty() ?
+ _delta1->prio() : std::numeric_limits<Value>::max();
+
+ Value d2 = !_delta2->empty() ?
+ _delta2->prio() : std::numeric_limits<Value>::max();
+
+ Value d3 = !_delta3->empty() ?
+ _delta3->prio() : std::numeric_limits<Value>::max();
+
+ Value d4 = !_delta4->empty() ?
+ _delta4->prio() : std::numeric_limits<Value>::max();
+
+ _delta_sum = d1; OpType ot = D1;
+ if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
+ if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
+ if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
+
+
+ switch (ot) {
+ case D1:
+ {
+ Node n = _delta1->top();
+ unmatchNode(n);
+ --unmatched;
+ }
+ break;
+ case D2:
+ {
+ int blossom = _delta2->top();
+ Node n = _blossom_set->classTop(blossom);
+ Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
+ extendOnArc(e);
+ }
+ break;
+ case D3:
+ {
+ Edge e = _delta3->top();
+
+ int left_blossom = _blossom_set->find(_graph.u(e));
+ int right_blossom = _blossom_set->find(_graph.v(e));
+
+ if (left_blossom == right_blossom) {
+ _delta3->pop();
+ } else {
+ int left_tree;
+ if ((*_blossom_data)[left_blossom].status == EVEN) {
+ left_tree = _tree_set->find(left_blossom);
+ } else {
+ left_tree = -1;
+ ++unmatched;
+ }
+ int right_tree;
+ if ((*_blossom_data)[right_blossom].status == EVEN) {
+ right_tree = _tree_set->find(right_blossom);
+ } else {
+ right_tree = -1;
+ ++unmatched;
+ }
+
+ if (left_tree == right_tree) {
+ shrinkOnEdge(e, left_tree);
+ } else {
+ augmentOnEdge(e);
+ unmatched -= 2;
+ }
+ }
+ } break;
+ case D4:
+ splitBlossom(_delta4->top());
+ break;
+ }
+ }
+ extractMatching();
+ }
+
+ /// \brief Run the algorithm.
+ ///
+ /// This method runs the \c %MaxWeightedMatching algorithm.
+ ///
+ /// \note mwm.run() is just a shortcut of the following code.
+ /// \code
+ /// mwm.init();
+ /// mwm.start();
+ /// \endcode
+ void run() {
+ init();
+ start();
+ }
+
+ /// @}
+
+ /// \name Primal Solution
+ /// Functions to get the primal solution, i.e. the maximum weighted
+ /// matching.\n
+ /// Either \ref run() or \ref start() function should be called before
+ /// using them.
+
+ /// @{
+
+ /// \brief Return the weight of the matching.
+ ///
+ /// This function returns the weight of the found matching.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ Value matchingWeight() const {
+ Value sum = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ if ((*_matching)[n] != INVALID) {
+ sum += _weight[(*_matching)[n]];
+ }
+ }
+ return sum /= 2;
+ }
+
+ /// \brief Return the size (cardinality) of the matching.
+ ///
+ /// This function returns the size (cardinality) of the found matching.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ int matchingSize() const {
+ int num = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ if ((*_matching)[n] != INVALID) {
+ ++num;
+ }
+ }
+ return num /= 2;
+ }
+
+ /// \brief Return \c true if the given edge is in the matching.
+ ///
+ /// This function returns \c true if the given edge is in the found
+ /// matching.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ bool matching(const Edge& edge) const {
+ return edge == (*_matching)[_graph.u(edge)];
+ }
+
+ /// \brief Return the matching arc (or edge) incident to the given node.
+ ///
+ /// This function returns the matching arc (or edge) incident to the
+ /// given node in the found matching or \c INVALID if the node is
+ /// not covered by the matching.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ Arc matching(const Node& node) const {
+ return (*_matching)[node];
+ }
+
+ /// \brief Return a const reference to the matching map.
+ ///
+ /// This function returns a const reference to a node map that stores
+ /// the matching arc (or edge) incident to each node.
+ const MatchingMap& matchingMap() const {
+ return *_matching;
+ }
+
+ /// \brief Return the mate of the given node.
+ ///
+ /// This function returns the mate of the given node in the found
+ /// matching or \c INVALID if the node is not covered by the matching.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ Node mate(const Node& node) const {
+ return (*_matching)[node] != INVALID ?
+ _graph.target((*_matching)[node]) : INVALID;
+ }
+
+ /// @}
+
+ /// \name Dual Solution
+ /// Functions to get the dual solution.\n
+ /// Either \ref run() or \ref start() function should be called before
+ /// using them.
+
+ /// @{
+
+ /// \brief Return the value of the dual solution.
+ ///
+ /// This function returns the value of the dual solution.
+ /// It should be equal to the primal value scaled by \ref dualScale
+ /// "dual scale".
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ Value dualValue() const {
+ Value sum = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ sum += nodeValue(n);
+ }
+ for (int i = 0; i < blossomNum(); ++i) {
+ sum += blossomValue(i) * (blossomSize(i) / 2);
+ }
+ return sum;
+ }
+
+ /// \brief Return the dual value (potential) of the given node.
+ ///
+ /// This function returns the dual value (potential) of the given node.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ Value nodeValue(const Node& n) const {
+ return (*_node_potential)[n];
+ }
+
+ /// \brief Return the number of the blossoms in the basis.
+ ///
+ /// This function returns the number of the blossoms in the basis.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ /// \see BlossomIt
+ int blossomNum() const {
+ return _blossom_potential.size();
+ }
+
+ /// \brief Return the number of the nodes in the given blossom.
+ ///
+ /// This function returns the number of the nodes in the given blossom.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ /// \see BlossomIt
+ int blossomSize(int k) const {
+ return _blossom_potential[k].end - _blossom_potential[k].begin;
+ }
+
+ /// \brief Return the dual value (ptential) of the given blossom.
+ ///
+ /// This function returns the dual value (ptential) of the given blossom.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ Value blossomValue(int k) const {
+ return _blossom_potential[k].value;
+ }
+
+ /// \brief Iterator for obtaining the nodes of a blossom.
+ ///
+ /// This class provides an iterator for obtaining the nodes of the
+ /// given blossom. It lists a subset of the nodes.
+ /// Before using this iterator, you must allocate a
+ /// MaxWeightedMatching class and execute it.
+ class BlossomIt {
+ public:
+
+ /// \brief Constructor.
+ ///
+ /// Constructor to get the nodes of the given variable.
+ ///
+ /// \pre Either \ref MaxWeightedMatching::run() "algorithm.run()" or
+ /// \ref MaxWeightedMatching::start() "algorithm.start()" must be
+ /// called before initializing this iterator.
+ BlossomIt(const MaxWeightedMatching& algorithm, int variable)
+ : _algorithm(&algorithm)
+ {
+ _index = _algorithm->_blossom_potential[variable].begin;
+ _last = _algorithm->_blossom_potential[variable].end;
+ }
+
+ /// \brief Conversion to \c Node.
+ ///
+ /// Conversion to \c Node.
+ operator Node() const {
+ return _algorithm->_blossom_node_list[_index];
+ }
+
+ /// \brief Increment operator.
+ ///
+ /// Increment operator.
+ BlossomIt& operator++() {
+ ++_index;
+ return *this;
+ }
+
+ /// \brief Validity checking
+ ///
+ /// Checks whether the iterator is invalid.
+ bool operator==(Invalid) const { return _index == _last; }
+
+ /// \brief Validity checking
+ ///
+ /// Checks whether the iterator is valid.
+ bool operator!=(Invalid) const { return _index != _last; }
+
+ private:
+ const MaxWeightedMatching* _algorithm;
+ int _last;
+ int _index;
+ };
+
+ /// @}
+
+ };
+
+ /// \ingroup matching
+ ///
+ /// \brief Weighted perfect matching in general graphs
+ ///
+ /// This class provides an efficient implementation of Edmond's
+ /// maximum weighted perfect matching algorithm. The implementation
+ /// is based on extensive use of priority queues and provides
+ /// \f$O(nm\log n)\f$ time complexity.
+ ///
+ /// The maximum weighted perfect matching problem is to find a subset of
+ /// the edges in an undirected graph with maximum overall weight for which
+ /// each node has exactly one incident edge.
+ /// It can be formulated with the following linear program.
+ /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f]
+ /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
+ \quad \forall B\in\mathcal{O}\f] */
+ /// \f[x_e \ge 0\quad \forall e\in E\f]
+ /// \f[\max \sum_{e\in E}x_ew_e\f]
+ /// where \f$\delta(X)\f$ is the set of edges incident to a node in
+ /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
+ /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
+ /// subsets of the nodes.
+ ///
+ /// The algorithm calculates an optimal matching and a proof of the
+ /// optimality. The solution of the dual problem can be used to check
+ /// the result of the algorithm. The dual linear problem is the
+ /// following.
+ /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge
+ w_{uv} \quad \forall uv\in E\f] */
+ /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
+ /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
+ \frac{\vert B \vert - 1}{2}z_B\f] */
+ ///
+ /// The algorithm can be executed with the run() function.
+ /// After it the matching (the primal solution) and the dual solution
+ /// can be obtained using the query functions and the
+ /// \ref MaxWeightedPerfectMatching::BlossomIt "BlossomIt" nested class,
+ /// which is able to iterate on the nodes of a blossom.
+ /// If the value type is integer, then the dual solution is multiplied
+ /// by \ref MaxWeightedMatching::dualScale "4".
+ ///
+ /// \tparam GR The undirected graph type the algorithm runs on.
+ /// \tparam WM The type edge weight map. The default type is
+ /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".
+#ifdef DOXYGEN
+ template <typename GR, typename WM>
+#else
+ template <typename GR,
+ typename WM = typename GR::template EdgeMap<int> >
+#endif
+ class MaxWeightedPerfectMatching {
+ public:
+
+ /// The graph type of the algorithm
+ typedef GR Graph;
+ /// The type of the edge weight map
+ typedef WM WeightMap;
+ /// The value type of the edge weights
+ typedef typename WeightMap::Value Value;
+
+ /// \brief Scaling factor for dual solution
+ ///
+ /// Scaling factor for dual solution, it is equal to 4 or 1
+ /// according to the value type.
+ static const int dualScale =
+ std::numeric_limits<Value>::is_integer ? 4 : 1;
+
+ /// The type of the matching map
+ typedef typename Graph::template NodeMap<typename Graph::Arc>
+ MatchingMap;
+
+ private:
+
+ TEMPLATE_GRAPH_TYPEDEFS(Graph);
+
+ typedef typename Graph::template NodeMap<Value> NodePotential;
+ typedef std::vector<Node> BlossomNodeList;
+
+ struct BlossomVariable {
+ int begin, end;
+ Value value;
+
+ BlossomVariable(int _begin, int _end, Value _value)
+ : begin(_begin), end(_end), value(_value) {}
+
+ };
+
+ typedef std::vector<BlossomVariable> BlossomPotential;
+
+ const Graph& _graph;
+ const WeightMap& _weight;
+
+ MatchingMap* _matching;
+
+ NodePotential* _node_potential;
+
+ BlossomPotential _blossom_potential;
+ BlossomNodeList _blossom_node_list;
+
+ int _node_num;
+ int _blossom_num;
+
+ typedef RangeMap<int> IntIntMap;
+
+ enum Status {
+ EVEN = -1, MATCHED = 0, ODD = 1
+ };
+
+ typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
+ struct BlossomData {
+ int tree;
+ Status status;
+ Arc pred, next;
+ Value pot, offset;
+ };
+
+ IntNodeMap *_blossom_index;
+ BlossomSet *_blossom_set;
+ RangeMap<BlossomData>* _blossom_data;
+
+ IntNodeMap *_node_index;
+ IntArcMap *_node_heap_index;
+
+ struct NodeData {
+
+ NodeData(IntArcMap& node_heap_index)
+ : heap(node_heap_index) {}
+
+ int blossom;
+ Value pot;
+ BinHeap<Value, IntArcMap> heap;
+ std::map<int, Arc> heap_index;
+
+ int tree;
+ };
+
+ RangeMap<NodeData>* _node_data;
+
+ typedef ExtendFindEnum<IntIntMap> TreeSet;
+
+ IntIntMap *_tree_set_index;
+ TreeSet *_tree_set;
+
+ IntIntMap *_delta2_index;
+ BinHeap<Value, IntIntMap> *_delta2;
+
+ IntEdgeMap *_delta3_index;
+ BinHeap<Value, IntEdgeMap> *_delta3;
+
+ IntIntMap *_delta4_index;
+ BinHeap<Value, IntIntMap> *_delta4;
+
+ Value _delta_sum;
+
+ void createStructures() {
+ _node_num = countNodes(_graph);
+ _blossom_num = _node_num * 3 / 2;
+
+ if (!_matching) {
+ _matching = new MatchingMap(_graph);
+ }
+ if (!_node_potential) {
+ _node_potential = new NodePotential(_graph);
+ }
+ if (!_blossom_set) {
+ _blossom_index = new IntNodeMap(_graph);
+ _blossom_set = new BlossomSet(*_blossom_index);
+ _blossom_data = new RangeMap<BlossomData>(_blossom_num);
+ }
+
+ if (!_node_index) {
+ _node_index = new IntNodeMap(_graph);
+ _node_heap_index = new IntArcMap(_graph);
+ _node_data = new RangeMap<NodeData>(_node_num,
+ NodeData(*_node_heap_index));
+ }
+
+ if (!_tree_set) {
+ _tree_set_index = new IntIntMap(_blossom_num);
+ _tree_set = new TreeSet(*_tree_set_index);
+ }
+ if (!_delta2) {
+ _delta2_index = new IntIntMap(_blossom_num);
+ _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
+ }
+ if (!_delta3) {
+ _delta3_index = new IntEdgeMap(_graph);
+ _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
+ }
+ if (!_delta4) {
+ _delta4_index = new IntIntMap(_blossom_num);
+ _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
+ }
+ }
+
+ void destroyStructures() {
+ _node_num = countNodes(_graph);
+ _blossom_num = _node_num * 3 / 2;
+
+ if (_matching) {
+ delete _matching;
+ }
+ if (_node_potential) {
+ delete _node_potential;
+ }
+ if (_blossom_set) {
+ delete _blossom_index;
+ delete _blossom_set;
+ delete _blossom_data;
+ }
+
+ if (_node_index) {
+ delete _node_index;
+ delete _node_heap_index;
+ delete _node_data;
+ }
+
+ if (_tree_set) {
+ delete _tree_set_index;
+ delete _tree_set;
+ }
+ if (_delta2) {
+ delete _delta2_index;
+ delete _delta2;
+ }
+ if (_delta3) {
+ delete _delta3_index;
+ delete _delta3;
+ }
+ if (_delta4) {
+ delete _delta4_index;
+ delete _delta4;
+ }
+ }
+
+ void matchedToEven(int blossom, int tree) {
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+
+ if (!_blossom_set->trivial(blossom)) {
+ (*_blossom_data)[blossom].pot -=
+ 2 * (_delta_sum - (*_blossom_data)[blossom].offset);
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+
+ _blossom_set->increase(n, std::numeric_limits<Value>::max());
+ int ni = (*_node_index)[n];
+
+ (*_node_data)[ni].heap.clear();
+ (*_node_data)[ni].heap_index.clear();
+
+ (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if ((*_blossom_data)[vb].status == EVEN) {
+ if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
+ _delta3->push(e, rw / 2);
+ }
+ } else {
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[vi].heap_index.find(tree);
+
+ if (it != (*_node_data)[vi].heap_index.end()) {
+ if ((*_node_data)[vi].heap[it->second] > rw) {
+ (*_node_data)[vi].heap.replace(it->second, e);
+ (*_node_data)[vi].heap.decrease(e, rw);
+ it->second = e;
+ }
+ } else {
+ (*_node_data)[vi].heap.push(e, rw);
+ (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
+ }
+
+ if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
+ _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
+
+ if ((*_blossom_data)[vb].status == MATCHED) {
+ if (_delta2->state(vb) != _delta2->IN_HEAP) {
+ _delta2->push(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset){
+ _delta2->decrease(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ }
+ }
+ }
+ }
+ }
+ }
+ (*_blossom_data)[blossom].offset = 0;
+ }
+
+ void matchedToOdd(int blossom) {
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+ (*_blossom_data)[blossom].offset += _delta_sum;
+ if (!_blossom_set->trivial(blossom)) {
+ _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
+ (*_blossom_data)[blossom].offset);
+ }
+ }
+
+ void evenToMatched(int blossom, int tree) {
+ if (!_blossom_set->trivial(blossom)) {
+ (*_blossom_data)[blossom].pot += 2 * _delta_sum;
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+ int ni = (*_node_index)[n];
+ (*_node_data)[ni].pot -= _delta_sum;
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if (vb == blossom) {
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+ } else if ((*_blossom_data)[vb].status == EVEN) {
+
+ if (_delta3->state(e) == _delta3->IN_HEAP) {
+ _delta3->erase(e);
+ }
+
+ int vt = _tree_set->find(vb);
+
+ if (vt != tree) {
+
+ Arc r = _graph.oppositeArc(e);
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[ni].heap_index.find(vt);
+
+ if (it != (*_node_data)[ni].heap_index.end()) {
+ if ((*_node_data)[ni].heap[it->second] > rw) {
+ (*_node_data)[ni].heap.replace(it->second, r);
+ (*_node_data)[ni].heap.decrease(r, rw);
+ it->second = r;
+ }
+ } else {
+ (*_node_data)[ni].heap.push(r, rw);
+ (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
+ }
+
+ if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
+ _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
+
+ if (_delta2->state(blossom) != _delta2->IN_HEAP) {
+ _delta2->push(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ } else if ((*_delta2)[blossom] >
+ _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset){
+ _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ }
+ }
+ }
+ } else {
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[vi].heap_index.find(tree);
+
+ if (it != (*_node_data)[vi].heap_index.end()) {
+ (*_node_data)[vi].heap.erase(it->second);
+ (*_node_data)[vi].heap_index.erase(it);
+ if ((*_node_data)[vi].heap.empty()) {
+ _blossom_set->increase(v, std::numeric_limits<Value>::max());
+ } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
+ _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
+ }
+
+ if ((*_blossom_data)[vb].status == MATCHED) {
+ if (_blossom_set->classPrio(vb) ==
+ std::numeric_limits<Value>::max()) {
+ _delta2->erase(vb);
+ } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset) {
+ _delta2->increase(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+
+ void oddToMatched(int blossom) {
+ (*_blossom_data)[blossom].offset -= _delta_sum;
+
+ if (_blossom_set->classPrio(blossom) !=
+ std::numeric_limits<Value>::max()) {
+ _delta2->push(blossom, _blossom_set->classPrio(blossom) -
+ (*_blossom_data)[blossom].offset);
+ }
+
+ if (!_blossom_set->trivial(blossom)) {
+ _delta4->erase(blossom);
+ }
+ }
+
+ void oddToEven(int blossom, int tree) {
+ if (!_blossom_set->trivial(blossom)) {
+ _delta4->erase(blossom);
+ (*_blossom_data)[blossom].pot -=
+ 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
+ }
+
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+ n != INVALID; ++n) {
+ int ni = (*_node_index)[n];
+
+ _blossom_set->increase(n, std::numeric_limits<Value>::max());
+
+ (*_node_data)[ni].heap.clear();
+ (*_node_data)[ni].heap_index.clear();
+ (*_node_data)[ni].pot +=
+ 2 * _delta_sum - (*_blossom_data)[blossom].offset;
+
+ for (InArcIt e(_graph, n); e != INVALID; ++e) {
+ Node v = _graph.source(e);
+ int vb = _blossom_set->find(v);
+ int vi = (*_node_index)[v];
+
+ Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+ dualScale * _weight[e];
+
+ if ((*_blossom_data)[vb].status == EVEN) {
+ if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
+ _delta3->push(e, rw / 2);
+ }
+ } else {
+
+ typename std::map<int, Arc>::iterator it =
+ (*_node_data)[vi].heap_index.find(tree);
+
+ if (it != (*_node_data)[vi].heap_index.end()) {
+ if ((*_node_data)[vi].heap[it->second] > rw) {
+ (*_node_data)[vi].heap.replace(it->second, e);
+ (*_node_data)[vi].heap.decrease(e, rw);
+ it->second = e;
+ }
+ } else {
+ (*_node_data)[vi].heap.push(e, rw);
+ (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
+ }
+
+ if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
+ _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
+
+ if ((*_blossom_data)[vb].status == MATCHED) {
+ if (_delta2->state(vb) != _delta2->IN_HEAP) {
+ _delta2->push(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset) {
+ _delta2->decrease(vb, _blossom_set->classPrio(vb) -
+ (*_blossom_data)[vb].offset);
+ }
+ }
+ }
+ }
+ }
+ }
+ (*_blossom_data)[blossom].offset = 0;
+ }
+
+ void alternatePath(int even, int tree) {
+ int odd;
+
+ evenToMatched(even, tree);
+ (*_blossom_data)[even].status = MATCHED;
+
+ while ((*_blossom_data)[even].pred != INVALID) {
+ odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
+ (*_blossom_data)[odd].status = MATCHED;
+ oddToMatched(odd);
+ (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
+
+ even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
+ (*_blossom_data)[even].status = MATCHED;
+ evenToMatched(even, tree);
+ (*_blossom_data)[even].next =
+ _graph.oppositeArc((*_blossom_data)[odd].pred);
+ }
+
+ }
+
+ void destroyTree(int tree) {
+ for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
+ if ((*_blossom_data)[b].status == EVEN) {
+ (*_blossom_data)[b].status = MATCHED;
+ evenToMatched(b, tree);
+ } else if ((*_blossom_data)[b].status == ODD) {
+ (*_blossom_data)[b].status = MATCHED;
+ oddToMatched(b);
+ }
+ }
+ _tree_set->eraseClass(tree);
+ }
+
+ void augmentOnEdge(const Edge& edge) {
+
+ int left = _blossom_set->find(_graph.u(edge));
+ int right = _blossom_set->find(_graph.v(edge));
+
+ int left_tree = _tree_set->find(left);
+ alternatePath(left, left_tree);
+ destroyTree(left_tree);
+
+ int right_tree = _tree_set->find(right);
+ alternatePath(right, right_tree);
+ destroyTree(right_tree);
+
+ (*_blossom_data)[left].next = _graph.direct(edge, true);
+ (*_blossom_data)[right].next = _graph.direct(edge, false);
+ }
+
+ void extendOnArc(const Arc& arc) {
+ int base = _blossom_set->find(_graph.target(arc));
+ int tree = _tree_set->find(base);
+
+ int odd = _blossom_set->find(_graph.source(arc));
+ _tree_set->insert(odd, tree);
+ (*_blossom_data)[odd].status = ODD;
+ matchedToOdd(odd);
+ (*_blossom_data)[odd].pred = arc;
+
+ int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
+ (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
+ _tree_set->insert(even, tree);
+ (*_blossom_data)[even].status = EVEN;
+ matchedToEven(even, tree);
+ }
+
+ void shrinkOnEdge(const Edge& edge, int tree) {
+ int nca = -1;
+ std::vector<int> left_path, right_path;
+
+ {
+ std::set<int> left_set, right_set;
+ int left = _blossom_set->find(_graph.u(edge));
+ left_path.push_back(left);
+ left_set.insert(left);
+
+ int right = _blossom_set->find(_graph.v(edge));
+ right_path.push_back(right);
+ right_set.insert(right);
+
+ while (true) {
+
+ if ((*_blossom_data)[left].pred == INVALID) break;
+
+ left =
+ _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
+ left_path.push_back(left);
+ left =
+ _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
+ left_path.push_back(left);
+
+ left_set.insert(left);
+
+ if (right_set.find(left) != right_set.end()) {
+ nca = left;
+ break;
+ }
+
+ if ((*_blossom_data)[right].pred == INVALID) break;
+
+ right =
+ _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
+ right_path.push_back(right);
+ right =
+ _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
+ right_path.push_back(right);
+
+ right_set.insert(right);
+
+ if (left_set.find(right) != left_set.end()) {
+ nca = right;
+ break;
+ }
+
+ }
+
+ if (nca == -1) {
+ if ((*_blossom_data)[left].pred == INVALID) {
+ nca = right;
+ while (left_set.find(nca) == left_set.end()) {
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ right_path.push_back(nca);
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ right_path.push_back(nca);
+ }
+ } else {
+ nca = left;
+ while (right_set.find(nca) == right_set.end()) {
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ left_path.push_back(nca);
+ nca =
+ _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+ left_path.push_back(nca);
+ }
+ }
+ }
+ }
+
+ std::vector<int> subblossoms;
+ Arc prev;
+
+ prev = _graph.direct(edge, true);
+ for (int i = 0; left_path[i] != nca; i += 2) {
+ subblossoms.push_back(left_path[i]);
+ (*_blossom_data)[left_path[i]].next = prev;
+ _tree_set->erase(left_path[i]);
+
+ subblossoms.push_back(left_path[i + 1]);
+ (*_blossom_data)[left_path[i + 1]].status = EVEN;
+ oddToEven(left_path[i + 1], tree);
+ _tree_set->erase(left_path[i + 1]);
+ prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
+ }
+
+ int k = 0;
+ while (right_path[k] != nca) ++k;
+
+ subblossoms.push_back(nca);
+ (*_blossom_data)[nca].next = prev;
+
+ for (int i = k - 2; i >= 0; i -= 2) {
+ subblossoms.push_back(right_path[i + 1]);
+ (*_blossom_data)[right_path[i + 1]].status = EVEN;
+ oddToEven(right_path[i + 1], tree);
+ _tree_set->erase(right_path[i + 1]);
+
+ (*_blossom_data)[right_path[i + 1]].next =
+ (*_blossom_data)[right_path[i + 1]].pred;
+
+ subblossoms.push_back(right_path[i]);
+ _tree_set->erase(right_path[i]);
+ }
+
+ int surface =
+ _blossom_set->join(subblossoms.begin(), subblossoms.end());
+
+ for (int i = 0; i < int(subblossoms.size()); ++i) {
+ if (!_blossom_set->trivial(subblossoms[i])) {
+ (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
+ }
+ (*_blossom_data)[subblossoms[i]].status = MATCHED;
+ }
+
+ (*_blossom_data)[surface].pot = -2 * _delta_sum;
+ (*_blossom_data)[surface].offset = 0;
+ (*_blossom_data)[surface].status = EVEN;
+ (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
+ (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
+
+ _tree_set->insert(surface, tree);
+ _tree_set->erase(nca);
+ }
+
+ void splitBlossom(int blossom) {
+ Arc next = (*_blossom_data)[blossom].next;
+ Arc pred = (*_blossom_data)[blossom].pred;
+
+ int tree = _tree_set->find(blossom);
+
+ (*_blossom_data)[blossom].status = MATCHED;
+ oddToMatched(blossom);
+ if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+ _delta2->erase(blossom);
+ }
+
+ std::vector<int> subblossoms;
+ _blossom_set->split(blossom, std::back_inserter(subblossoms));
+
+ Value offset = (*_blossom_data)[blossom].offset;
+ int b = _blossom_set->find(_graph.source(pred));
+ int d = _blossom_set->find(_graph.source(next));
+
+ int ib = -1, id = -1;
+ for (int i = 0; i < int(subblossoms.size()); ++i) {
+ if (subblossoms[i] == b) ib = i;
+ if (subblossoms[i] == d) id = i;
+
+ (*_blossom_data)[subblossoms[i]].offset = offset;
+ if (!_blossom_set->trivial(subblossoms[i])) {
+ (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
+ }
+ if (_blossom_set->classPrio(subblossoms[i]) !=
+ std::numeric_limits<Value>::max()) {
+ _delta2->push(subblossoms[i],
+ _blossom_set->classPrio(subblossoms[i]) -
+ (*_blossom_data)[subblossoms[i]].offset);
+ }
+ }
+
+ if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
+ for (int i = (id + 1) % subblossoms.size();
+ i != ib; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ (*_blossom_data)[sb].next =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+ }
+
+ for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ int ub = subblossoms[(i + 2) % subblossoms.size()];
+
+ (*_blossom_data)[sb].status = ODD;
+ matchedToOdd(sb);
+ _tree_set->insert(sb, tree);
+ (*_blossom_data)[sb].pred = pred;
+ (*_blossom_data)[sb].next =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+
+ pred = (*_blossom_data)[ub].next;
+
+ (*_blossom_data)[tb].status = EVEN;
+ matchedToEven(tb, tree);
+ _tree_set->insert(tb, tree);
+ (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
+ }
+
+ (*_blossom_data)[subblossoms[id]].status = ODD;
+ matchedToOdd(subblossoms[id]);
+ _tree_set->insert(subblossoms[id], tree);
+ (*_blossom_data)[subblossoms[id]].next = next;
+ (*_blossom_data)[subblossoms[id]].pred = pred;
+
+ } else {
+
+ for (int i = (ib + 1) % subblossoms.size();
+ i != id; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ (*_blossom_data)[sb].next =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+ }
+
+ for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
+ int sb = subblossoms[i];
+ int tb = subblossoms[(i + 1) % subblossoms.size()];
+ int ub = subblossoms[(i + 2) % subblossoms.size()];
+
+ (*_blossom_data)[sb].status = ODD;
+ matchedToOdd(sb);
+ _tree_set->insert(sb, tree);
+ (*_blossom_data)[sb].next = next;
+ (*_blossom_data)[sb].pred =
+ _graph.oppositeArc((*_blossom_data)[tb].next);
+
+ (*_blossom_data)[tb].status = EVEN;
+ matchedToEven(tb, tree);
+ _tree_set->insert(tb, tree);
+ (*_blossom_data)[tb].pred =
+ (*_blossom_data)[tb].next =
+ _graph.oppositeArc((*_blossom_data)[ub].next);
+ next = (*_blossom_data)[ub].next;
+ }
+
+ (*_blossom_data)[subblossoms[ib]].status = ODD;
+ matchedToOdd(subblossoms[ib]);
+ _tree_set->insert(subblossoms[ib], tree);
+ (*_blossom_data)[subblossoms[ib]].next = next;
+ (*_blossom_data)[subblossoms[ib]].pred = pred;
+ }
+ _tree_set->erase(blossom);
+ }
+
+ void extractBlossom(int blossom, const Node& base, const Arc& matching) {
+ if (_blossom_set->trivial(blossom)) {
+ int bi = (*_node_index)[base];
+ Value pot = (*_node_data)[bi].pot;
+
+ (*_matching)[base] = matching;
+ _blossom_node_list.push_back(base);
+ (*_node_potential)[base] = pot;
+ } else {
+
+ Value pot = (*_blossom_data)[blossom].pot;
+ int bn = _blossom_node_list.size();
+
+ std::vector<int> subblossoms;
+ _blossom_set->split(blossom, std::back_inserter(subblossoms));
+ int b = _blossom_set->find(base);
+ int ib = -1;
+ for (int i = 0; i < int(subblossoms.size()); ++i) {
+ if (subblossoms[i] == b) { ib = i; break; }
+ }
+
+ for (int i = 1; i < int(subblossoms.size()); i += 2) {
+ int sb = subblossoms[(ib + i) % subblossoms.size()];
+ int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
+
+ Arc m = (*_blossom_data)[tb].next;
+ extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
+ extractBlossom(tb, _graph.source(m), m);
+ }
+ extractBlossom(subblossoms[ib], base, matching);
+
+ int en = _blossom_node_list.size();
+
+ _blossom_potential.push_back(BlossomVariable(bn, en, pot));
+ }
+ }
+
+ void extractMatching() {
+ std::vector<int> blossoms;
+ for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
+ blossoms.push_back(c);
+ }
+
+ for (int i = 0; i < int(blossoms.size()); ++i) {
+
+ Value offset = (*_blossom_data)[blossoms[i]].offset;
+ (*_blossom_data)[blossoms[i]].pot += 2 * offset;
+ for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
+ n != INVALID; ++n) {
+ (*_node_data)[(*_node_index)[n]].pot -= offset;
+ }
+
+ Arc matching = (*_blossom_data)[blossoms[i]].next;
+ Node base = _graph.source(matching);
+ extractBlossom(blossoms[i], base, matching);
+ }
+ }
+
+ public:
+
+ /// \brief Constructor
+ ///
+ /// Constructor.
+ MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight)
+ : _graph(graph), _weight(weight), _matching(0),
+ _node_potential(0), _blossom_potential(), _blossom_node_list(),
+ _node_num(0), _blossom_num(0),
+
+ _blossom_index(0), _blossom_set(0), _blossom_data(0),
+ _node_index(0), _node_heap_index(0), _node_data(0),
+ _tree_set_index(0), _tree_set(0),
+
+ _delta2_index(0), _delta2(0),
+ _delta3_index(0), _delta3(0),
+ _delta4_index(0), _delta4(0),
+
+ _delta_sum() {}
+
+ ~MaxWeightedPerfectMatching() {
+ destroyStructures();
+ }
+
+ /// \name Execution Control
+ /// The simplest way to execute the algorithm is to use the
+ /// \ref run() member function.
+
+ ///@{
+
+ /// \brief Initialize the algorithm
+ ///
+ /// This function initializes the algorithm.
+ void init() {
+ createStructures();
+
+ for (ArcIt e(_graph); e != INVALID; ++e) {
+ (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
+ }
+ for (EdgeIt e(_graph); e != INVALID; ++e) {
+ (*_delta3_index)[e] = _delta3->PRE_HEAP;
+ }
+ for (int i = 0; i < _blossom_num; ++i) {
+ (*_delta2_index)[i] = _delta2->PRE_HEAP;
+ (*_delta4_index)[i] = _delta4->PRE_HEAP;
+ }
+
+ int index = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ Value max = - std::numeric_limits<Value>::max();
+ for (OutArcIt e(_graph, n); e != INVALID; ++e) {
+ if (_graph.target(e) == n) continue;
+ if ((dualScale * _weight[e]) / 2 > max) {
+ max = (dualScale * _weight[e]) / 2;
+ }
+ }
+ (*_node_index)[n] = index;
+ (*_node_data)[index].pot = max;
+ int blossom =
+ _blossom_set->insert(n, std::numeric_limits<Value>::max());
+
+ _tree_set->insert(blossom);
+
+ (*_blossom_data)[blossom].status = EVEN;
+ (*_blossom_data)[blossom].pred = INVALID;
+ (*_blossom_data)[blossom].next = INVALID;
+ (*_blossom_data)[blossom].pot = 0;
+ (*_blossom_data)[blossom].offset = 0;
+ ++index;
+ }
+ for (EdgeIt e(_graph); e != INVALID; ++e) {
+ int si = (*_node_index)[_graph.u(e)];
+ int ti = (*_node_index)[_graph.v(e)];
+ if (_graph.u(e) != _graph.v(e)) {
+ _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
+ dualScale * _weight[e]) / 2);
+ }
+ }
+ }
+
+ /// \brief Start the algorithm
+ ///
+ /// This function starts the algorithm.
+ ///
+ /// \pre \ref init() must be called before using this function.
+ bool start() {
+ enum OpType {
+ D2, D3, D4
+ };
+
+ int unmatched = _node_num;
+ while (unmatched > 0) {
+ Value d2 = !_delta2->empty() ?
+ _delta2->prio() : std::numeric_limits<Value>::max();
+
+ Value d3 = !_delta3->empty() ?
+ _delta3->prio() : std::numeric_limits<Value>::max();
+
+ Value d4 = !_delta4->empty() ?
+ _delta4->prio() : std::numeric_limits<Value>::max();
+
+ _delta_sum = d2; OpType ot = D2;
+ if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
+ if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
+
+ if (_delta_sum == std::numeric_limits<Value>::max()) {
+ return false;
+ }
+
+ switch (ot) {
+ case D2:
+ {
+ int blossom = _delta2->top();
+ Node n = _blossom_set->classTop(blossom);
+ Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
+ extendOnArc(e);
+ }
+ break;
+ case D3:
+ {
+ Edge e = _delta3->top();
+
+ int left_blossom = _blossom_set->find(_graph.u(e));
+ int right_blossom = _blossom_set->find(_graph.v(e));
+
+ if (left_blossom == right_blossom) {
+ _delta3->pop();
+ } else {
+ int left_tree = _tree_set->find(left_blossom);
+ int right_tree = _tree_set->find(right_blossom);
+
+ if (left_tree == right_tree) {
+ shrinkOnEdge(e, left_tree);
+ } else {
+ augmentOnEdge(e);
+ unmatched -= 2;
+ }
+ }
+ } break;
+ case D4:
+ splitBlossom(_delta4->top());
+ break;
+ }
+ }
+ extractMatching();
+ return true;
+ }
+
+ /// \brief Run the algorithm.
+ ///
+ /// This method runs the \c %MaxWeightedPerfectMatching algorithm.
+ ///
+ /// \note mwpm.run() is just a shortcut of the following code.
+ /// \code
+ /// mwpm.init();
+ /// mwpm.start();
+ /// \endcode
+ bool run() {
+ init();
+ return start();
+ }
+
+ /// @}
+
+ /// \name Primal Solution
+ /// Functions to get the primal solution, i.e. the maximum weighted
+ /// perfect matching.\n
+ /// Either \ref run() or \ref start() function should be called before
+ /// using them.
+
+ /// @{
+
+ /// \brief Return the weight of the matching.
+ ///
+ /// This function returns the weight of the found matching.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ Value matchingWeight() const {
+ Value sum = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ if ((*_matching)[n] != INVALID) {
+ sum += _weight[(*_matching)[n]];
+ }
+ }
+ return sum /= 2;
+ }
+
+ /// \brief Return \c true if the given edge is in the matching.
+ ///
+ /// This function returns \c true if the given edge is in the found
+ /// matching.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ bool matching(const Edge& edge) const {
+ return static_cast<const Edge&>((*_matching)[_graph.u(edge)]) == edge;
+ }
+
+ /// \brief Return the matching arc (or edge) incident to the given node.
+ ///
+ /// This function returns the matching arc (or edge) incident to the
+ /// given node in the found matching or \c INVALID if the node is
+ /// not covered by the matching.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ Arc matching(const Node& node) const {
+ return (*_matching)[node];
+ }
+
+ /// \brief Return a const reference to the matching map.
+ ///
+ /// This function returns a const reference to a node map that stores
+ /// the matching arc (or edge) incident to each node.
+ const MatchingMap& matchingMap() const {
+ return *_matching;
+ }
+
+ /// \brief Return the mate of the given node.
+ ///
+ /// This function returns the mate of the given node in the found
+ /// matching or \c INVALID if the node is not covered by the matching.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ Node mate(const Node& node) const {
+ return _graph.target((*_matching)[node]);
+ }
+
+ /// @}
+
+ /// \name Dual Solution
+ /// Functions to get the dual solution.\n
+ /// Either \ref run() or \ref start() function should be called before
+ /// using them.
+
+ /// @{
+
+ /// \brief Return the value of the dual solution.
+ ///
+ /// This function returns the value of the dual solution.
+ /// It should be equal to the primal value scaled by \ref dualScale
+ /// "dual scale".
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ Value dualValue() const {
+ Value sum = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ sum += nodeValue(n);
+ }
+ for (int i = 0; i < blossomNum(); ++i) {
+ sum += blossomValue(i) * (blossomSize(i) / 2);
+ }
+ return sum;
+ }
+
+ /// \brief Return the dual value (potential) of the given node.
+ ///
+ /// This function returns the dual value (potential) of the given node.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ Value nodeValue(const Node& n) const {
+ return (*_node_potential)[n];
+ }
+
+ /// \brief Return the number of the blossoms in the basis.
+ ///
+ /// This function returns the number of the blossoms in the basis.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ /// \see BlossomIt
+ int blossomNum() const {
+ return _blossom_potential.size();
+ }
+
+ /// \brief Return the number of the nodes in the given blossom.
+ ///
+ /// This function returns the number of the nodes in the given blossom.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ /// \see BlossomIt
+ int blossomSize(int k) const {
+ return _blossom_potential[k].end - _blossom_potential[k].begin;
+ }
+
+ /// \brief Return the dual value (ptential) of the given blossom.
+ ///
+ /// This function returns the dual value (ptential) of the given blossom.
+ ///
+ /// \pre Either run() or start() must be called before using this function.
+ Value blossomValue(int k) const {
+ return _blossom_potential[k].value;
+ }
+
+ /// \brief Iterator for obtaining the nodes of a blossom.
+ ///
+ /// This class provides an iterator for obtaining the nodes of the
+ /// given blossom. It lists a subset of the nodes.
+ /// Before using this iterator, you must allocate a
+ /// MaxWeightedPerfectMatching class and execute it.
+ class BlossomIt {
+ public:
+
+ /// \brief Constructor.
+ ///
+ /// Constructor to get the nodes of the given variable.
+ ///
+ /// \pre Either \ref MaxWeightedPerfectMatching::run() "algorithm.run()"
+ /// or \ref MaxWeightedPerfectMatching::start() "algorithm.start()"
+ /// must be called before initializing this iterator.
+ BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable)
+ : _algorithm(&algorithm)
+ {
+ _index = _algorithm->_blossom_potential[variable].begin;
+ _last = _algorithm->_blossom_potential[variable].end;
+ }
+
+ /// \brief Conversion to \c Node.
+ ///
+ /// Conversion to \c Node.
+ operator Node() const {
+ return _algorithm->_blossom_node_list[_index];
+ }
+
+ /// \brief Increment operator.
+ ///
+ /// Increment operator.
+ BlossomIt& operator++() {
+ ++_index;
+ return *this;
+ }
+
+ /// \brief Validity checking
+ ///
+ /// This function checks whether the iterator is invalid.
+ bool operator==(Invalid) const { return _index == _last; }
+
+ /// \brief Validity checking
+ ///
+ /// This function checks whether the iterator is valid.
+ bool operator!=(Invalid) const { return _index != _last; }
+
+ private:
+ const MaxWeightedPerfectMatching* _algorithm;
+ int _last;
+ int _index;
+ };
+
+ /// @}
+
+ };
+
+} //END OF NAMESPACE LEMON
+
+#endif //LEMON_MAX_MATCHING_H
diff -r f63e87b9748e -r 0ba8dfce7259 lemon/max_matching.h
--- a/lemon/max_matching.h Tue Apr 21 10:34:49 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,3107 +0,0 @@
-/* -*- mode: C++; indent-tabs-mode: nil; -*-
- *
- * This file is a part of LEMON, a generic C++ optimization library.
- *
- * Copyright (C) 2003-2009
- * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
- * (Egervary Research Group on Combinatorial Optimization, EGRES).
- *
- * Permission to use, modify and distribute this software is granted
- * provided that this copyright notice appears in all copies. For
- * precise terms see the accompanying LICENSE file.
- *
- * This software is provided "AS IS" with no warranty of any kind,
- * express or implied, and with no claim as to its suitability for any
- * purpose.
- *
- */
-
-#ifndef LEMON_MAX_MATCHING_H
-#define LEMON_MAX_MATCHING_H
-
-#include <vector>
-#include <queue>
-#include <set>
-#include <limits>
-
-#include <lemon/core.h>
-#include <lemon/unionfind.h>
-#include <lemon/bin_heap.h>
-#include <lemon/maps.h>
-
-///\ingroup matching
-///\file
-///\brief Maximum matching algorithms in general graphs.
-
-namespace lemon {
-
- /// \ingroup matching
- ///
- /// \brief Edmonds' alternating forest maximum matching algorithm.
- ///
- /// This class implements Edmonds' alternating forest matching
- /// algorithm. The algorithm can be started from an arbitrary initial
- /// matching (the default is the empty one)
- ///
- /// The dual solution of the problem is a map of the nodes to
- /// MaxMatching::Status, having values \c EVEN/D, \c ODD/A and \c
- /// MATCHED/C showing the Gallai-Edmonds decomposition of the
- /// graph. The nodes in \c EVEN/D induce a graph with
- /// factor-critical components, the nodes in \c ODD/A form the
- /// barrier, and the nodes in \c MATCHED/C induce a graph having a
- /// perfect matching. The number of the factor-critical components
- /// minus the number of barrier nodes is a lower bound on the
- /// unmatched nodes, and the matching is optimal if and only if this bound is
- /// tight. This decomposition can be attained by calling \c
- /// decomposition() after running the algorithm.
- ///
- /// \param GR The graph type the algorithm runs on.
- template <typename GR>
- class MaxMatching {
- public:
-
- typedef GR Graph;
- typedef typename Graph::template NodeMap<typename Graph::Arc>
- MatchingMap;
-
- ///\brief Indicates the Gallai-Edmonds decomposition of the graph.
- ///
- ///Indicates the Gallai-Edmonds decomposition of the graph. The
- ///nodes with Status \c EVEN/D induce a graph with factor-critical
- ///components, the nodes in \c ODD/A form the canonical barrier,
- ///and the nodes in \c MATCHED/C induce a graph having a perfect
- ///matching.
- enum Status {
- EVEN = 1, D = 1, MATCHED = 0, C = 0, ODD = -1, A = -1, UNMATCHED = -2
- };
-
- typedef typename Graph::template NodeMap<Status> StatusMap;
-
- private:
-
- TEMPLATE_GRAPH_TYPEDEFS(Graph);
-
- typedef UnionFindEnum<IntNodeMap> BlossomSet;
- typedef ExtendFindEnum<IntNodeMap> TreeSet;
- typedef RangeMap<Node> NodeIntMap;
- typedef MatchingMap EarMap;
- typedef std::vector<Node> NodeQueue;
-
- const Graph& _graph;
- MatchingMap* _matching;
- StatusMap* _status;
-
- EarMap* _ear;
-
- IntNodeMap* _blossom_set_index;
- BlossomSet* _blossom_set;
- NodeIntMap* _blossom_rep;
-
- IntNodeMap* _tree_set_index;
- TreeSet* _tree_set;
-
- NodeQueue _node_queue;
- int _process, _postpone, _last;
-
- int _node_num;
-
- private:
-
- void createStructures() {
- _node_num = countNodes(_graph);
- if (!_matching) {
- _matching = new MatchingMap(_graph);
- }
- if (!_status) {
- _status = new StatusMap(_graph);
- }
- if (!_ear) {
- _ear = new EarMap(_graph);
- }
- if (!_blossom_set) {
- _blossom_set_index = new IntNodeMap(_graph);
- _blossom_set = new BlossomSet(*_blossom_set_index);
- }
- if (!_blossom_rep) {
- _blossom_rep = new NodeIntMap(_node_num);
- }
- if (!_tree_set) {
- _tree_set_index = new IntNodeMap(_graph);
- _tree_set = new TreeSet(*_tree_set_index);
- }
- _node_queue.resize(_node_num);
- }
-
- void destroyStructures() {
- if (_matching) {
- delete _matching;
- }
- if (_status) {
- delete _status;
- }
- if (_ear) {
- delete _ear;
- }
- if (_blossom_set) {
- delete _blossom_set;
- delete _blossom_set_index;
- }
- if (_blossom_rep) {
- delete _blossom_rep;
- }
- if (_tree_set) {
- delete _tree_set_index;
- delete _tree_set;
- }
- }
-
- void processDense(const Node& n) {
- _process = _postpone = _last = 0;
- _node_queue[_last++] = n;
-
- while (_process != _last) {
- Node u = _node_queue[_process++];
- for (OutArcIt a(_graph, u); a != INVALID; ++a) {
- Node v = _graph.target(a);
- if ((*_status)[v] == MATCHED) {
- extendOnArc(a);
- } else if ((*_status)[v] == UNMATCHED) {
- augmentOnArc(a);
- return;
- }
- }
- }
-
- while (_postpone != _last) {
- Node u = _node_queue[_postpone++];
-
- for (OutArcIt a(_graph, u); a != INVALID ; ++a) {
- Node v = _graph.target(a);
-
- if ((*_status)[v] == EVEN) {
- if (_blossom_set->find(u) != _blossom_set->find(v)) {
- shrinkOnEdge(a);
- }
- }
-
- while (_process != _last) {
- Node w = _node_queue[_process++];
- for (OutArcIt b(_graph, w); b != INVALID; ++b) {
- Node x = _graph.target(b);
- if ((*_status)[x] == MATCHED) {
- extendOnArc(b);
- } else if ((*_status)[x] == UNMATCHED) {
- augmentOnArc(b);
- return;
- }
- }
- }
- }
- }
- }
-
- void processSparse(const Node& n) {
- _process = _last = 0;
- _node_queue[_last++] = n;
- while (_process != _last) {
- Node u = _node_queue[_process++];
- for (OutArcIt a(_graph, u); a != INVALID; ++a) {
- Node v = _graph.target(a);
-
- if ((*_status)[v] == EVEN) {
- if (_blossom_set->find(u) != _blossom_set->find(v)) {
- shrinkOnEdge(a);
- }
- } else if ((*_status)[v] == MATCHED) {
- extendOnArc(a);
- } else if ((*_status)[v] == UNMATCHED) {
- augmentOnArc(a);
- return;
- }
- }
- }
- }
-
- void shrinkOnEdge(const Edge& e) {
- Node nca = INVALID;
-
- {
- std::set<Node> left_set, right_set;
-
- Node left = (*_blossom_rep)[_blossom_set->find(_graph.u(e))];
- left_set.insert(left);
-
- Node right = (*_blossom_rep)[_blossom_set->find(_graph.v(e))];
- right_set.insert(right);
-
- while (true) {
- if ((*_matching)[left] == INVALID) break;
- left = _graph.target((*_matching)[left]);
- left = (*_blossom_rep)[_blossom_set->
- find(_graph.target((*_ear)[left]))];
- if (right_set.find(left) != right_set.end()) {
- nca = left;
- break;
- }
- left_set.insert(left);
-
- if ((*_matching)[right] == INVALID) break;
- right = _graph.target((*_matching)[right]);
- right = (*_blossom_rep)[_blossom_set->
- find(_graph.target((*_ear)[right]))];
- if (left_set.find(right) != left_set.end()) {
- nca = right;
- break;
- }
- right_set.insert(right);
- }
-
- if (nca == INVALID) {
- if ((*_matching)[left] == INVALID) {
- nca = right;
- while (left_set.find(nca) == left_set.end()) {
- nca = _graph.target((*_matching)[nca]);
- nca =(*_blossom_rep)[_blossom_set->
- find(_graph.target((*_ear)[nca]))];
- }
- } else {
- nca = left;
- while (right_set.find(nca) == right_set.end()) {
- nca = _graph.target((*_matching)[nca]);
- nca = (*_blossom_rep)[_blossom_set->
- find(_graph.target((*_ear)[nca]))];
- }
- }
- }
- }
-
- {
-
- Node node = _graph.u(e);
- Arc arc = _graph.direct(e, true);
- Node base = (*_blossom_rep)[_blossom_set->find(node)];
-
- while (base != nca) {
- (*_ear)[node] = arc;
-
- Node n = node;
- while (n != base) {
- n = _graph.target((*_matching)[n]);
- Arc a = (*_ear)[n];
- n = _graph.target(a);
- (*_ear)[n] = _graph.oppositeArc(a);
- }
- node = _graph.target((*_matching)[base]);
- _tree_set->erase(base);
- _tree_set->erase(node);
- _blossom_set->insert(node, _blossom_set->find(base));
- (*_status)[node] = EVEN;
- _node_queue[_last++] = node;
- arc = _graph.oppositeArc((*_ear)[node]);
- node = _graph.target((*_ear)[node]);
- base = (*_blossom_rep)[_blossom_set->find(node)];
- _blossom_set->join(_graph.target(arc), base);
- }
- }
-
- (*_blossom_rep)[_blossom_set->find(nca)] = nca;
-
- {
-
- Node node = _graph.v(e);
- Arc arc = _graph.direct(e, false);
- Node base = (*_blossom_rep)[_blossom_set->find(node)];
-
- while (base != nca) {
- (*_ear)[node] = arc;
-
- Node n = node;
- while (n != base) {
- n = _graph.target((*_matching)[n]);
- Arc a = (*_ear)[n];
- n = _graph.target(a);
- (*_ear)[n] = _graph.oppositeArc(a);
- }
- node = _graph.target((*_matching)[base]);
- _tree_set->erase(base);
- _tree_set->erase(node);
- _blossom_set->insert(node, _blossom_set->find(base));
- (*_status)[node] = EVEN;
- _node_queue[_last++] = node;
- arc = _graph.oppositeArc((*_ear)[node]);
- node = _graph.target((*_ear)[node]);
- base = (*_blossom_rep)[_blossom_set->find(node)];
- _blossom_set->join(_graph.target(arc), base);
- }
- }
-
- (*_blossom_rep)[_blossom_set->find(nca)] = nca;
- }
-
-
-
- void extendOnArc(const Arc& a) {
- Node base = _graph.source(a);
- Node odd = _graph.target(a);
-
- (*_ear)[odd] = _graph.oppositeArc(a);
- Node even = _graph.target((*_matching)[odd]);
- (*_blossom_rep)[_blossom_set->insert(even)] = even;
- (*_status)[odd] = ODD;
- (*_status)[even] = EVEN;
- int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(base)]);
- _tree_set->insert(odd, tree);
- _tree_set->insert(even, tree);
- _node_queue[_last++] = even;
-
- }
-
- void augmentOnArc(const Arc& a) {
- Node even = _graph.source(a);
- Node odd = _graph.target(a);
-
- int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(even)]);
-
- (*_matching)[odd] = _graph.oppositeArc(a);
- (*_status)[odd] = MATCHED;
-
- Arc arc = (*_matching)[even];
- (*_matching)[even] = a;
-
- while (arc != INVALID) {
- odd = _graph.target(arc);
- arc = (*_ear)[odd];
- even = _graph.target(arc);
- (*_matching)[odd] = arc;
- arc = (*_matching)[even];
- (*_matching)[even] = _graph.oppositeArc((*_matching)[odd]);
- }
-
- for (typename TreeSet::ItemIt it(*_tree_set, tree);
- it != INVALID; ++it) {
- if ((*_status)[it] == ODD) {
- (*_status)[it] = MATCHED;
- } else {
- int blossom = _blossom_set->find(it);
- for (typename BlossomSet::ItemIt jt(*_blossom_set, blossom);
- jt != INVALID; ++jt) {
- (*_status)[jt] = MATCHED;
- }
- _blossom_set->eraseClass(blossom);
- }
- }
- _tree_set->eraseClass(tree);
-
- }
-
- public:
-
- /// \brief Constructor
- ///
- /// Constructor.
- MaxMatching(const Graph& graph)
- : _graph(graph), _matching(0), _status(0), _ear(0),
- _blossom_set_index(0), _blossom_set(0), _blossom_rep(0),
- _tree_set_index(0), _tree_set(0) {}
-
- ~MaxMatching() {
- destroyStructures();
- }
-
- /// \name Execution control
- /// The simplest way to execute the algorithm is to use the
- /// \c run() member function.
- /// \n
-
- /// If you need better control on the execution, you must call
- /// \ref init(), \ref greedyInit() or \ref matchingInit()
- /// functions first, then you can start the algorithm with the \ref
- /// startSparse() or startDense() functions.
-
- ///@{
-
- /// \brief Sets the actual matching to the empty matching.
- ///
- /// Sets the actual matching to the empty matching.
- ///
- void init() {
- createStructures();
- for(NodeIt n(_graph); n != INVALID; ++n) {
- (*_matching)[n] = INVALID;
- (*_status)[n] = UNMATCHED;
- }
- }
-
- ///\brief Finds an initial matching in a greedy way
- ///
- ///It finds an initial matching in a greedy way.
- void greedyInit() {
- createStructures();
- for (NodeIt n(_graph); n != INVALID; ++n) {
- (*_matching)[n] = INVALID;
- (*_status)[n] = UNMATCHED;
- }
- for (NodeIt n(_graph); n != INVALID; ++n) {
- if ((*_matching)[n] == INVALID) {
- for (OutArcIt a(_graph, n); a != INVALID ; ++a) {
- Node v = _graph.target(a);
- if ((*_matching)[v] == INVALID && v != n) {
- (*_matching)[n] = a;
- (*_status)[n] = MATCHED;
- (*_matching)[v] = _graph.oppositeArc(a);
- (*_status)[v] = MATCHED;
- break;
- }
- }
- }
- }
- }
-
-
- /// \brief Initialize the matching from a map containing.
- ///
- /// Initialize the matching from a \c bool valued \c Edge map. This
- /// map must have the property that there are no two incident edges
- /// with true value, ie. it contains a matching.
- /// \return \c true if the map contains a matching.
- template <typename MatchingMap>
- bool matchingInit(const MatchingMap& matching) {
- createStructures();
-
- for (NodeIt n(_graph); n != INVALID; ++n) {
- (*_matching)[n] = INVALID;
- (*_status)[n] = UNMATCHED;
- }
- for(EdgeIt e(_graph); e!=INVALID; ++e) {
- if (matching[e]) {
-
- Node u = _graph.u(e);
- if ((*_matching)[u] != INVALID) return false;
- (*_matching)[u] = _graph.direct(e, true);
- (*_status)[u] = MATCHED;
-
- Node v = _graph.v(e);
- if ((*_matching)[v] != INVALID) return false;
- (*_matching)[v] = _graph.direct(e, false);
- (*_status)[v] = MATCHED;
- }
- }
- return true;
- }
-
- /// \brief Starts Edmonds' algorithm
- ///
- /// If runs the original Edmonds' algorithm.
- void startSparse() {
- for(NodeIt n(_graph); n != INVALID; ++n) {
- if ((*_status)[n] == UNMATCHED) {
- (*_blossom_rep)[_blossom_set->insert(n)] = n;
- _tree_set->insert(n);
- (*_status)[n] = EVEN;
- processSparse(n);
- }
- }
- }
-
- /// \brief Starts Edmonds' algorithm.
- ///
- /// It runs Edmonds' algorithm with a heuristic of postponing
- /// shrinks, therefore resulting in a faster algorithm for dense graphs.
- void startDense() {
- for(NodeIt n(_graph); n != INVALID; ++n) {
- if ((*_status)[n] == UNMATCHED) {
- (*_blossom_rep)[_blossom_set->insert(n)] = n;
- _tree_set->insert(n);
- (*_status)[n] = EVEN;
- processDense(n);
- }
- }
- }
-
-
- /// \brief Runs Edmonds' algorithm
- ///
- /// Runs Edmonds' algorithm for sparse graphs (<tt>m<2*n</tt>)
- /// or Edmonds' algorithm with a heuristic of
- /// postponing shrinks for dense graphs.
- void run() {
- if (countEdges(_graph) < 2 * countNodes(_graph)) {
- greedyInit();
- startSparse();
- } else {
- init();
- startDense();
- }
- }
-
- /// @}
-
- /// \name Primal solution
- /// Functions to get the primal solution, ie. the matching.
-
- /// @{
-
- ///\brief Returns the size of the current matching.
- ///
- ///Returns the size of the current matching. After \ref
- ///run() it returns the size of the maximum matching in the graph.
- int matchingSize() const {
- int size = 0;
- for (NodeIt n(_graph); n != INVALID; ++n) {
- if ((*_matching)[n] != INVALID) {
- ++size;
- }
- }
- return size / 2;
- }
-
- /// \brief Returns true when the edge is in the matching.
- ///
- /// Returns true when the edge is in the matching.
- bool matching(const Edge& edge) const {
- return edge == (*_matching)[_graph.u(edge)];
- }
-
- /// \brief Returns the matching edge incident to the given node.
- ///
- /// Returns the matching edge of a \c node in the actual matching or
- /// INVALID if the \c node is not covered by the actual matching.
- Arc matching(const Node& n) const {
- return (*_matching)[n];
- }
-
- ///\brief Returns the mate of a node in the actual matching.
- ///
- ///Returns the mate of a \c node in the actual matching or
- ///INVALID if the \c node is not covered by the actual matching.
- Node mate(const Node& n) const {
- return (*_matching)[n] != INVALID ?
- _graph.target((*_matching)[n]) : INVALID;
- }
-
- /// @}
-
- /// \name Dual solution
- /// Functions to get the dual solution, ie. the decomposition.
-
- /// @{
-
- /// \brief Returns the class of the node in the Edmonds-Gallai
- /// decomposition.
- ///
- /// Returns the class of the node in the Edmonds-Gallai
- /// decomposition.
- Status decomposition(const Node& n) const {
- return (*_status)[n];
- }
-
- /// \brief Returns true when the node is in the barrier.
- ///
- /// Returns true when the node is in the barrier.
- bool barrier(const Node& n) const {
- return (*_status)[n] == ODD;
- }
-
- /// @}
-
- };
-
- /// \ingroup matching
- ///
- /// \brief Weighted matching in general graphs
- ///
- /// This class provides an efficient implementation of Edmond's
- /// maximum weighted matching algorithm. The implementation is based
- /// on extensive use of priority queues and provides
- /// \f$O(nm\log n)\f$ time complexity.
- ///
- /// The maximum weighted matching problem is to find undirected
- /// edges in the graph with maximum overall weight and no two of
- /// them shares their ends. The problem can be formulated with the
- /// following linear program.
- /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]
- /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
- \quad \forall B\in\mathcal{O}\f] */
- /// \f[x_e \ge 0\quad \forall e\in E\f]
- /// \f[\max \sum_{e\in E}x_ew_e\f]
- /// where \f$\delta(X)\f$ is the set of edges incident to a node in
- /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
- /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
- /// subsets of the nodes.
- ///
- /// The algorithm calculates an optimal matching and a proof of the
- /// optimality. The solution of the dual problem can be used to check
- /// the result of the algorithm. The dual linear problem is the
- /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}
- z_B \ge w_{uv} \quad \forall uv\in E\f] */
- /// \f[y_u \ge 0 \quad \forall u \in V\f]
- /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
- /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
- \frac{\vert B \vert - 1}{2}z_B\f] */
- ///
- /// The algorithm can be executed with \c run() or the \c init() and
- /// then the \c start() member functions. After it the matching can
- /// be asked with \c matching() or mate() functions. The dual
- /// solution can be get with \c nodeValue(), \c blossomNum() and \c
- /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
- /// "BlossomIt" nested class, which is able to iterate on the nodes
- /// of a blossom. If the value type is integral then the dual
- /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
- template <typename GR,
- typename WM = typename GR::template EdgeMap<int> >
- class MaxWeightedMatching {
- public:
-
- ///\e
- typedef GR Graph;
- ///\e
- typedef WM WeightMap;
- ///\e
- typedef typename WeightMap::Value Value;
-
- /// \brief Scaling factor for dual solution
- ///
- /// Scaling factor for dual solution, it is equal to 4 or 1
- /// according to the value type.
- static const int dualScale =
- std::numeric_limits<Value>::is_integer ? 4 : 1;
-
- typedef typename Graph::template NodeMap<typename Graph::Arc>
- MatchingMap;
-
- private:
-
- TEMPLATE_GRAPH_TYPEDEFS(Graph);
-
- typedef typename Graph::template NodeMap<Value> NodePotential;
- typedef std::vector<Node> BlossomNodeList;
-
- struct BlossomVariable {
- int begin, end;
- Value value;
-
- BlossomVariable(int _begin, int _end, Value _value)
- : begin(_begin), end(_end), value(_value) {}
-
- };
-
- typedef std::vector<BlossomVariable> BlossomPotential;
-
- const Graph& _graph;
- const WeightMap& _weight;
-
- MatchingMap* _matching;
-
- NodePotential* _node_potential;
-
- BlossomPotential _blossom_potential;
- BlossomNodeList _blossom_node_list;
-
- int _node_num;
- int _blossom_num;
-
- typedef RangeMap<int> IntIntMap;
-
- enum Status {
- EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2
- };
-
- typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
- struct BlossomData {
- int tree;
- Status status;
- Arc pred, next;
- Value pot, offset;
- Node base;
- };
-
- IntNodeMap *_blossom_index;
- BlossomSet *_blossom_set;
- RangeMap<BlossomData>* _blossom_data;
-
- IntNodeMap *_node_index;
- IntArcMap *_node_heap_index;
-
- struct NodeData {
-
- NodeData(IntArcMap& node_heap_index)
- : heap(node_heap_index) {}
-
- int blossom;
- Value pot;
- BinHeap<Value, IntArcMap> heap;
- std::map<int, Arc> heap_index;
-
- int tree;
- };
-
- RangeMap<NodeData>* _node_data;
-
- typedef ExtendFindEnum<IntIntMap> TreeSet;
-
- IntIntMap *_tree_set_index;
- TreeSet *_tree_set;
-
- IntNodeMap *_delta1_index;
- BinHeap<Value, IntNodeMap> *_delta1;
-
- IntIntMap *_delta2_index;
- BinHeap<Value, IntIntMap> *_delta2;
-
- IntEdgeMap *_delta3_index;
- BinHeap<Value, IntEdgeMap> *_delta3;
-
- IntIntMap *_delta4_index;
- BinHeap<Value, IntIntMap> *_delta4;
-
- Value _delta_sum;
-
- void createStructures() {
- _node_num = countNodes(_graph);
- _blossom_num = _node_num * 3 / 2;
-
- if (!_matching) {
- _matching = new MatchingMap(_graph);
- }
- if (!_node_potential) {
- _node_potential = new NodePotential(_graph);
- }
- if (!_blossom_set) {
- _blossom_index = new IntNodeMap(_graph);
- _blossom_set = new BlossomSet(*_blossom_index);
- _blossom_data = new RangeMap<BlossomData>(_blossom_num);
- }
-
- if (!_node_index) {
- _node_index = new IntNodeMap(_graph);
- _node_heap_index = new IntArcMap(_graph);
- _node_data = new RangeMap<NodeData>(_node_num,
- NodeData(*_node_heap_index));
- }
-
- if (!_tree_set) {
- _tree_set_index = new IntIntMap(_blossom_num);
- _tree_set = new TreeSet(*_tree_set_index);
- }
- if (!_delta1) {
- _delta1_index = new IntNodeMap(_graph);
- _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index);
- }
- if (!_delta2) {
- _delta2_index = new IntIntMap(_blossom_num);
- _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
- }
- if (!_delta3) {
- _delta3_index = new IntEdgeMap(_graph);
- _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
- }
- if (!_delta4) {
- _delta4_index = new IntIntMap(_blossom_num);
- _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
- }
- }
-
- void destroyStructures() {
- _node_num = countNodes(_graph);
- _blossom_num = _node_num * 3 / 2;
-
- if (_matching) {
- delete _matching;
- }
- if (_node_potential) {
- delete _node_potential;
- }
- if (_blossom_set) {
- delete _blossom_index;
- delete _blossom_set;
- delete _blossom_data;
- }
-
- if (_node_index) {
- delete _node_index;
- delete _node_heap_index;
- delete _node_data;
- }
-
- if (_tree_set) {
- delete _tree_set_index;
- delete _tree_set;
- }
- if (_delta1) {
- delete _delta1_index;
- delete _delta1;
- }
- if (_delta2) {
- delete _delta2_index;
- delete _delta2;
- }
- if (_delta3) {
- delete _delta3_index;
- delete _delta3;
- }
- if (_delta4) {
- delete _delta4_index;
- delete _delta4;
- }
- }
-
- void matchedToEven(int blossom, int tree) {
- if (_delta2->state(blossom) == _delta2->IN_HEAP) {
- _delta2->erase(blossom);
- }
-
- if (!_blossom_set->trivial(blossom)) {
- (*_blossom_data)[blossom].pot -=
- 2 * (_delta_sum - (*_blossom_data)[blossom].offset);
- }
-
- for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
- n != INVALID; ++n) {
-
- _blossom_set->increase(n, std::numeric_limits<Value>::max());
- int ni = (*_node_index)[n];
-
- (*_node_data)[ni].heap.clear();
- (*_node_data)[ni].heap_index.clear();
-
- (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
-
- _delta1->push(n, (*_node_data)[ni].pot);
-
- for (InArcIt e(_graph, n); e != INVALID; ++e) {
- Node v = _graph.source(e);
- int vb = _blossom_set->find(v);
- int vi = (*_node_index)[v];
-
- Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
- dualScale * _weight[e];
-
- if ((*_blossom_data)[vb].status == EVEN) {
- if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
- _delta3->push(e, rw / 2);
- }
- } else if ((*_blossom_data)[vb].status == UNMATCHED) {
- if (_delta3->state(e) != _delta3->IN_HEAP) {
- _delta3->push(e, rw);
- }
- } else {
- typename std::map<int, Arc>::iterator it =
- (*_node_data)[vi].heap_index.find(tree);
-
- if (it != (*_node_data)[vi].heap_index.end()) {
- if ((*_node_data)[vi].heap[it->second] > rw) {
- (*_node_data)[vi].heap.replace(it->second, e);
- (*_node_data)[vi].heap.decrease(e, rw);
- it->second = e;
- }
- } else {
- (*_node_data)[vi].heap.push(e, rw);
- (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
- }
-
- if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
- _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
-
- if ((*_blossom_data)[vb].status == MATCHED) {
- if (_delta2->state(vb) != _delta2->IN_HEAP) {
- _delta2->push(vb, _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset);
- } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset){
- _delta2->decrease(vb, _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset);
- }
- }
- }
- }
- }
- }
- (*_blossom_data)[blossom].offset = 0;
- }
-
- void matchedToOdd(int blossom) {
- if (_delta2->state(blossom) == _delta2->IN_HEAP) {
- _delta2->erase(blossom);
- }
- (*_blossom_data)[blossom].offset += _delta_sum;
- if (!_blossom_set->trivial(blossom)) {
- _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
- (*_blossom_data)[blossom].offset);
- }
- }
-
- void evenToMatched(int blossom, int tree) {
- if (!_blossom_set->trivial(blossom)) {
- (*_blossom_data)[blossom].pot += 2 * _delta_sum;
- }
-
- for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
- n != INVALID; ++n) {
- int ni = (*_node_index)[n];
- (*_node_data)[ni].pot -= _delta_sum;
-
- _delta1->erase(n);
-
- for (InArcIt e(_graph, n); e != INVALID; ++e) {
- Node v = _graph.source(e);
- int vb = _blossom_set->find(v);
- int vi = (*_node_index)[v];
-
- Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
- dualScale * _weight[e];
-
- if (vb == blossom) {
- if (_delta3->state(e) == _delta3->IN_HEAP) {
- _delta3->erase(e);
- }
- } else if ((*_blossom_data)[vb].status == EVEN) {
-
- if (_delta3->state(e) == _delta3->IN_HEAP) {
- _delta3->erase(e);
- }
-
- int vt = _tree_set->find(vb);
-
- if (vt != tree) {
-
- Arc r = _graph.oppositeArc(e);
-
- typename std::map<int, Arc>::iterator it =
- (*_node_data)[ni].heap_index.find(vt);
-
- if (it != (*_node_data)[ni].heap_index.end()) {
- if ((*_node_data)[ni].heap[it->second] > rw) {
- (*_node_data)[ni].heap.replace(it->second, r);
- (*_node_data)[ni].heap.decrease(r, rw);
- it->second = r;
- }
- } else {
- (*_node_data)[ni].heap.push(r, rw);
- (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
- }
-
- if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
- _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
-
- if (_delta2->state(blossom) != _delta2->IN_HEAP) {
- _delta2->push(blossom, _blossom_set->classPrio(blossom) -
- (*_blossom_data)[blossom].offset);
- } else if ((*_delta2)[blossom] >
- _blossom_set->classPrio(blossom) -
- (*_blossom_data)[blossom].offset){
- _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
- (*_blossom_data)[blossom].offset);
- }
- }
- }
-
- } else if ((*_blossom_data)[vb].status == UNMATCHED) {
- if (_delta3->state(e) == _delta3->IN_HEAP) {
- _delta3->erase(e);
- }
- } else {
-
- typename std::map<int, Arc>::iterator it =
- (*_node_data)[vi].heap_index.find(tree);
-
- if (it != (*_node_data)[vi].heap_index.end()) {
- (*_node_data)[vi].heap.erase(it->second);
- (*_node_data)[vi].heap_index.erase(it);
- if ((*_node_data)[vi].heap.empty()) {
- _blossom_set->increase(v, std::numeric_limits<Value>::max());
- } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
- _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
- }
-
- if ((*_blossom_data)[vb].status == MATCHED) {
- if (_blossom_set->classPrio(vb) ==
- std::numeric_limits<Value>::max()) {
- _delta2->erase(vb);
- } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset) {
- _delta2->increase(vb, _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset);
- }
- }
- }
- }
- }
- }
- }
-
- void oddToMatched(int blossom) {
- (*_blossom_data)[blossom].offset -= _delta_sum;
-
- if (_blossom_set->classPrio(blossom) !=
- std::numeric_limits<Value>::max()) {
- _delta2->push(blossom, _blossom_set->classPrio(blossom) -
- (*_blossom_data)[blossom].offset);
- }
-
- if (!_blossom_set->trivial(blossom)) {
- _delta4->erase(blossom);
- }
- }
-
- void oddToEven(int blossom, int tree) {
- if (!_blossom_set->trivial(blossom)) {
- _delta4->erase(blossom);
- (*_blossom_data)[blossom].pot -=
- 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
- }
-
- for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
- n != INVALID; ++n) {
- int ni = (*_node_index)[n];
-
- _blossom_set->increase(n, std::numeric_limits<Value>::max());
-
- (*_node_data)[ni].heap.clear();
- (*_node_data)[ni].heap_index.clear();
- (*_node_data)[ni].pot +=
- 2 * _delta_sum - (*_blossom_data)[blossom].offset;
-
- _delta1->push(n, (*_node_data)[ni].pot);
-
- for (InArcIt e(_graph, n); e != INVALID; ++e) {
- Node v = _graph.source(e);
- int vb = _blossom_set->find(v);
- int vi = (*_node_index)[v];
-
- Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
- dualScale * _weight[e];
-
- if ((*_blossom_data)[vb].status == EVEN) {
- if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
- _delta3->push(e, rw / 2);
- }
- } else if ((*_blossom_data)[vb].status == UNMATCHED) {
- if (_delta3->state(e) != _delta3->IN_HEAP) {
- _delta3->push(e, rw);
- }
- } else {
-
- typename std::map<int, Arc>::iterator it =
- (*_node_data)[vi].heap_index.find(tree);
-
- if (it != (*_node_data)[vi].heap_index.end()) {
- if ((*_node_data)[vi].heap[it->second] > rw) {
- (*_node_data)[vi].heap.replace(it->second, e);
- (*_node_data)[vi].heap.decrease(e, rw);
- it->second = e;
- }
- } else {
- (*_node_data)[vi].heap.push(e, rw);
- (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
- }
-
- if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
- _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
-
- if ((*_blossom_data)[vb].status == MATCHED) {
- if (_delta2->state(vb) != _delta2->IN_HEAP) {
- _delta2->push(vb, _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset);
- } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset) {
- _delta2->decrease(vb, _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset);
- }
- }
- }
- }
- }
- }
- (*_blossom_data)[blossom].offset = 0;
- }
-
-
- void matchedToUnmatched(int blossom) {
- if (_delta2->state(blossom) == _delta2->IN_HEAP) {
- _delta2->erase(blossom);
- }
-
- for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
- n != INVALID; ++n) {
- int ni = (*_node_index)[n];
-
- _blossom_set->increase(n, std::numeric_limits<Value>::max());
-
- (*_node_data)[ni].heap.clear();
- (*_node_data)[ni].heap_index.clear();
-
- for (OutArcIt e(_graph, n); e != INVALID; ++e) {
- Node v = _graph.target(e);
- int vb = _blossom_set->find(v);
- int vi = (*_node_index)[v];
-
- Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
- dualScale * _weight[e];
-
- if ((*_blossom_data)[vb].status == EVEN) {
- if (_delta3->state(e) != _delta3->IN_HEAP) {
- _delta3->push(e, rw);
- }
- }
- }
- }
- }
-
- void unmatchedToMatched(int blossom) {
- for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
- n != INVALID; ++n) {
- int ni = (*_node_index)[n];
-
- for (InArcIt e(_graph, n); e != INVALID; ++e) {
- Node v = _graph.source(e);
- int vb = _blossom_set->find(v);
- int vi = (*_node_index)[v];
-
- Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
- dualScale * _weight[e];
-
- if (vb == blossom) {
- if (_delta3->state(e) == _delta3->IN_HEAP) {
- _delta3->erase(e);
- }
- } else if ((*_blossom_data)[vb].status == EVEN) {
-
- if (_delta3->state(e) == _delta3->IN_HEAP) {
- _delta3->erase(e);
- }
-
- int vt = _tree_set->find(vb);
-
- Arc r = _graph.oppositeArc(e);
-
- typename std::map<int, Arc>::iterator it =
- (*_node_data)[ni].heap_index.find(vt);
-
- if (it != (*_node_data)[ni].heap_index.end()) {
- if ((*_node_data)[ni].heap[it->second] > rw) {
- (*_node_data)[ni].heap.replace(it->second, r);
- (*_node_data)[ni].heap.decrease(r, rw);
- it->second = r;
- }
- } else {
- (*_node_data)[ni].heap.push(r, rw);
- (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
- }
-
- if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
- _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
-
- if (_delta2->state(blossom) != _delta2->IN_HEAP) {
- _delta2->push(blossom, _blossom_set->classPrio(blossom) -
- (*_blossom_data)[blossom].offset);
- } else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)-
- (*_blossom_data)[blossom].offset){
- _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
- (*_blossom_data)[blossom].offset);
- }
- }
-
- } else if ((*_blossom_data)[vb].status == UNMATCHED) {
- if (_delta3->state(e) == _delta3->IN_HEAP) {
- _delta3->erase(e);
- }
- }
- }
- }
- }
-
- void alternatePath(int even, int tree) {
- int odd;
-
- evenToMatched(even, tree);
- (*_blossom_data)[even].status = MATCHED;
-
- while ((*_blossom_data)[even].pred != INVALID) {
- odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
- (*_blossom_data)[odd].status = MATCHED;
- oddToMatched(odd);
- (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
-
- even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
- (*_blossom_data)[even].status = MATCHED;
- evenToMatched(even, tree);
- (*_blossom_data)[even].next =
- _graph.oppositeArc((*_blossom_data)[odd].pred);
- }
-
- }
-
- void destroyTree(int tree) {
- for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
- if ((*_blossom_data)[b].status == EVEN) {
- (*_blossom_data)[b].status = MATCHED;
- evenToMatched(b, tree);
- } else if ((*_blossom_data)[b].status == ODD) {
- (*_blossom_data)[b].status = MATCHED;
- oddToMatched(b);
- }
- }
- _tree_set->eraseClass(tree);
- }
-
-
- void unmatchNode(const Node& node) {
- int blossom = _blossom_set->find(node);
- int tree = _tree_set->find(blossom);
-
- alternatePath(blossom, tree);
- destroyTree(tree);
-
- (*_blossom_data)[blossom].status = UNMATCHED;
- (*_blossom_data)[blossom].base = node;
- matchedToUnmatched(blossom);
- }
-
-
- void augmentOnEdge(const Edge& edge) {
-
- int left = _blossom_set->find(_graph.u(edge));
- int right = _blossom_set->find(_graph.v(edge));
-
- if ((*_blossom_data)[left].status == EVEN) {
- int left_tree = _tree_set->find(left);
- alternatePath(left, left_tree);
- destroyTree(left_tree);
- } else {
- (*_blossom_data)[left].status = MATCHED;
- unmatchedToMatched(left);
- }
-
- if ((*_blossom_data)[right].status == EVEN) {
- int right_tree = _tree_set->find(right);
- alternatePath(right, right_tree);
- destroyTree(right_tree);
- } else {
- (*_blossom_data)[right].status = MATCHED;
- unmatchedToMatched(right);
- }
-
- (*_blossom_data)[left].next = _graph.direct(edge, true);
- (*_blossom_data)[right].next = _graph.direct(edge, false);
- }
-
- void extendOnArc(const Arc& arc) {
- int base = _blossom_set->find(_graph.target(arc));
- int tree = _tree_set->find(base);
-
- int odd = _blossom_set->find(_graph.source(arc));
- _tree_set->insert(odd, tree);
- (*_blossom_data)[odd].status = ODD;
- matchedToOdd(odd);
- (*_blossom_data)[odd].pred = arc;
-
- int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
- (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
- _tree_set->insert(even, tree);
- (*_blossom_data)[even].status = EVEN;
- matchedToEven(even, tree);
- }
-
- void shrinkOnEdge(const Edge& edge, int tree) {
- int nca = -1;
- std::vector<int> left_path, right_path;
-
- {
- std::set<int> left_set, right_set;
- int left = _blossom_set->find(_graph.u(edge));
- left_path.push_back(left);
- left_set.insert(left);
-
- int right = _blossom_set->find(_graph.v(edge));
- right_path.push_back(right);
- right_set.insert(right);
-
- while (true) {
-
- if ((*_blossom_data)[left].pred == INVALID) break;
-
- left =
- _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
- left_path.push_back(left);
- left =
- _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
- left_path.push_back(left);
-
- left_set.insert(left);
-
- if (right_set.find(left) != right_set.end()) {
- nca = left;
- break;
- }
-
- if ((*_blossom_data)[right].pred == INVALID) break;
-
- right =
- _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
- right_path.push_back(right);
- right =
- _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
- right_path.push_back(right);
-
- right_set.insert(right);
-
- if (left_set.find(right) != left_set.end()) {
- nca = right;
- break;
- }
-
- }
-
- if (nca == -1) {
- if ((*_blossom_data)[left].pred == INVALID) {
- nca = right;
- while (left_set.find(nca) == left_set.end()) {
- nca =
- _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
- right_path.push_back(nca);
- nca =
- _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
- right_path.push_back(nca);
- }
- } else {
- nca = left;
- while (right_set.find(nca) == right_set.end()) {
- nca =
- _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
- left_path.push_back(nca);
- nca =
- _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
- left_path.push_back(nca);
- }
- }
- }
- }
-
- std::vector<int> subblossoms;
- Arc prev;
-
- prev = _graph.direct(edge, true);
- for (int i = 0; left_path[i] != nca; i += 2) {
- subblossoms.push_back(left_path[i]);
- (*_blossom_data)[left_path[i]].next = prev;
- _tree_set->erase(left_path[i]);
-
- subblossoms.push_back(left_path[i + 1]);
- (*_blossom_data)[left_path[i + 1]].status = EVEN;
- oddToEven(left_path[i + 1], tree);
- _tree_set->erase(left_path[i + 1]);
- prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
- }
-
- int k = 0;
- while (right_path[k] != nca) ++k;
-
- subblossoms.push_back(nca);
- (*_blossom_data)[nca].next = prev;
-
- for (int i = k - 2; i >= 0; i -= 2) {
- subblossoms.push_back(right_path[i + 1]);
- (*_blossom_data)[right_path[i + 1]].status = EVEN;
- oddToEven(right_path[i + 1], tree);
- _tree_set->erase(right_path[i + 1]);
-
- (*_blossom_data)[right_path[i + 1]].next =
- (*_blossom_data)[right_path[i + 1]].pred;
-
- subblossoms.push_back(right_path[i]);
- _tree_set->erase(right_path[i]);
- }
-
- int surface =
- _blossom_set->join(subblossoms.begin(), subblossoms.end());
-
- for (int i = 0; i < int(subblossoms.size()); ++i) {
- if (!_blossom_set->trivial(subblossoms[i])) {
- (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
- }
- (*_blossom_data)[subblossoms[i]].status = MATCHED;
- }
-
- (*_blossom_data)[surface].pot = -2 * _delta_sum;
- (*_blossom_data)[surface].offset = 0;
- (*_blossom_data)[surface].status = EVEN;
- (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
- (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
-
- _tree_set->insert(surface, tree);
- _tree_set->erase(nca);
- }
-
- void splitBlossom(int blossom) {
- Arc next = (*_blossom_data)[blossom].next;
- Arc pred = (*_blossom_data)[blossom].pred;
-
- int tree = _tree_set->find(blossom);
-
- (*_blossom_data)[blossom].status = MATCHED;
- oddToMatched(blossom);
- if (_delta2->state(blossom) == _delta2->IN_HEAP) {
- _delta2->erase(blossom);
- }
-
- std::vector<int> subblossoms;
- _blossom_set->split(blossom, std::back_inserter(subblossoms));
-
- Value offset = (*_blossom_data)[blossom].offset;
- int b = _blossom_set->find(_graph.source(pred));
- int d = _blossom_set->find(_graph.source(next));
-
- int ib = -1, id = -1;
- for (int i = 0; i < int(subblossoms.size()); ++i) {
- if (subblossoms[i] == b) ib = i;
- if (subblossoms[i] == d) id = i;
-
- (*_blossom_data)[subblossoms[i]].offset = offset;
- if (!_blossom_set->trivial(subblossoms[i])) {
- (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
- }
- if (_blossom_set->classPrio(subblossoms[i]) !=
- std::numeric_limits<Value>::max()) {
- _delta2->push(subblossoms[i],
- _blossom_set->classPrio(subblossoms[i]) -
- (*_blossom_data)[subblossoms[i]].offset);
- }
- }
-
- if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
- for (int i = (id + 1) % subblossoms.size();
- i != ib; i = (i + 2) % subblossoms.size()) {
- int sb = subblossoms[i];
- int tb = subblossoms[(i + 1) % subblossoms.size()];
- (*_blossom_data)[sb].next =
- _graph.oppositeArc((*_blossom_data)[tb].next);
- }
-
- for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
- int sb = subblossoms[i];
- int tb = subblossoms[(i + 1) % subblossoms.size()];
- int ub = subblossoms[(i + 2) % subblossoms.size()];
-
- (*_blossom_data)[sb].status = ODD;
- matchedToOdd(sb);
- _tree_set->insert(sb, tree);
- (*_blossom_data)[sb].pred = pred;
- (*_blossom_data)[sb].next =
- _graph.oppositeArc((*_blossom_data)[tb].next);
-
- pred = (*_blossom_data)[ub].next;
-
- (*_blossom_data)[tb].status = EVEN;
- matchedToEven(tb, tree);
- _tree_set->insert(tb, tree);
- (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
- }
-
- (*_blossom_data)[subblossoms[id]].status = ODD;
- matchedToOdd(subblossoms[id]);
- _tree_set->insert(subblossoms[id], tree);
- (*_blossom_data)[subblossoms[id]].next = next;
- (*_blossom_data)[subblossoms[id]].pred = pred;
-
- } else {
-
- for (int i = (ib + 1) % subblossoms.size();
- i != id; i = (i + 2) % subblossoms.size()) {
- int sb = subblossoms[i];
- int tb = subblossoms[(i + 1) % subblossoms.size()];
- (*_blossom_data)[sb].next =
- _graph.oppositeArc((*_blossom_data)[tb].next);
- }
-
- for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
- int sb = subblossoms[i];
- int tb = subblossoms[(i + 1) % subblossoms.size()];
- int ub = subblossoms[(i + 2) % subblossoms.size()];
-
- (*_blossom_data)[sb].status = ODD;
- matchedToOdd(sb);
- _tree_set->insert(sb, tree);
- (*_blossom_data)[sb].next = next;
- (*_blossom_data)[sb].pred =
- _graph.oppositeArc((*_blossom_data)[tb].next);
-
- (*_blossom_data)[tb].status = EVEN;
- matchedToEven(tb, tree);
- _tree_set->insert(tb, tree);
- (*_blossom_data)[tb].pred =
- (*_blossom_data)[tb].next =
- _graph.oppositeArc((*_blossom_data)[ub].next);
- next = (*_blossom_data)[ub].next;
- }
-
- (*_blossom_data)[subblossoms[ib]].status = ODD;
- matchedToOdd(subblossoms[ib]);
- _tree_set->insert(subblossoms[ib], tree);
- (*_blossom_data)[subblossoms[ib]].next = next;
- (*_blossom_data)[subblossoms[ib]].pred = pred;
- }
- _tree_set->erase(blossom);
- }
-
- void extractBlossom(int blossom, const Node& base, const Arc& matching) {
- if (_blossom_set->trivial(blossom)) {
- int bi = (*_node_index)[base];
- Value pot = (*_node_data)[bi].pot;
-
- (*_matching)[base] = matching;
- _blossom_node_list.push_back(base);
- (*_node_potential)[base] = pot;
- } else {
-
- Value pot = (*_blossom_data)[blossom].pot;
- int bn = _blossom_node_list.size();
-
- std::vector<int> subblossoms;
- _blossom_set->split(blossom, std::back_inserter(subblossoms));
- int b = _blossom_set->find(base);
- int ib = -1;
- for (int i = 0; i < int(subblossoms.size()); ++i) {
- if (subblossoms[i] == b) { ib = i; break; }
- }
-
- for (int i = 1; i < int(subblossoms.size()); i += 2) {
- int sb = subblossoms[(ib + i) % subblossoms.size()];
- int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
-
- Arc m = (*_blossom_data)[tb].next;
- extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
- extractBlossom(tb, _graph.source(m), m);
- }
- extractBlossom(subblossoms[ib], base, matching);
-
- int en = _blossom_node_list.size();
-
- _blossom_potential.push_back(BlossomVariable(bn, en, pot));
- }
- }
-
- void extractMatching() {
- std::vector<int> blossoms;
- for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
- blossoms.push_back(c);
- }
-
- for (int i = 0; i < int(blossoms.size()); ++i) {
- if ((*_blossom_data)[blossoms[i]].status == MATCHED) {
-
- Value offset = (*_blossom_data)[blossoms[i]].offset;
- (*_blossom_data)[blossoms[i]].pot += 2 * offset;
- for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
- n != INVALID; ++n) {
- (*_node_data)[(*_node_index)[n]].pot -= offset;
- }
-
- Arc matching = (*_blossom_data)[blossoms[i]].next;
- Node base = _graph.source(matching);
- extractBlossom(blossoms[i], base, matching);
- } else {
- Node base = (*_blossom_data)[blossoms[i]].base;
- extractBlossom(blossoms[i], base, INVALID);
- }
- }
- }
-
- public:
-
- /// \brief Constructor
- ///
- /// Constructor.
- MaxWeightedMatching(const Graph& graph, const WeightMap& weight)
- : _graph(graph), _weight(weight), _matching(0),
- _node_potential(0), _blossom_potential(), _blossom_node_list(),
- _node_num(0), _blossom_num(0),
-
- _blossom_index(0), _blossom_set(0), _blossom_data(0),
- _node_index(0), _node_heap_index(0), _node_data(0),
- _tree_set_index(0), _tree_set(0),
-
- _delta1_index(0), _delta1(0),
- _delta2_index(0), _delta2(0),
- _delta3_index(0), _delta3(0),
- _delta4_index(0), _delta4(0),
-
- _delta_sum() {}
-
- ~MaxWeightedMatching() {
- destroyStructures();
- }
-
- /// \name Execution control
- /// The simplest way to execute the algorithm is to use the
- /// \c run() member function.
-
- ///@{
-
- /// \brief Initialize the algorithm
- ///
- /// Initialize the algorithm
- void init() {
- createStructures();
-
- for (ArcIt e(_graph); e != INVALID; ++e) {
- (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
- }
- for (NodeIt n(_graph); n != INVALID; ++n) {
- (*_delta1_index)[n] = _delta1->PRE_HEAP;
- }
- for (EdgeIt e(_graph); e != INVALID; ++e) {
- (*_delta3_index)[e] = _delta3->PRE_HEAP;
- }
- for (int i = 0; i < _blossom_num; ++i) {
- (*_delta2_index)[i] = _delta2->PRE_HEAP;
- (*_delta4_index)[i] = _delta4->PRE_HEAP;
- }
-
- int index = 0;
- for (NodeIt n(_graph); n != INVALID; ++n) {
- Value max = 0;
- for (OutArcIt e(_graph, n); e != INVALID; ++e) {
- if (_graph.target(e) == n) continue;
- if ((dualScale * _weight[e]) / 2 > max) {
- max = (dualScale * _weight[e]) / 2;
- }
- }
- (*_node_index)[n] = index;
- (*_node_data)[index].pot = max;
- _delta1->push(n, max);
- int blossom =
- _blossom_set->insert(n, std::numeric_limits<Value>::max());
-
- _tree_set->insert(blossom);
-
- (*_blossom_data)[blossom].status = EVEN;
- (*_blossom_data)[blossom].pred = INVALID;
- (*_blossom_data)[blossom].next = INVALID;
- (*_blossom_data)[blossom].pot = 0;
- (*_blossom_data)[blossom].offset = 0;
- ++index;
- }
- for (EdgeIt e(_graph); e != INVALID; ++e) {
- int si = (*_node_index)[_graph.u(e)];
- int ti = (*_node_index)[_graph.v(e)];
- if (_graph.u(e) != _graph.v(e)) {
- _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
- dualScale * _weight[e]) / 2);
- }
- }
- }
-
- /// \brief Starts the algorithm
- ///
- /// Starts the algorithm
- void start() {
- enum OpType {
- D1, D2, D3, D4
- };
-
- int unmatched = _node_num;
- while (unmatched > 0) {
- Value d1 = !_delta1->empty() ?
- _delta1->prio() : std::numeric_limits<Value>::max();
-
- Value d2 = !_delta2->empty() ?
- _delta2->prio() : std::numeric_limits<Value>::max();
-
- Value d3 = !_delta3->empty() ?
- _delta3->prio() : std::numeric_limits<Value>::max();
-
- Value d4 = !_delta4->empty() ?
- _delta4->prio() : std::numeric_limits<Value>::max();
-
- _delta_sum = d1; OpType ot = D1;
- if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
- if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
- if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
-
-
- switch (ot) {
- case D1:
- {
- Node n = _delta1->top();
- unmatchNode(n);
- --unmatched;
- }
- break;
- case D2:
- {
- int blossom = _delta2->top();
- Node n = _blossom_set->classTop(blossom);
- Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
- extendOnArc(e);
- }
- break;
- case D3:
- {
- Edge e = _delta3->top();
-
- int left_blossom = _blossom_set->find(_graph.u(e));
- int right_blossom = _blossom_set->find(_graph.v(e));
-
- if (left_blossom == right_blossom) {
- _delta3->pop();
- } else {
- int left_tree;
- if ((*_blossom_data)[left_blossom].status == EVEN) {
- left_tree = _tree_set->find(left_blossom);
- } else {
- left_tree = -1;
- ++unmatched;
- }
- int right_tree;
- if ((*_blossom_data)[right_blossom].status == EVEN) {
- right_tree = _tree_set->find(right_blossom);
- } else {
- right_tree = -1;
- ++unmatched;
- }
-
- if (left_tree == right_tree) {
- shrinkOnEdge(e, left_tree);
- } else {
- augmentOnEdge(e);
- unmatched -= 2;
- }
- }
- } break;
- case D4:
- splitBlossom(_delta4->top());
- break;
- }
- }
- extractMatching();
- }
-
- /// \brief Runs %MaxWeightedMatching algorithm.
- ///
- /// This method runs the %MaxWeightedMatching algorithm.
- ///
- /// \note mwm.run() is just a shortcut of the following code.
- /// \code
- /// mwm.init();
- /// mwm.start();
- /// \endcode
- void run() {
- init();
- start();
- }
-
- /// @}
-
- /// \name Primal solution
- /// Functions to get the primal solution, ie. the matching.
-
- /// @{
-
- /// \brief Returns the weight of the matching.
- ///
- /// Returns the weight of the matching.
- Value matchingValue() const {
- Value sum = 0;
- for (NodeIt n(_graph); n != INVALID; ++n) {
- if ((*_matching)[n] != INVALID) {
- sum += _weight[(*_matching)[n]];
- }
- }
- return sum /= 2;
- }
-
- /// \brief Returns the cardinality of the matching.
- ///
- /// Returns the cardinality of the matching.
- int matchingSize() const {
- int num = 0;
- for (NodeIt n(_graph); n != INVALID; ++n) {
- if ((*_matching)[n] != INVALID) {
- ++num;
- }
- }
- return num /= 2;
- }
-
- /// \brief Returns true when the edge is in the matching.
- ///
- /// Returns true when the edge is in the matching.
- bool matching(const Edge& edge) const {
- return edge == (*_matching)[_graph.u(edge)];
- }
-
- /// \brief Returns the incident matching arc.
- ///
- /// Returns the incident matching arc from given node. If the
- /// node is not matched then it gives back \c INVALID.
- Arc matching(const Node& node) const {
- return (*_matching)[node];
- }
-
- /// \brief Returns the mate of the node.
- ///
- /// Returns the adjancent node in a mathcing arc. If the node is
- /// not matched then it gives back \c INVALID.
- Node mate(const Node& node) const {
- return (*_matching)[node] != INVALID ?
- _graph.target((*_matching)[node]) : INVALID;
- }
-
- /// @}
-
- /// \name Dual solution
- /// Functions to get the dual solution.
-
- /// @{
-
- /// \brief Returns the value of the dual solution.
- ///
- /// Returns the value of the dual solution. It should be equal to
- /// the primal value scaled by \ref dualScale "dual scale".
- Value dualValue() const {
- Value sum = 0;
- for (NodeIt n(_graph); n != INVALID; ++n) {
- sum += nodeValue(n);
- }
- for (int i = 0; i < blossomNum(); ++i) {
- sum += blossomValue(i) * (blossomSize(i) / 2);
- }
- return sum;
- }
-
- /// \brief Returns the value of the node.
- ///
- /// Returns the the value of the node.
- Value nodeValue(const Node& n) const {
- return (*_node_potential)[n];
- }
-
- /// \brief Returns the number of the blossoms in the basis.
- ///
- /// Returns the number of the blossoms in the basis.
- /// \see BlossomIt
- int blossomNum() const {
- return _blossom_potential.size();
- }
-
-
- /// \brief Returns the number of the nodes in the blossom.
- ///
- /// Returns the number of the nodes in the blossom.
- int blossomSize(int k) const {
- return _blossom_potential[k].end - _blossom_potential[k].begin;
- }
-
- /// \brief Returns the value of the blossom.
- ///
- /// Returns the the value of the blossom.
- /// \see BlossomIt
- Value blossomValue(int k) const {
- return _blossom_potential[k].value;
- }
-
- /// \brief Iterator for obtaining the nodes of the blossom.
- ///
- /// Iterator for obtaining the nodes of the blossom. This class
- /// provides a common lemon style iterator for listing a
- /// subset of the nodes.
- class BlossomIt {
- public:
-
- /// \brief Constructor.
- ///
- /// Constructor to get the nodes of the variable.
- BlossomIt(const MaxWeightedMatching& algorithm, int variable)
- : _algorithm(&algorithm)
- {
- _index = _algorithm->_blossom_potential[variable].begin;
- _last = _algorithm->_blossom_potential[variable].end;
- }
-
- /// \brief Conversion to node.
- ///
- /// Conversion to node.
- operator Node() const {
- return _algorithm->_blossom_node_list[_index];
- }
-
- /// \brief Increment operator.
- ///
- /// Increment operator.
- BlossomIt& operator++() {
- ++_index;
- return *this;
- }
-
- /// \brief Validity checking
- ///
- /// Checks whether the iterator is invalid.
- bool operator==(Invalid) const { return _index == _last; }
-
- /// \brief Validity checking
- ///
- /// Checks whether the iterator is valid.
- bool operator!=(Invalid) const { return _index != _last; }
-
- private:
- const MaxWeightedMatching* _algorithm;
- int _last;
- int _index;
- };
-
- /// @}
-
- };
-
- /// \ingroup matching
- ///
- /// \brief Weighted perfect matching in general graphs
- ///
- /// This class provides an efficient implementation of Edmond's
- /// maximum weighted perfect matching algorithm. The implementation
- /// is based on extensive use of priority queues and provides
- /// \f$O(nm\log n)\f$ time complexity.
- ///
- /// The maximum weighted matching problem is to find undirected
- /// edges in the graph with maximum overall weight and no two of
- /// them shares their ends and covers all nodes. The problem can be
- /// formulated with the following linear program.
- /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f]
- /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
- \quad \forall B\in\mathcal{O}\f] */
- /// \f[x_e \ge 0\quad \forall e\in E\f]
- /// \f[\max \sum_{e\in E}x_ew_e\f]
- /// where \f$\delta(X)\f$ is the set of edges incident to a node in
- /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
- /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
- /// subsets of the nodes.
- ///
- /// The algorithm calculates an optimal matching and a proof of the
- /// optimality. The solution of the dual problem can be used to check
- /// the result of the algorithm. The dual linear problem is the
- /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge
- w_{uv} \quad \forall uv\in E\f] */
- /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
- /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
- \frac{\vert B \vert - 1}{2}z_B\f] */
- ///
- /// The algorithm can be executed with \c run() or the \c init() and
- /// then the \c start() member functions. After it the matching can
- /// be asked with \c matching() or mate() functions. The dual
- /// solution can be get with \c nodeValue(), \c blossomNum() and \c
- /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
- /// "BlossomIt" nested class which is able to iterate on the nodes
- /// of a blossom. If the value type is integral then the dual
- /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
- template <typename GR,
- typename WM = typename GR::template EdgeMap<int> >
- class MaxWeightedPerfectMatching {
- public:
-
- typedef GR Graph;
- typedef WM WeightMap;
- typedef typename WeightMap::Value Value;
-
- /// \brief Scaling factor for dual solution
- ///
- /// Scaling factor for dual solution, it is equal to 4 or 1
- /// according to the value type.
- static const int dualScale =
- std::numeric_limits<Value>::is_integer ? 4 : 1;
-
- typedef typename Graph::template NodeMap<typename Graph::Arc>
- MatchingMap;
-
- private:
-
- TEMPLATE_GRAPH_TYPEDEFS(Graph);
-
- typedef typename Graph::template NodeMap<Value> NodePotential;
- typedef std::vector<Node> BlossomNodeList;
-
- struct BlossomVariable {
- int begin, end;
- Value value;
-
- BlossomVariable(int _begin, int _end, Value _value)
- : begin(_begin), end(_end), value(_value) {}
-
- };
-
- typedef std::vector<BlossomVariable> BlossomPotential;
-
- const Graph& _graph;
- const WeightMap& _weight;
-
- MatchingMap* _matching;
-
- NodePotential* _node_potential;
-
- BlossomPotential _blossom_potential;
- BlossomNodeList _blossom_node_list;
-
- int _node_num;
- int _blossom_num;
-
- typedef RangeMap<int> IntIntMap;
-
- enum Status {
- EVEN = -1, MATCHED = 0, ODD = 1
- };
-
- typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
- struct BlossomData {
- int tree;
- Status status;
- Arc pred, next;
- Value pot, offset;
- };
-
- IntNodeMap *_blossom_index;
- BlossomSet *_blossom_set;
- RangeMap<BlossomData>* _blossom_data;
-
- IntNodeMap *_node_index;
- IntArcMap *_node_heap_index;
-
- struct NodeData {
-
- NodeData(IntArcMap& node_heap_index)
- : heap(node_heap_index) {}
-
- int blossom;
- Value pot;
- BinHeap<Value, IntArcMap> heap;
- std::map<int, Arc> heap_index;
-
- int tree;
- };
-
- RangeMap<NodeData>* _node_data;
-
- typedef ExtendFindEnum<IntIntMap> TreeSet;
-
- IntIntMap *_tree_set_index;
- TreeSet *_tree_set;
-
- IntIntMap *_delta2_index;
- BinHeap<Value, IntIntMap> *_delta2;
-
- IntEdgeMap *_delta3_index;
- BinHeap<Value, IntEdgeMap> *_delta3;
-
- IntIntMap *_delta4_index;
- BinHeap<Value, IntIntMap> *_delta4;
-
- Value _delta_sum;
-
- void createStructures() {
- _node_num = countNodes(_graph);
- _blossom_num = _node_num * 3 / 2;
-
- if (!_matching) {
- _matching = new MatchingMap(_graph);
- }
- if (!_node_potential) {
- _node_potential = new NodePotential(_graph);
- }
- if (!_blossom_set) {
- _blossom_index = new IntNodeMap(_graph);
- _blossom_set = new BlossomSet(*_blossom_index);
- _blossom_data = new RangeMap<BlossomData>(_blossom_num);
- }
-
- if (!_node_index) {
- _node_index = new IntNodeMap(_graph);
- _node_heap_index = new IntArcMap(_graph);
- _node_data = new RangeMap<NodeData>(_node_num,
- NodeData(*_node_heap_index));
- }
-
- if (!_tree_set) {
- _tree_set_index = new IntIntMap(_blossom_num);
- _tree_set = new TreeSet(*_tree_set_index);
- }
- if (!_delta2) {
- _delta2_index = new IntIntMap(_blossom_num);
- _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
- }
- if (!_delta3) {
- _delta3_index = new IntEdgeMap(_graph);
- _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
- }
- if (!_delta4) {
- _delta4_index = new IntIntMap(_blossom_num);
- _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
- }
- }
-
- void destroyStructures() {
- _node_num = countNodes(_graph);
- _blossom_num = _node_num * 3 / 2;
-
- if (_matching) {
- delete _matching;
- }
- if (_node_potential) {
- delete _node_potential;
- }
- if (_blossom_set) {
- delete _blossom_index;
- delete _blossom_set;
- delete _blossom_data;
- }
-
- if (_node_index) {
- delete _node_index;
- delete _node_heap_index;
- delete _node_data;
- }
-
- if (_tree_set) {
- delete _tree_set_index;
- delete _tree_set;
- }
- if (_delta2) {
- delete _delta2_index;
- delete _delta2;
- }
- if (_delta3) {
- delete _delta3_index;
- delete _delta3;
- }
- if (_delta4) {
- delete _delta4_index;
- delete _delta4;
- }
- }
-
- void matchedToEven(int blossom, int tree) {
- if (_delta2->state(blossom) == _delta2->IN_HEAP) {
- _delta2->erase(blossom);
- }
-
- if (!_blossom_set->trivial(blossom)) {
- (*_blossom_data)[blossom].pot -=
- 2 * (_delta_sum - (*_blossom_data)[blossom].offset);
- }
-
- for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
- n != INVALID; ++n) {
-
- _blossom_set->increase(n, std::numeric_limits<Value>::max());
- int ni = (*_node_index)[n];
-
- (*_node_data)[ni].heap.clear();
- (*_node_data)[ni].heap_index.clear();
-
- (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
-
- for (InArcIt e(_graph, n); e != INVALID; ++e) {
- Node v = _graph.source(e);
- int vb = _blossom_set->find(v);
- int vi = (*_node_index)[v];
-
- Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
- dualScale * _weight[e];
-
- if ((*_blossom_data)[vb].status == EVEN) {
- if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
- _delta3->push(e, rw / 2);
- }
- } else {
- typename std::map<int, Arc>::iterator it =
- (*_node_data)[vi].heap_index.find(tree);
-
- if (it != (*_node_data)[vi].heap_index.end()) {
- if ((*_node_data)[vi].heap[it->second] > rw) {
- (*_node_data)[vi].heap.replace(it->second, e);
- (*_node_data)[vi].heap.decrease(e, rw);
- it->second = e;
- }
- } else {
- (*_node_data)[vi].heap.push(e, rw);
- (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
- }
-
- if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
- _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
-
- if ((*_blossom_data)[vb].status == MATCHED) {
- if (_delta2->state(vb) != _delta2->IN_HEAP) {
- _delta2->push(vb, _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset);
- } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset){
- _delta2->decrease(vb, _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset);
- }
- }
- }
- }
- }
- }
- (*_blossom_data)[blossom].offset = 0;
- }
-
- void matchedToOdd(int blossom) {
- if (_delta2->state(blossom) == _delta2->IN_HEAP) {
- _delta2->erase(blossom);
- }
- (*_blossom_data)[blossom].offset += _delta_sum;
- if (!_blossom_set->trivial(blossom)) {
- _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
- (*_blossom_data)[blossom].offset);
- }
- }
-
- void evenToMatched(int blossom, int tree) {
- if (!_blossom_set->trivial(blossom)) {
- (*_blossom_data)[blossom].pot += 2 * _delta_sum;
- }
-
- for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
- n != INVALID; ++n) {
- int ni = (*_node_index)[n];
- (*_node_data)[ni].pot -= _delta_sum;
-
- for (InArcIt e(_graph, n); e != INVALID; ++e) {
- Node v = _graph.source(e);
- int vb = _blossom_set->find(v);
- int vi = (*_node_index)[v];
-
- Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
- dualScale * _weight[e];
-
- if (vb == blossom) {
- if (_delta3->state(e) == _delta3->IN_HEAP) {
- _delta3->erase(e);
- }
- } else if ((*_blossom_data)[vb].status == EVEN) {
-
- if (_delta3->state(e) == _delta3->IN_HEAP) {
- _delta3->erase(e);
- }
-
- int vt = _tree_set->find(vb);
-
- if (vt != tree) {
-
- Arc r = _graph.oppositeArc(e);
-
- typename std::map<int, Arc>::iterator it =
- (*_node_data)[ni].heap_index.find(vt);
-
- if (it != (*_node_data)[ni].heap_index.end()) {
- if ((*_node_data)[ni].heap[it->second] > rw) {
- (*_node_data)[ni].heap.replace(it->second, r);
- (*_node_data)[ni].heap.decrease(r, rw);
- it->second = r;
- }
- } else {
- (*_node_data)[ni].heap.push(r, rw);
- (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
- }
-
- if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
- _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
-
- if (_delta2->state(blossom) != _delta2->IN_HEAP) {
- _delta2->push(blossom, _blossom_set->classPrio(blossom) -
- (*_blossom_data)[blossom].offset);
- } else if ((*_delta2)[blossom] >
- _blossom_set->classPrio(blossom) -
- (*_blossom_data)[blossom].offset){
- _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
- (*_blossom_data)[blossom].offset);
- }
- }
- }
- } else {
-
- typename std::map<int, Arc>::iterator it =
- (*_node_data)[vi].heap_index.find(tree);
-
- if (it != (*_node_data)[vi].heap_index.end()) {
- (*_node_data)[vi].heap.erase(it->second);
- (*_node_data)[vi].heap_index.erase(it);
- if ((*_node_data)[vi].heap.empty()) {
- _blossom_set->increase(v, std::numeric_limits<Value>::max());
- } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
- _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
- }
-
- if ((*_blossom_data)[vb].status == MATCHED) {
- if (_blossom_set->classPrio(vb) ==
- std::numeric_limits<Value>::max()) {
- _delta2->erase(vb);
- } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset) {
- _delta2->increase(vb, _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset);
- }
- }
- }
- }
- }
- }
- }
-
- void oddToMatched(int blossom) {
- (*_blossom_data)[blossom].offset -= _delta_sum;
-
- if (_blossom_set->classPrio(blossom) !=
- std::numeric_limits<Value>::max()) {
- _delta2->push(blossom, _blossom_set->classPrio(blossom) -
- (*_blossom_data)[blossom].offset);
- }
-
- if (!_blossom_set->trivial(blossom)) {
- _delta4->erase(blossom);
- }
- }
-
- void oddToEven(int blossom, int tree) {
- if (!_blossom_set->trivial(blossom)) {
- _delta4->erase(blossom);
- (*_blossom_data)[blossom].pot -=
- 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
- }
-
- for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
- n != INVALID; ++n) {
- int ni = (*_node_index)[n];
-
- _blossom_set->increase(n, std::numeric_limits<Value>::max());
-
- (*_node_data)[ni].heap.clear();
- (*_node_data)[ni].heap_index.clear();
- (*_node_data)[ni].pot +=
- 2 * _delta_sum - (*_blossom_data)[blossom].offset;
-
- for (InArcIt e(_graph, n); e != INVALID; ++e) {
- Node v = _graph.source(e);
- int vb = _blossom_set->find(v);
- int vi = (*_node_index)[v];
-
- Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
- dualScale * _weight[e];
-
- if ((*_blossom_data)[vb].status == EVEN) {
- if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
- _delta3->push(e, rw / 2);
- }
- } else {
-
- typename std::map<int, Arc>::iterator it =
- (*_node_data)[vi].heap_index.find(tree);
-
- if (it != (*_node_data)[vi].heap_index.end()) {
- if ((*_node_data)[vi].heap[it->second] > rw) {
- (*_node_data)[vi].heap.replace(it->second, e);
- (*_node_data)[vi].heap.decrease(e, rw);
- it->second = e;
- }
- } else {
- (*_node_data)[vi].heap.push(e, rw);
- (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
- }
-
- if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
- _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
-
- if ((*_blossom_data)[vb].status == MATCHED) {
- if (_delta2->state(vb) != _delta2->IN_HEAP) {
- _delta2->push(vb, _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset);
- } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset) {
- _delta2->decrease(vb, _blossom_set->classPrio(vb) -
- (*_blossom_data)[vb].offset);
- }
- }
- }
- }
- }
- }
- (*_blossom_data)[blossom].offset = 0;
- }
-
- void alternatePath(int even, int tree) {
- int odd;
-
- evenToMatched(even, tree);
- (*_blossom_data)[even].status = MATCHED;
-
- while ((*_blossom_data)[even].pred != INVALID) {
- odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
- (*_blossom_data)[odd].status = MATCHED;
- oddToMatched(odd);
- (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
-
- even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
- (*_blossom_data)[even].status = MATCHED;
- evenToMatched(even, tree);
- (*_blossom_data)[even].next =
- _graph.oppositeArc((*_blossom_data)[odd].pred);
- }
-
- }
-
- void destroyTree(int tree) {
- for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
- if ((*_blossom_data)[b].status == EVEN) {
- (*_blossom_data)[b].status = MATCHED;
- evenToMatched(b, tree);
- } else if ((*_blossom_data)[b].status == ODD) {
- (*_blossom_data)[b].status = MATCHED;
- oddToMatched(b);
- }
- }
- _tree_set->eraseClass(tree);
- }
-
- void augmentOnEdge(const Edge& edge) {
-
- int left = _blossom_set->find(_graph.u(edge));
- int right = _blossom_set->find(_graph.v(edge));
-
- int left_tree = _tree_set->find(left);
- alternatePath(left, left_tree);
- destroyTree(left_tree);
-
- int right_tree = _tree_set->find(right);
- alternatePath(right, right_tree);
- destroyTree(right_tree);
-
- (*_blossom_data)[left].next = _graph.direct(edge, true);
- (*_blossom_data)[right].next = _graph.direct(edge, false);
- }
-
- void extendOnArc(const Arc& arc) {
- int base = _blossom_set->find(_graph.target(arc));
- int tree = _tree_set->find(base);
-
- int odd = _blossom_set->find(_graph.source(arc));
- _tree_set->insert(odd, tree);
- (*_blossom_data)[odd].status = ODD;
- matchedToOdd(odd);
- (*_blossom_data)[odd].pred = arc;
-
- int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
- (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
- _tree_set->insert(even, tree);
- (*_blossom_data)[even].status = EVEN;
- matchedToEven(even, tree);
- }
-
- void shrinkOnEdge(const Edge& edge, int tree) {
- int nca = -1;
- std::vector<int> left_path, right_path;
-
- {
- std::set<int> left_set, right_set;
- int left = _blossom_set->find(_graph.u(edge));
- left_path.push_back(left);
- left_set.insert(left);
-
- int right = _blossom_set->find(_graph.v(edge));
- right_path.push_back(right);
- right_set.insert(right);
-
- while (true) {
-
- if ((*_blossom_data)[left].pred == INVALID) break;
-
- left =
- _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
- left_path.push_back(left);
- left =
- _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
- left_path.push_back(left);
-
- left_set.insert(left);
-
- if (right_set.find(left) != right_set.end()) {
- nca = left;
- break;
- }
-
- if ((*_blossom_data)[right].pred == INVALID) break;
-
- right =
- _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
- right_path.push_back(right);
- right =
- _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
- right_path.push_back(right);
-
- right_set.insert(right);
-
- if (left_set.find(right) != left_set.end()) {
- nca = right;
- break;
- }
-
- }
-
- if (nca == -1) {
- if ((*_blossom_data)[left].pred == INVALID) {
- nca = right;
- while (left_set.find(nca) == left_set.end()) {
- nca =
- _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
- right_path.push_back(nca);
- nca =
- _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
- right_path.push_back(nca);
- }
- } else {
- nca = left;
- while (right_set.find(nca) == right_set.end()) {
- nca =
- _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
- left_path.push_back(nca);
- nca =
- _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
- left_path.push_back(nca);
- }
- }
- }
- }
-
- std::vector<int> subblossoms;
- Arc prev;
-
- prev = _graph.direct(edge, true);
- for (int i = 0; left_path[i] != nca; i += 2) {
- subblossoms.push_back(left_path[i]);
- (*_blossom_data)[left_path[i]].next = prev;
- _tree_set->erase(left_path[i]);
-
- subblossoms.push_back(left_path[i + 1]);
- (*_blossom_data)[left_path[i + 1]].status = EVEN;
- oddToEven(left_path[i + 1], tree);
- _tree_set->erase(left_path[i + 1]);
- prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
- }
-
- int k = 0;
- while (right_path[k] != nca) ++k;
-
- subblossoms.push_back(nca);
- (*_blossom_data)[nca].next = prev;
-
- for (int i = k - 2; i >= 0; i -= 2) {
- subblossoms.push_back(right_path[i + 1]);
- (*_blossom_data)[right_path[i + 1]].status = EVEN;
- oddToEven(right_path[i + 1], tree);
- _tree_set->erase(right_path[i + 1]);
-
- (*_blossom_data)[right_path[i + 1]].next =
- (*_blossom_data)[right_path[i + 1]].pred;
-
- subblossoms.push_back(right_path[i]);
- _tree_set->erase(right_path[i]);
- }
-
- int surface =
- _blossom_set->join(subblossoms.begin(), subblossoms.end());
-
- for (int i = 0; i < int(subblossoms.size()); ++i) {
- if (!_blossom_set->trivial(subblossoms[i])) {
- (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
- }
- (*_blossom_data)[subblossoms[i]].status = MATCHED;
- }
-
- (*_blossom_data)[surface].pot = -2 * _delta_sum;
- (*_blossom_data)[surface].offset = 0;
- (*_blossom_data)[surface].status = EVEN;
- (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
- (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
-
- _tree_set->insert(surface, tree);
- _tree_set->erase(nca);
- }
-
- void splitBlossom(int blossom) {
- Arc next = (*_blossom_data)[blossom].next;
- Arc pred = (*_blossom_data)[blossom].pred;
-
- int tree = _tree_set->find(blossom);
-
- (*_blossom_data)[blossom].status = MATCHED;
- oddToMatched(blossom);
- if (_delta2->state(blossom) == _delta2->IN_HEAP) {
- _delta2->erase(blossom);
- }
-
- std::vector<int> subblossoms;
- _blossom_set->split(blossom, std::back_inserter(subblossoms));
-
- Value offset = (*_blossom_data)[blossom].offset;
- int b = _blossom_set->find(_graph.source(pred));
- int d = _blossom_set->find(_graph.source(next));
-
- int ib = -1, id = -1;
- for (int i = 0; i < int(subblossoms.size()); ++i) {
- if (subblossoms[i] == b) ib = i;
- if (subblossoms[i] == d) id = i;
-
- (*_blossom_data)[subblossoms[i]].offset = offset;
- if (!_blossom_set->trivial(subblossoms[i])) {
- (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
- }
- if (_blossom_set->classPrio(subblossoms[i]) !=
- std::numeric_limits<Value>::max()) {
- _delta2->push(subblossoms[i],
- _blossom_set->classPrio(subblossoms[i]) -
- (*_blossom_data)[subblossoms[i]].offset);
- }
- }
-
- if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
- for (int i = (id + 1) % subblossoms.size();
- i != ib; i = (i + 2) % subblossoms.size()) {
- int sb = subblossoms[i];
- int tb = subblossoms[(i + 1) % subblossoms.size()];
- (*_blossom_data)[sb].next =
- _graph.oppositeArc((*_blossom_data)[tb].next);
- }
-
- for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
- int sb = subblossoms[i];
- int tb = subblossoms[(i + 1) % subblossoms.size()];
- int ub = subblossoms[(i + 2) % subblossoms.size()];
-
- (*_blossom_data)[sb].status = ODD;
- matchedToOdd(sb);
- _tree_set->insert(sb, tree);
- (*_blossom_data)[sb].pred = pred;
- (*_blossom_data)[sb].next =
- _graph.oppositeArc((*_blossom_data)[tb].next);
-
- pred = (*_blossom_data)[ub].next;
-
- (*_blossom_data)[tb].status = EVEN;
- matchedToEven(tb, tree);
- _tree_set->insert(tb, tree);
- (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
- }
-
- (*_blossom_data)[subblossoms[id]].status = ODD;
- matchedToOdd(subblossoms[id]);
- _tree_set->insert(subblossoms[id], tree);
- (*_blossom_data)[subblossoms[id]].next = next;
- (*_blossom_data)[subblossoms[id]].pred = pred;
-
- } else {
-
- for (int i = (ib + 1) % subblossoms.size();
- i != id; i = (i + 2) % subblossoms.size()) {
- int sb = subblossoms[i];
- int tb = subblossoms[(i + 1) % subblossoms.size()];
- (*_blossom_data)[sb].next =
- _graph.oppositeArc((*_blossom_data)[tb].next);
- }
-
- for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
- int sb = subblossoms[i];
- int tb = subblossoms[(i + 1) % subblossoms.size()];
- int ub = subblossoms[(i + 2) % subblossoms.size()];
-
- (*_blossom_data)[sb].status = ODD;
- matchedToOdd(sb);
- _tree_set->insert(sb, tree);
- (*_blossom_data)[sb].next = next;
- (*_blossom_data)[sb].pred =
- _graph.oppositeArc((*_blossom_data)[tb].next);
-
- (*_blossom_data)[tb].status = EVEN;
- matchedToEven(tb, tree);
- _tree_set->insert(tb, tree);
- (*_blossom_data)[tb].pred =
- (*_blossom_data)[tb].next =
- _graph.oppositeArc((*_blossom_data)[ub].next);
- next = (*_blossom_data)[ub].next;
- }
-
- (*_blossom_data)[subblossoms[ib]].status = ODD;
- matchedToOdd(subblossoms[ib]);
- _tree_set->insert(subblossoms[ib], tree);
- (*_blossom_data)[subblossoms[ib]].next = next;
- (*_blossom_data)[subblossoms[ib]].pred = pred;
- }
- _tree_set->erase(blossom);
- }
-
- void extractBlossom(int blossom, const Node& base, const Arc& matching) {
- if (_blossom_set->trivial(blossom)) {
- int bi = (*_node_index)[base];
- Value pot = (*_node_data)[bi].pot;
-
- (*_matching)[base] = matching;
- _blossom_node_list.push_back(base);
- (*_node_potential)[base] = pot;
- } else {
-
- Value pot = (*_blossom_data)[blossom].pot;
- int bn = _blossom_node_list.size();
-
- std::vector<int> subblossoms;
- _blossom_set->split(blossom, std::back_inserter(subblossoms));
- int b = _blossom_set->find(base);
- int ib = -1;
- for (int i = 0; i < int(subblossoms.size()); ++i) {
- if (subblossoms[i] == b) { ib = i; break; }
- }
-
- for (int i = 1; i < int(subblossoms.size()); i += 2) {
- int sb = subblossoms[(ib + i) % subblossoms.size()];
- int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
-
- Arc m = (*_blossom_data)[tb].next;
- extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
- extractBlossom(tb, _graph.source(m), m);
- }
- extractBlossom(subblossoms[ib], base, matching);
-
- int en = _blossom_node_list.size();
-
- _blossom_potential.push_back(BlossomVariable(bn, en, pot));
- }
- }
-
- void extractMatching() {
- std::vector<int> blossoms;
- for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
- blossoms.push_back(c);
- }
-
- for (int i = 0; i < int(blossoms.size()); ++i) {
-
- Value offset = (*_blossom_data)[blossoms[i]].offset;
- (*_blossom_data)[blossoms[i]].pot += 2 * offset;
- for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
- n != INVALID; ++n) {
- (*_node_data)[(*_node_index)[n]].pot -= offset;
- }
-
- Arc matching = (*_blossom_data)[blossoms[i]].next;
- Node base = _graph.source(matching);
- extractBlossom(blossoms[i], base, matching);
- }
- }
-
- public:
-
- /// \brief Constructor
- ///
- /// Constructor.
- MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight)
- : _graph(graph), _weight(weight), _matching(0),
- _node_potential(0), _blossom_potential(), _blossom_node_list(),
- _node_num(0), _blossom_num(0),
-
- _blossom_index(0), _blossom_set(0), _blossom_data(0),
- _node_index(0), _node_heap_index(0), _node_data(0),
- _tree_set_index(0), _tree_set(0),
-
- _delta2_index(0), _delta2(0),
- _delta3_index(0), _delta3(0),
- _delta4_index(0), _delta4(0),
-
- _delta_sum() {}
-
- ~MaxWeightedPerfectMatching() {
- destroyStructures();
- }
-
- /// \name Execution control
- /// The simplest way to execute the algorithm is to use the
- /// \c run() member function.
-
- ///@{
-
- /// \brief Initialize the algorithm
- ///
- /// Initialize the algorithm
- void init() {
- createStructures();
-
- for (ArcIt e(_graph); e != INVALID; ++e) {
- (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
- }
- for (EdgeIt e(_graph); e != INVALID; ++e) {
- (*_delta3_index)[e] = _delta3->PRE_HEAP;
- }
- for (int i = 0; i < _blossom_num; ++i) {
- (*_delta2_index)[i] = _delta2->PRE_HEAP;
- (*_delta4_index)[i] = _delta4->PRE_HEAP;
- }
-
- int index = 0;
- for (NodeIt n(_graph); n != INVALID; ++n) {
- Value max = - std::numeric_limits<Value>::max();
- for (OutArcIt e(_graph, n); e != INVALID; ++e) {
- if (_graph.target(e) == n) continue;
- if ((dualScale * _weight[e]) / 2 > max) {
- max = (dualScale * _weight[e]) / 2;
- }
- }
- (*_node_index)[n] = index;
- (*_node_data)[index].pot = max;
- int blossom =
- _blossom_set->insert(n, std::numeric_limits<Value>::max());
-
- _tree_set->insert(blossom);
-
- (*_blossom_data)[blossom].status = EVEN;
- (*_blossom_data)[blossom].pred = INVALID;
- (*_blossom_data)[blossom].next = INVALID;
- (*_blossom_data)[blossom].pot = 0;
- (*_blossom_data)[blossom].offset = 0;
- ++index;
- }
- for (EdgeIt e(_graph); e != INVALID; ++e) {
- int si = (*_node_index)[_graph.u(e)];
- int ti = (*_node_index)[_graph.v(e)];
- if (_graph.u(e) != _graph.v(e)) {
- _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
- dualScale * _weight[e]) / 2);
- }
- }
- }
-
- /// \brief Starts the algorithm
- ///
- /// Starts the algorithm
- bool start() {
- enum OpType {
- D2, D3, D4
- };
-
- int unmatched = _node_num;
- while (unmatched > 0) {
- Value d2 = !_delta2->empty() ?
- _delta2->prio() : std::numeric_limits<Value>::max();
-
- Value d3 = !_delta3->empty() ?
- _delta3->prio() : std::numeric_limits<Value>::max();
-
- Value d4 = !_delta4->empty() ?
- _delta4->prio() : std::numeric_limits<Value>::max();
-
- _delta_sum = d2; OpType ot = D2;
- if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
- if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
-
- if (_delta_sum == std::numeric_limits<Value>::max()) {
- return false;
- }
-
- switch (ot) {
- case D2:
- {
- int blossom = _delta2->top();
- Node n = _blossom_set->classTop(blossom);
- Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
- extendOnArc(e);
- }
- break;
- case D3:
- {
- Edge e = _delta3->top();
-
- int left_blossom = _blossom_set->find(_graph.u(e));
- int right_blossom = _blossom_set->find(_graph.v(e));
-
- if (left_blossom == right_blossom) {
- _delta3->pop();
- } else {
- int left_tree = _tree_set->find(left_blossom);
- int right_tree = _tree_set->find(right_blossom);
-
- if (left_tree == right_tree) {
- shrinkOnEdge(e, left_tree);
- } else {
- augmentOnEdge(e);
- unmatched -= 2;
- }
- }
- } break;
- case D4:
- splitBlossom(_delta4->top());
- break;
- }
- }
- extractMatching();
- return true;
- }
-
- /// \brief Runs %MaxWeightedPerfectMatching algorithm.
- ///
- /// This method runs the %MaxWeightedPerfectMatching algorithm.
- ///
- /// \note mwm.run() is just a shortcut of the following code.
- /// \code
- /// mwm.init();
- /// mwm.start();
- /// \endcode
- bool run() {
- init();
- return start();
- }
-
- /// @}
-
- /// \name Primal solution
- /// Functions to get the primal solution, ie. the matching.
-
- /// @{
-
- /// \brief Returns the matching value.
- ///
- /// Returns the matching value.
- Value matchingValue() const {
- Value sum = 0;
- for (NodeIt n(_graph); n != INVALID; ++n) {
- if ((*_matching)[n] != INVALID) {
- sum += _weight[(*_matching)[n]];
- }
- }
- return sum /= 2;
- }
-
- /// \brief Returns true when the edge is in the matching.
- ///
- /// Returns true when the edge is in the matching.
- bool matching(const Edge& edge) const {
- return static_cast<const Edge&>((*_matching)[_graph.u(edge)]) == edge;
- }
-
- /// \brief Returns the incident matching edge.
- ///
- /// Returns the incident matching arc from given edge.
- Arc matching(const Node& node) const {
- return (*_matching)[node];
- }
-
- /// \brief Returns the mate of the node.
- ///
- /// Returns the adjancent node in a mathcing arc.
- Node mate(const Node& node) const {
- return _graph.target((*_matching)[node]);
- }
-
- /// @}
-
- /// \name Dual solution
- /// Functions to get the dual solution.
-
- /// @{
-
- /// \brief Returns the value of the dual solution.
- ///
- /// Returns the value of the dual solution. It should be equal to
- /// the primal value scaled by \ref dualScale "dual scale".
- Value dualValue() const {
- Value sum = 0;
- for (NodeIt n(_graph); n != INVALID; ++n) {
- sum += nodeValue(n);
- }
- for (int i = 0; i < blossomNum(); ++i) {
- sum += blossomValue(i) * (blossomSize(i) / 2);
- }
- return sum;
- }
-
- /// \brief Returns the value of the node.
- ///
- /// Returns the the value of the node.
- Value nodeValue(const Node& n) const {
- return (*_node_potential)[n];
- }
-
- /// \brief Returns the number of the blossoms in the basis.
- ///
- /// Returns the number of the blossoms in the basis.
- /// \see BlossomIt
- int blossomNum() const {
- return _blossom_potential.size();
- }
-
-
- /// \brief Returns the number of the nodes in the blossom.
- ///
- /// Returns the number of the nodes in the blossom.
- int blossomSize(int k) const {
- return _blossom_potential[k].end - _blossom_potential[k].begin;
- }
-
- /// \brief Returns the value of the blossom.
- ///
- /// Returns the the value of the blossom.
- /// \see BlossomIt
- Value blossomValue(int k) const {
- return _blossom_potential[k].value;
- }
-
- /// \brief Iterator for obtaining the nodes of the blossom.
- ///
- /// Iterator for obtaining the nodes of the blossom. This class
- /// provides a common lemon style iterator for listing a
- /// subset of the nodes.
- class BlossomIt {
- public:
-
- /// \brief Constructor.
- ///
- /// Constructor to get the nodes of the variable.
- BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable)
- : _algorithm(&algorithm)
- {
- _index = _algorithm->_blossom_potential[variable].begin;
- _last = _algorithm->_blossom_potential[variable].end;
- }
-
- /// \brief Conversion to node.
- ///
- /// Conversion to node.
- operator Node() const {
- return _algorithm->_blossom_node_list[_index];
- }
-
- /// \brief Increment operator.
- ///
- /// Increment operator.
- BlossomIt& operator++() {
- ++_index;
- return *this;
- }
-
- /// \brief Validity checking
- ///
- /// Checks whether the iterator is invalid.
- bool operator==(Invalid) const { return _index == _last; }
-
- /// \brief Validity checking
- ///
- /// Checks whether the iterator is valid.
- bool operator!=(Invalid) const { return _index != _last; }
-
- private:
- const MaxWeightedPerfectMatching* _algorithm;
- int _last;
- int _index;
- };
-
- /// @}
-
- };
-
-
-} //END OF NAMESPACE LEMON
-
-#endif //LEMON_MAX_MATCHING_H
diff -r f63e87b9748e -r 0ba8dfce7259 test/CMakeLists.txt
--- a/test/CMakeLists.txt Tue Apr 21 10:34:49 2009 +0100
+++ b/test/CMakeLists.txt Tue Apr 21 13:08:19 2009 +0100
@@ -29,7 +29,7 @@
heap_test
kruskal_test
maps_test
- max_matching_test
+ matching_test
min_cost_arborescence_test
path_test
preflow_test
diff -r f63e87b9748e -r 0ba8dfce7259 test/Makefile.am
--- a/test/Makefile.am Tue Apr 21 10:34:49 2009 +0100
+++ b/test/Makefile.am Tue Apr 21 13:08:19 2009 +0100
@@ -25,7 +25,7 @@
test/heap_test \
test/kruskal_test \
test/maps_test \
- test/max_matching_test \
+ test/matching_test \
test/min_cost_arborescence_test \
test/path_test \
test/preflow_test \
@@ -70,7 +70,7 @@
test_lp_test_SOURCES = test/lp_test.cc
test_maps_test_SOURCES = test/maps_test.cc
test_mip_test_SOURCES = test/mip_test.cc
-test_max_matching_test_SOURCES = test/max_matching_test.cc
+test_matching_test_SOURCES = test/matching_test.cc
test_min_cost_arborescence_test_SOURCES = test/min_cost_arborescence_test.cc
test_path_test_SOURCES = test/path_test.cc
test_preflow_test_SOURCES = test/preflow_test.cc
diff -r f63e87b9748e -r 0ba8dfce7259 test/euler_test.cc
--- a/test/euler_test.cc Tue Apr 21 10:34:49 2009 +0100
+++ b/test/euler_test.cc Tue Apr 21 13:08:19 2009 +0100
@@ -18,136 +18,206 @@
#include <lemon/euler.h>
#include <lemon/list_graph.h>
-#include <test/test_tools.h>
+#include <lemon/adaptors.h>
+#include "test_tools.h"
using namespace lemon;
template <typename Digraph>
-void checkDiEulerIt(const Digraph& g)
+void checkDiEulerIt(const Digraph& g,
+ const typename Digraph::Node& start = INVALID)
{
typename Digraph::template ArcMap<int> visitationNumber(g, 0);
- DiEulerIt<Digraph> e(g);
+ DiEulerIt<Digraph> e(g, start);
+ if (e == INVALID) return;
typename Digraph::Node firstNode = g.source(e);
typename Digraph::Node lastNode = g.target(e);
+ if (start != INVALID) {
+ check(firstNode == start, "checkDiEulerIt: Wrong first node");
+ }
- for (; e != INVALID; ++e)
- {
- if (e != INVALID)
- {
- lastNode = g.target(e);
- }
+ for (; e != INVALID; ++e) {
+ if (e != INVALID) lastNode = g.target(e);
++visitationNumber[e];
}
check(firstNode == lastNode,
- "checkDiEulerIt: first and last node are not the same");
+ "checkDiEulerIt: First and last nodes are not the same");
for (typename Digraph::ArcIt a(g); a != INVALID; ++a)
{
check(visitationNumber[a] == 1,
- "checkDiEulerIt: not visited or multiple times visited arc found");
+ "checkDiEulerIt: Not visited or multiple times visited arc found");
}
}
template <typename Graph>
-void checkEulerIt(const Graph& g)
+void checkEulerIt(const Graph& g,
+ const typename Graph::Node& start = INVALID)
{
typename Graph::template EdgeMap<int> visitationNumber(g, 0);
- EulerIt<Graph> e(g);
- typename Graph::Node firstNode = g.u(e);
- typename Graph::Node lastNode = g.v(e);
+ EulerIt<Graph> e(g, start);
+ if (e == INVALID) return;
+ typename Graph::Node firstNode = g.source(typename Graph::Arc(e));
+ typename Graph::Node lastNode = g.target(typename Graph::Arc(e));
+ if (start != INVALID) {
+ check(firstNode == start, "checkEulerIt: Wrong first node");
+ }
- for (; e != INVALID; ++e)
- {
- if (e != INVALID)
- {
- lastNode = g.v(e);
- }
+ for (; e != INVALID; ++e) {
+ if (e != INVALID) lastNode = g.target(typename Graph::Arc(e));
++visitationNumber[e];
}
check(firstNode == lastNode,
- "checkEulerIt: first and last node are not the same");
+ "checkEulerIt: First and last nodes are not the same");
for (typename Graph::EdgeIt e(g); e != INVALID; ++e)
{
check(visitationNumber[e] == 1,
- "checkEulerIt: not visited or multiple times visited edge found");
+ "checkEulerIt: Not visited or multiple times visited edge found");
}
}
int main()
{
typedef ListDigraph Digraph;
- typedef ListGraph Graph;
+ typedef Undirector<Digraph> Graph;
+
+ {
+ Digraph d;
+ Graph g(d);
+
+ checkDiEulerIt(d);
+ checkDiEulerIt(g);
+ checkEulerIt(g);
- Digraph digraphWithEulerianCircuit;
+ check(eulerian(d), "This graph is Eulerian");
+ check(eulerian(g), "This graph is Eulerian");
+ }
{
- Digraph& g = digraphWithEulerianCircuit;
+ Digraph d;
+ Graph g(d);
+ Digraph::Node n = d.addNode();
- Digraph::Node n0 = g.addNode();
- Digraph::Node n1 = g.addNode();
- Digraph::Node n2 = g.addNode();
+ checkDiEulerIt(d);
+ checkDiEulerIt(g);
+ checkEulerIt(g);
- g.addArc(n0, n1);
- g.addArc(n1, n0);
- g.addArc(n1, n2);
- g.addArc(n2, n1);
+ check(eulerian(d), "This graph is Eulerian");
+ check(eulerian(g), "This graph is Eulerian");
}
+ {
+ Digraph d;
+ Graph g(d);
+ Digraph::Node n = d.addNode();
+ d.addArc(n, n);
- Digraph digraphWithoutEulerianCircuit;
+ checkDiEulerIt(d);
+ checkDiEulerIt(g);
+ checkEulerIt(g);
+
+ check(eulerian(d), "This graph is Eulerian");
+ check(eulerian(g), "This graph is Eulerian");
+ }
{
- Digraph& g = digraphWithoutEulerianCircuit;
+ Digraph d;
+ Graph g(d);
+ Digraph::Node n1 = d.addNode();
+ Digraph::Node n2 = d.addNode();
+ Digraph::Node n3 = d.addNode();
+
+ d.addArc(n1, n2);
+ d.addArc(n2, n1);
+ d.addArc(n2, n3);
+ d.addArc(n3, n2);
- Digraph::Node n0 = g.addNode();
- Digraph::Node n1 = g.addNode();
- Digraph::Node n2 = g.addNode();
+ checkDiEulerIt(d);
+ checkDiEulerIt(d, n2);
+ checkDiEulerIt(g);
+ checkDiEulerIt(g, n2);
+ checkEulerIt(g);
+ checkEulerIt(g, n2);
- g.addArc(n0, n1);
- g.addArc(n1, n0);
- g.addArc(n1, n2);
+ check(eulerian(d), "This graph is Eulerian");
+ check(eulerian(g), "This graph is Eulerian");
}
+ {
+ Digraph d;
+ Graph g(d);
+ Digraph::Node n1 = d.addNode();
+ Digraph::Node n2 = d.addNode();
+ Digraph::Node n3 = d.addNode();
+ Digraph::Node n4 = d.addNode();
+ Digraph::Node n5 = d.addNode();
+ Digraph::Node n6 = d.addNode();
+
+ d.addArc(n1, n2);
+ d.addArc(n2, n4);
+ d.addArc(n1, n3);
+ d.addArc(n3, n4);
+ d.addArc(n4, n1);
+ d.addArc(n3, n5);
+ d.addArc(n5, n2);
+ d.addArc(n4, n6);
+ d.addArc(n2, n6);
+ d.addArc(n6, n1);
+ d.addArc(n6, n3);
- Graph graphWithEulerianCircuit;
+ checkDiEulerIt(d);
+ checkDiEulerIt(d, n1);
+ checkDiEulerIt(d, n5);
+
+ checkDiEulerIt(g);
+ checkDiEulerIt(g, n1);
+ checkDiEulerIt(g, n5);
+ checkEulerIt(g);
+ checkEulerIt(g, n1);
+ checkEulerIt(g, n5);
+
+ check(eulerian(d), "This graph is Eulerian");
+ check(eulerian(g), "This graph is Eulerian");
+ }
{
- Graph& g = graphWithEulerianCircuit;
+ Digraph d;
+ Graph g(d);
+ Digraph::Node n0 = d.addNode();
+ Digraph::Node n1 = d.addNode();
+ Digraph::Node n2 = d.addNode();
+ Digraph::Node n3 = d.addNode();
+ Digraph::Node n4 = d.addNode();
+ Digraph::Node n5 = d.addNode();
+
+ d.addArc(n1, n2);
+ d.addArc(n2, n3);
+ d.addArc(n3, n1);
- Graph::Node n0 = g.addNode();
- Graph::Node n1 = g.addNode();
- Graph::Node n2 = g.addNode();
+ checkDiEulerIt(d);
+ checkDiEulerIt(d, n2);
- g.addEdge(n0, n1);
- g.addEdge(n1, n2);
- g.addEdge(n2, n0);
+ checkDiEulerIt(g);
+ checkDiEulerIt(g, n2);
+ checkEulerIt(g);
+ checkEulerIt(g, n2);
+
+ check(!eulerian(d), "This graph is not Eulerian");
+ check(!eulerian(g), "This graph is not Eulerian");
}
+ {
+ Digraph d;
+ Graph g(d);
+ Digraph::Node n1 = d.addNode();
+ Digraph::Node n2 = d.addNode();
+ Digraph::Node n3 = d.addNode();
+
+ d.addArc(n1, n2);
+ d.addArc(n2, n3);
- Graph graphWithoutEulerianCircuit;
- {
- Graph& g = graphWithoutEulerianCircuit;
-
- Graph::Node n0 = g.addNode();
- Graph::Node n1 = g.addNode();
- Graph::Node n2 = g.addNode();
-
- g.addEdge(n0, n1);
- g.addEdge(n1, n2);
+ check(!eulerian(d), "This graph is not Eulerian");
+ check(!eulerian(g), "This graph is not Eulerian");
}
- checkDiEulerIt(digraphWithEulerianCircuit);
-
- checkEulerIt(graphWithEulerianCircuit);
-
- check(eulerian(digraphWithEulerianCircuit),
- "this graph should have an Eulerian circuit");
- check(!eulerian(digraphWithoutEulerianCircuit),
- "this graph should not have an Eulerian circuit");
-
- check(eulerian(graphWithEulerianCircuit),
- "this graph should have an Eulerian circuit");
- check(!eulerian(graphWithoutEulerianCircuit),
- "this graph should have an Eulerian circuit");
-
return 0;
}
diff -r f63e87b9748e -r 0ba8dfce7259 test/matching_test.cc
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/test/matching_test.cc Tue Apr 21 13:08:19 2009 +0100
@@ -0,0 +1,424 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2009
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#include <iostream>
+#include <sstream>
+#include <vector>
+#include <queue>
+#include <cstdlib>
+
+#include <lemon/matching.h>
+#include <lemon/smart_graph.h>
+#include <lemon/concepts/graph.h>
+#include <lemon/concepts/maps.h>
+#include <lemon/lgf_reader.h>
+#include <lemon/math.h>
+
+#include "test_tools.h"
+
+using namespace std;
+using namespace lemon;
+
+GRAPH_TYPEDEFS(SmartGraph);
+
+
+const int lgfn = 3;
+const std::string lgf[lgfn] = {
+ "@nodes\n"
+ "label\n"
+ "0\n"
+ "1\n"
+ "2\n"
+ "3\n"
+ "4\n"
+ "5\n"
+ "6\n"
+ "7\n"
+ "@edges\n"
+ " label weight\n"
+ "7 4 0 984\n"
+ "0 7 1 73\n"
+ "7 1 2 204\n"
+ "2 3 3 583\n"
+ "2 7 4 565\n"
+ "2 1 5 582\n"
+ "0 4 6 551\n"
+ "2 5 7 385\n"
+ "1 5 8 561\n"
+ "5 3 9 484\n"
+ "7 5 10 904\n"
+ "3 6 11 47\n"
+ "7 6 12 888\n"
+ "3 0 13 747\n"
+ "6 1 14 310\n",
+
+ "@nodes\n"
+ "label\n"
+ "0\n"
+ "1\n"
+ "2\n"
+ "3\n"
+ "4\n"
+ "5\n"
+ "6\n"
+ "7\n"
+ "@edges\n"
+ " label weight\n"
+ "2 5 0 710\n"
+ "0 5 1 241\n"
+ "2 4 2 856\n"
+ "2 6 3 762\n"
+ "4 1 4 747\n"
+ "6 1 5 962\n"
+ "4 7 6 723\n"
+ "1 7 7 661\n"
+ "2 3 8 376\n"
+ "1 0 9 416\n"
+ "6 7 10 391\n",
+
+ "@nodes\n"
+ "label\n"
+ "0\n"
+ "1\n"
+ "2\n"
+ "3\n"
+ "4\n"
+ "5\n"
+ "6\n"
+ "7\n"
+ "@edges\n"
+ " label weight\n"
+ "6 2 0 553\n"
+ "0 7 1 653\n"
+ "6 3 2 22\n"
+ "4 7 3 846\n"
+ "7 2 4 981\n"
+ "7 6 5 250\n"
+ "5 2 6 539\n",
+};
+
+void checkMaxMatchingCompile()
+{
+ typedef concepts::Graph Graph;
+ typedef Graph::Node Node;
+ typedef Graph::Edge Edge;
+ typedef Graph::EdgeMap<bool> MatMap;
+
+ Graph g;
+ Node n;
+ Edge e;
+ MatMap mat(g);
+
+ MaxMatching<Graph> mat_test(g);
+ const MaxMatching<Graph>&
+ const_mat_test = mat_test;
+
+ mat_test.init();
+ mat_test.greedyInit();
+ mat_test.matchingInit(mat);
+ mat_test.startSparse();
+ mat_test.startDense();
+ mat_test.run();
+
+ const_mat_test.matchingSize();
+ const_mat_test.matching(e);
+ const_mat_test.matching(n);
+ const MaxMatching<Graph>::MatchingMap& mmap =
+ const_mat_test.matchingMap();
+ e = mmap[n];
+ const_mat_test.mate(n);
+
+ MaxMatching<Graph>::Status stat =
+ const_mat_test.status(n);
+ const MaxMatching<Graph>::StatusMap& smap =
+ const_mat_test.statusMap();
+ stat = smap[n];
+ const_mat_test.barrier(n);
+}
+
+void checkMaxWeightedMatchingCompile()
+{
+ typedef concepts::Graph Graph;
+ typedef Graph::Node Node;
+ typedef Graph::Edge Edge;
+ typedef Graph::EdgeMap<int> WeightMap;
+
+ Graph g;
+ Node n;
+ Edge e;
+ WeightMap w(g);
+
+ MaxWeightedMatching<Graph> mat_test(g, w);
+ const MaxWeightedMatching<Graph>&
+ const_mat_test = mat_test;
+
+ mat_test.init();
+ mat_test.start();
+ mat_test.run();
+
+ const_mat_test.matchingWeight();
+ const_mat_test.matchingSize();
+ const_mat_test.matching(e);
+ const_mat_test.matching(n);
+ const MaxWeightedMatching<Graph>::MatchingMap& mmap =
+ const_mat_test.matchingMap();
+ e = mmap[n];
+ const_mat_test.mate(n);
+
+ int k = 0;
+ const_mat_test.dualValue();
+ const_mat_test.nodeValue(n);
+ const_mat_test.blossomNum();
+ const_mat_test.blossomSize(k);
+ const_mat_test.blossomValue(k);
+}
+
+void checkMaxWeightedPerfectMatchingCompile()
+{
+ typedef concepts::Graph Graph;
+ typedef Graph::Node Node;
+ typedef Graph::Edge Edge;
+ typedef Graph::EdgeMap<int> WeightMap;
+
+ Graph g;
+ Node n;
+ Edge e;
+ WeightMap w(g);
+
+ MaxWeightedPerfectMatching<Graph> mat_test(g, w);
+ const MaxWeightedPerfectMatching<Graph>&
+ const_mat_test = mat_test;
+
+ mat_test.init();
+ mat_test.start();
+ mat_test.run();
+
+ const_mat_test.matchingWeight();
+ const_mat_test.matching(e);
+ const_mat_test.matching(n);
+ const MaxWeightedPerfectMatching<Graph>::MatchingMap& mmap =
+ const_mat_test.matchingMap();
+ e = mmap[n];
+ const_mat_test.mate(n);
+
+ int k = 0;
+ const_mat_test.dualValue();
+ const_mat_test.nodeValue(n);
+ const_mat_test.blossomNum();
+ const_mat_test.blossomSize(k);
+ const_mat_test.blossomValue(k);
+}
+
+void checkMatching(const SmartGraph& graph,
+ const MaxMatching<SmartGraph>& mm) {
+ int num = 0;
+
+ IntNodeMap comp_index(graph);
+ UnionFind<IntNodeMap> comp(comp_index);
+
+ int barrier_num = 0;
+
+ for (NodeIt n(graph); n != INVALID; ++n) {
+ check(mm.status(n) == MaxMatching<SmartGraph>::EVEN ||
+ mm.matching(n) != INVALID, "Wrong Gallai-Edmonds decomposition");
+ if (mm.status(n) == MaxMatching<SmartGraph>::ODD) {
+ ++barrier_num;
+ } else {
+ comp.insert(n);
+ }
+ }
+
+ for (EdgeIt e(graph); e != INVALID; ++e) {
+ if (mm.matching(e)) {
+ check(e == mm.matching(graph.u(e)), "Wrong matching");
+ check(e == mm.matching(graph.v(e)), "Wrong matching");
+ ++num;
+ }
+ check(mm.status(graph.u(e)) != MaxMatching<SmartGraph>::EVEN ||
+ mm.status(graph.v(e)) != MaxMatching<SmartGraph>::MATCHED,
+ "Wrong Gallai-Edmonds decomposition");
+
+ check(mm.status(graph.v(e)) != MaxMatching<SmartGraph>::EVEN ||
+ mm.status(graph.u(e)) != MaxMatching<SmartGraph>::MATCHED,
+ "Wrong Gallai-Edmonds decomposition");
+
+ if (mm.status(graph.u(e)) != MaxMatching<SmartGraph>::ODD &&
+ mm.status(graph.v(e)) != MaxMatching<SmartGraph>::ODD) {
+ comp.join(graph.u(e), graph.v(e));
+ }
+ }
+
+ std::set<int> comp_root;
+ int odd_comp_num = 0;
+ for (NodeIt n(graph); n != INVALID; ++n) {
+ if (mm.status(n) != MaxMatching<SmartGraph>::ODD) {
+ int root = comp.find(n);
+ if (comp_root.find(root) == comp_root.end()) {
+ comp_root.insert(root);
+ if (comp.size(n) % 2 == 1) {
+ ++odd_comp_num;
+ }
+ }
+ }
+ }
+
+ check(mm.matchingSize() == num, "Wrong matching");
+ check(2 * num == countNodes(graph) - (odd_comp_num - barrier_num),
+ "Wrong matching");
+ return;
+}
+
+void checkWeightedMatching(const SmartGraph& graph,
+ const SmartGraph::EdgeMap<int>& weight,
+ const MaxWeightedMatching<SmartGraph>& mwm) {
+ for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
+ if (graph.u(e) == graph.v(e)) continue;
+ int rw = mwm.nodeValue(graph.u(e)) + mwm.nodeValue(graph.v(e));
+
+ for (int i = 0; i < mwm.blossomNum(); ++i) {
+ bool s = false, t = false;
+ for (MaxWeightedMatching<SmartGraph>::BlossomIt n(mwm, i);
+ n != INVALID; ++n) {
+ if (graph.u(e) == n) s = true;
+ if (graph.v(e) == n) t = true;
+ }
+ if (s == true && t == true) {
+ rw += mwm.blossomValue(i);
+ }
+ }
+ rw -= weight[e] * mwm.dualScale;
+
+ check(rw >= 0, "Negative reduced weight");
+ check(rw == 0 || !mwm.matching(e),
+ "Non-zero reduced weight on matching edge");
+ }
+
+ int pv = 0;
+ for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
+ if (mwm.matching(n) != INVALID) {
+ check(mwm.nodeValue(n) >= 0, "Invalid node value");
+ pv += weight[mwm.matching(n)];
+ SmartGraph::Node o = graph.target(mwm.matching(n));
+ check(mwm.mate(n) == o, "Invalid matching");
+ check(mwm.matching(n) == graph.oppositeArc(mwm.matching(o)),
+ "Invalid matching");
+ } else {
+ check(mwm.mate(n) == INVALID, "Invalid matching");
+ check(mwm.nodeValue(n) == 0, "Invalid matching");
+ }
+ }
+
+ int dv = 0;
+ for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
+ dv += mwm.nodeValue(n);
+ }
+
+ for (int i = 0; i < mwm.blossomNum(); ++i) {
+ check(mwm.blossomValue(i) >= 0, "Invalid blossom value");
+ check(mwm.blossomSize(i) % 2 == 1, "Even blossom size");
+ dv += mwm.blossomValue(i) * ((mwm.blossomSize(i) - 1) / 2);
+ }
+
+ check(pv * mwm.dualScale == dv * 2, "Wrong duality");
+
+ return;
+}
+
+void checkWeightedPerfectMatching(const SmartGraph& graph,
+ const SmartGraph::EdgeMap<int>& weight,
+ const MaxWeightedPerfectMatching<SmartGraph>& mwpm) {
+ for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
+ if (graph.u(e) == graph.v(e)) continue;
+ int rw = mwpm.nodeValue(graph.u(e)) + mwpm.nodeValue(graph.v(e));
+
+ for (int i = 0; i < mwpm.blossomNum(); ++i) {
+ bool s = false, t = false;
+ for (MaxWeightedPerfectMatching<SmartGraph>::BlossomIt n(mwpm, i);
+ n != INVALID; ++n) {
+ if (graph.u(e) == n) s = true;
+ if (graph.v(e) == n) t = true;
+ }
+ if (s == true && t == true) {
+ rw += mwpm.blossomValue(i);
+ }
+ }
+ rw -= weight[e] * mwpm.dualScale;
+
+ check(rw >= 0, "Negative reduced weight");
+ check(rw == 0 || !mwpm.matching(e),
+ "Non-zero reduced weight on matching edge");
+ }
+
+ int pv = 0;
+ for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
+ check(mwpm.matching(n) != INVALID, "Non perfect");
+ pv += weight[mwpm.matching(n)];
+ SmartGraph::Node o = graph.target(mwpm.matching(n));
+ check(mwpm.mate(n) == o, "Invalid matching");
+ check(mwpm.matching(n) == graph.oppositeArc(mwpm.matching(o)),
+ "Invalid matching");
+ }
+
+ int dv = 0;
+ for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
+ dv += mwpm.nodeValue(n);
+ }
+
+ for (int i = 0; i < mwpm.blossomNum(); ++i) {
+ check(mwpm.blossomValue(i) >= 0, "Invalid blossom value");
+ check(mwpm.blossomSize(i) % 2 == 1, "Even blossom size");
+ dv += mwpm.blossomValue(i) * ((mwpm.blossomSize(i) - 1) / 2);
+ }
+
+ check(pv * mwpm.dualScale == dv * 2, "Wrong duality");
+
+ return;
+}
+
+
+int main() {
+
+ for (int i = 0; i < lgfn; ++i) {
+ SmartGraph graph;
+ SmartGraph::EdgeMap<int> weight(graph);
+
+ istringstream lgfs(lgf[i]);
+ graphReader(graph, lgfs).
+ edgeMap("weight", weight).run();
+
+ MaxMatching<SmartGraph> mm(graph);
+ mm.run();
+ checkMatching(graph, mm);
+
+ MaxWeightedMatching<SmartGraph> mwm(graph, weight);
+ mwm.run();
+ checkWeightedMatching(graph, weight, mwm);
+
+ MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
+ bool perfect = mwpm.run();
+
+ check(perfect == (mm.matchingSize() * 2 == countNodes(graph)),
+ "Perfect matching found");
+
+ if (perfect) {
+ checkWeightedPerfectMatching(graph, weight, mwpm);
+ }
+ }
+
+ return 0;
+}
diff -r f63e87b9748e -r 0ba8dfce7259 test/max_matching_test.cc
--- a/test/max_matching_test.cc Tue Apr 21 10:34:49 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,310 +0,0 @@
-/* -*- mode: C++; indent-tabs-mode: nil; -*-
- *
- * This file is a part of LEMON, a generic C++ optimization library.
- *
- * Copyright (C) 2003-2009
- * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
- * (Egervary Research Group on Combinatorial Optimization, EGRES).
- *
- * Permission to use, modify and distribute this software is granted
- * provided that this copyright notice appears in all copies. For
- * precise terms see the accompanying LICENSE file.
- *
- * This software is provided "AS IS" with no warranty of any kind,
- * express or implied, and with no claim as to its suitability for any
- * purpose.
- *
- */
-
-#include <iostream>
-#include <sstream>
-#include <vector>
-#include <queue>
-#include <lemon/math.h>
-#include <cstdlib>
-
-#include <lemon/max_matching.h>
-#include <lemon/smart_graph.h>
-#include <lemon/lgf_reader.h>
-
-#include "test_tools.h"
-
-using namespace std;
-using namespace lemon;
-
-GRAPH_TYPEDEFS(SmartGraph);
-
-
-const int lgfn = 3;
-const std::string lgf[lgfn] = {
- "@nodes\n"
- "label\n"
- "0\n"
- "1\n"
- "2\n"
- "3\n"
- "4\n"
- "5\n"
- "6\n"
- "7\n"
- "@edges\n"
- " label weight\n"
- "7 4 0 984\n"
- "0 7 1 73\n"
- "7 1 2 204\n"
- "2 3 3 583\n"
- "2 7 4 565\n"
- "2 1 5 582\n"
- "0 4 6 551\n"
- "2 5 7 385\n"
- "1 5 8 561\n"
- "5 3 9 484\n"
- "7 5 10 904\n"
- "3 6 11 47\n"
- "7 6 12 888\n"
- "3 0 13 747\n"
- "6 1 14 310\n",
-
- "@nodes\n"
- "label\n"
- "0\n"
- "1\n"
- "2\n"
- "3\n"
- "4\n"
- "5\n"
- "6\n"
- "7\n"
- "@edges\n"
- " label weight\n"
- "2 5 0 710\n"
- "0 5 1 241\n"
- "2 4 2 856\n"
- "2 6 3 762\n"
- "4 1 4 747\n"
- "6 1 5 962\n"
- "4 7 6 723\n"
- "1 7 7 661\n"
- "2 3 8 376\n"
- "1 0 9 416\n"
- "6 7 10 391\n",
-
- "@nodes\n"
- "label\n"
- "0\n"
- "1\n"
- "2\n"
- "3\n"
- "4\n"
- "5\n"
- "6\n"
- "7\n"
- "@edges\n"
- " label weight\n"
- "6 2 0 553\n"
- "0 7 1 653\n"
- "6 3 2 22\n"
- "4 7 3 846\n"
- "7 2 4 981\n"
- "7 6 5 250\n"
- "5 2 6 539\n",
-};
-
-void checkMatching(const SmartGraph& graph,
- const MaxMatching<SmartGraph>& mm) {
- int num = 0;
-
- IntNodeMap comp_index(graph);
- UnionFind<IntNodeMap> comp(comp_index);
-
- int barrier_num = 0;
-
- for (NodeIt n(graph); n != INVALID; ++n) {
- check(mm.decomposition(n) == MaxMatching<SmartGraph>::EVEN ||
- mm.matching(n) != INVALID, "Wrong Gallai-Edmonds decomposition");
- if (mm.decomposition(n) == MaxMatching<SmartGraph>::ODD) {
- ++barrier_num;
- } else {
- comp.insert(n);
- }
- }
-
- for (EdgeIt e(graph); e != INVALID; ++e) {
- if (mm.matching(e)) {
- check(e == mm.matching(graph.u(e)), "Wrong matching");
- check(e == mm.matching(graph.v(e)), "Wrong matching");
- ++num;
- }
- check(mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::EVEN ||
- mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::MATCHED,
- "Wrong Gallai-Edmonds decomposition");
-
- check(mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::EVEN ||
- mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::MATCHED,
- "Wrong Gallai-Edmonds decomposition");
-
- if (mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::ODD &&
- mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::ODD) {
- comp.join(graph.u(e), graph.v(e));
- }
- }
-
- std::set<int> comp_root;
- int odd_comp_num = 0;
- for (NodeIt n(graph); n != INVALID; ++n) {
- if (mm.decomposition(n) != MaxMatching<SmartGraph>::ODD) {
- int root = comp.find(n);
- if (comp_root.find(root) == comp_root.end()) {
- comp_root.insert(root);
- if (comp.size(n) % 2 == 1) {
- ++odd_comp_num;
- }
- }
- }
- }
-
- check(mm.matchingSize() == num, "Wrong matching");
- check(2 * num == countNodes(graph) - (odd_comp_num - barrier_num),
- "Wrong matching");
- return;
-}
-
-void checkWeightedMatching(const SmartGraph& graph,
- const SmartGraph::EdgeMap<int>& weight,
- const MaxWeightedMatching<SmartGraph>& mwm) {
- for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
- if (graph.u(e) == graph.v(e)) continue;
- int rw = mwm.nodeValue(graph.u(e)) + mwm.nodeValue(graph.v(e));
-
- for (int i = 0; i < mwm.blossomNum(); ++i) {
- bool s = false, t = false;
- for (MaxWeightedMatching<SmartGraph>::BlossomIt n(mwm, i);
- n != INVALID; ++n) {
- if (graph.u(e) == n) s = true;
- if (graph.v(e) == n) t = true;
- }
- if (s == true && t == true) {
- rw += mwm.blossomValue(i);
- }
- }
- rw -= weight[e] * mwm.dualScale;
-
- check(rw >= 0, "Negative reduced weight");
- check(rw == 0 || !mwm.matching(e),
- "Non-zero reduced weight on matching edge");
- }
-
- int pv = 0;
- for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
- if (mwm.matching(n) != INVALID) {
- check(mwm.nodeValue(n) >= 0, "Invalid node value");
- pv += weight[mwm.matching(n)];
- SmartGraph::Node o = graph.target(mwm.matching(n));
- check(mwm.mate(n) == o, "Invalid matching");
- check(mwm.matching(n) == graph.oppositeArc(mwm.matching(o)),
- "Invalid matching");
- } else {
- check(mwm.mate(n) == INVALID, "Invalid matching");
- check(mwm.nodeValue(n) == 0, "Invalid matching");
- }
- }
-
- int dv = 0;
- for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
- dv += mwm.nodeValue(n);
- }
-
- for (int i = 0; i < mwm.blossomNum(); ++i) {
- check(mwm.blossomValue(i) >= 0, "Invalid blossom value");
- check(mwm.blossomSize(i) % 2 == 1, "Even blossom size");
- dv += mwm.blossomValue(i) * ((mwm.blossomSize(i) - 1) / 2);
- }
-
- check(pv * mwm.dualScale == dv * 2, "Wrong duality");
-
- return;
-}
-
-void checkWeightedPerfectMatching(const SmartGraph& graph,
- const SmartGraph::EdgeMap<int>& weight,
- const MaxWeightedPerfectMatching<SmartGraph>& mwpm) {
- for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
- if (graph.u(e) == graph.v(e)) continue;
- int rw = mwpm.nodeValue(graph.u(e)) + mwpm.nodeValue(graph.v(e));
-
- for (int i = 0; i < mwpm.blossomNum(); ++i) {
- bool s = false, t = false;
- for (MaxWeightedPerfectMatching<SmartGraph>::BlossomIt n(mwpm, i);
- n != INVALID; ++n) {
- if (graph.u(e) == n) s = true;
- if (graph.v(e) == n) t = true;
- }
- if (s == true && t == true) {
- rw += mwpm.blossomValue(i);
- }
- }
- rw -= weight[e] * mwpm.dualScale;
-
- check(rw >= 0, "Negative reduced weight");
- check(rw == 0 || !mwpm.matching(e),
- "Non-zero reduced weight on matching edge");
- }
-
- int pv = 0;
- for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
- check(mwpm.matching(n) != INVALID, "Non perfect");
- pv += weight[mwpm.matching(n)];
- SmartGraph::Node o = graph.target(mwpm.matching(n));
- check(mwpm.mate(n) == o, "Invalid matching");
- check(mwpm.matching(n) == graph.oppositeArc(mwpm.matching(o)),
- "Invalid matching");
- }
-
- int dv = 0;
- for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
- dv += mwpm.nodeValue(n);
- }
-
- for (int i = 0; i < mwpm.blossomNum(); ++i) {
- check(mwpm.blossomValue(i) >= 0, "Invalid blossom value");
- check(mwpm.blossomSize(i) % 2 == 1, "Even blossom size");
- dv += mwpm.blossomValue(i) * ((mwpm.blossomSize(i) - 1) / 2);
- }
-
- check(pv * mwpm.dualScale == dv * 2, "Wrong duality");
-
- return;
-}
-
-
-int main() {
-
- for (int i = 0; i < lgfn; ++i) {
- SmartGraph graph;
- SmartGraph::EdgeMap<int> weight(graph);
-
- istringstream lgfs(lgf[i]);
- graphReader(graph, lgfs).
- edgeMap("weight", weight).run();
-
- MaxMatching<SmartGraph> mm(graph);
- mm.run();
- checkMatching(graph, mm);
-
- MaxWeightedMatching<SmartGraph> mwm(graph, weight);
- mwm.run();
- checkWeightedMatching(graph, weight, mwm);
-
- MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
- bool perfect = mwpm.run();
-
- check(perfect == (mm.matchingSize() * 2 == countNodes(graph)),
- "Perfect matching found");
-
- if (perfect) {
- checkWeightedPerfectMatching(graph, weight, mwpm);
- }
- }
-
- return 0;
-}
diff -r f63e87b9748e -r 0ba8dfce7259 tools/dimacs-solver.cc
--- a/tools/dimacs-solver.cc Tue Apr 21 10:34:49 2009 +0100
+++ b/tools/dimacs-solver.cc Tue Apr 21 13:08:19 2009 +0100
@@ -42,7 +42,7 @@
#include <lemon/dijkstra.h>
#include <lemon/preflow.h>
-#include <lemon/max_matching.h>
+#include <lemon/matching.h>
using namespace lemon;
typedef SmartDigraph Digraph;