deba@326: /* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@326:  *
deba@326:  * This file is a part of LEMON, a generic C++ optimization library.
deba@326:  *
alpar@1092:  * Copyright (C) 2003-2013
deba@326:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@326:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@326:  *
deba@326:  * Permission to use, modify and distribute this software is granted
deba@326:  * provided that this copyright notice appears in all copies. For
deba@326:  * precise terms see the accompanying LICENSE file.
deba@326:  *
deba@326:  * This software is provided "AS IS" with no warranty of any kind,
deba@326:  * express or implied, and with no claim as to its suitability for any
deba@326:  * purpose.
deba@326:  *
deba@326:  */
deba@326: 
deba@868: #ifndef LEMON_MATCHING_H
deba@868: #define LEMON_MATCHING_H
deba@326: 
deba@326: #include <vector>
deba@326: #include <queue>
deba@326: #include <set>
deba@326: #include <limits>
deba@326: 
deba@326: #include <lemon/core.h>
deba@326: #include <lemon/unionfind.h>
deba@326: #include <lemon/bin_heap.h>
deba@326: #include <lemon/maps.h>
deba@870: #include <lemon/fractional_matching.h>
deba@326: 
deba@326: ///\ingroup matching
deba@326: ///\file
deba@327: ///\brief Maximum matching algorithms in general graphs.
deba@326: 
deba@326: namespace lemon {
deba@326: 
deba@327:   /// \ingroup matching
deba@326:   ///
kpeter@590:   /// \brief Maximum cardinality matching in general graphs
deba@326:   ///
kpeter@590:   /// This class implements Edmonds' alternating forest matching algorithm
kpeter@593:   /// for finding a maximum cardinality matching in a general undirected graph.
deba@868:   /// It can be started from an arbitrary initial matching
kpeter@590:   /// (the default is the empty one).
deba@326:   ///
alpar@330:   /// The dual solution of the problem is a map of the nodes to
kpeter@590:   /// \ref MaxMatching::Status "Status", having values \c EVEN (or \c D),
kpeter@590:   /// \c ODD (or \c A) and \c MATCHED (or \c C) defining the Gallai-Edmonds
kpeter@590:   /// decomposition of the graph. The nodes in \c EVEN/D induce a subgraph
kpeter@590:   /// with factor-critical components, the nodes in \c ODD/A form the
kpeter@590:   /// canonical barrier, and the nodes in \c MATCHED/C induce a graph having
kpeter@590:   /// a perfect matching. The number of the factor-critical components
deba@327:   /// minus the number of barrier nodes is a lower bound on the
alpar@330:   /// unmatched nodes, and the matching is optimal if and only if this bound is
kpeter@593:   /// tight. This decomposition can be obtained using \ref status() or
kpeter@593:   /// \ref statusMap() after running the algorithm.
deba@326:   ///
kpeter@593:   /// \tparam GR The undirected graph type the algorithm runs on.
kpeter@559:   template <typename GR>
deba@326:   class MaxMatching {
deba@327:   public:
deba@327: 
kpeter@590:     /// The graph type of the algorithm
kpeter@559:     typedef GR Graph;
kpeter@593:     /// The type of the matching map
deba@327:     typedef typename Graph::template NodeMap<typename Graph::Arc>
deba@327:     MatchingMap;
deba@327: 
kpeter@590:     ///\brief Status constants for Gallai-Edmonds decomposition.
deba@327:     ///
deba@868:     ///These constants are used for indicating the Gallai-Edmonds
kpeter@590:     ///decomposition of a graph. The nodes with status \c EVEN (or \c D)
kpeter@590:     ///induce a subgraph with factor-critical components, the nodes with
kpeter@590:     ///status \c ODD (or \c A) form the canonical barrier, and the nodes
deba@868:     ///with status \c MATCHED (or \c C) induce a subgraph having a
kpeter@590:     ///perfect matching.
deba@327:     enum Status {
kpeter@590:       EVEN = 1,       ///< = 1. (\c D is an alias for \c EVEN.)
kpeter@590:       D = 1,
kpeter@590:       MATCHED = 0,    ///< = 0. (\c C is an alias for \c MATCHED.)
kpeter@590:       C = 0,
kpeter@590:       ODD = -1,       ///< = -1. (\c A is an alias for \c ODD.)
kpeter@590:       A = -1,
kpeter@590:       UNMATCHED = -2  ///< = -2.
deba@327:     };
deba@327: 
kpeter@593:     /// The type of the status map
deba@327:     typedef typename Graph::template NodeMap<Status> StatusMap;
deba@327: 
deba@327:   private:
deba@326: 
deba@326:     TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@326: 
deba@327:     typedef UnionFindEnum<IntNodeMap> BlossomSet;
deba@327:     typedef ExtendFindEnum<IntNodeMap> TreeSet;
deba@327:     typedef RangeMap<Node> NodeIntMap;
deba@327:     typedef MatchingMap EarMap;
deba@327:     typedef std::vector<Node> NodeQueue;
deba@327: 
deba@327:     const Graph& _graph;
deba@327:     MatchingMap* _matching;
deba@327:     StatusMap* _status;
deba@327: 
deba@327:     EarMap* _ear;
deba@327: 
deba@327:     IntNodeMap* _blossom_set_index;
deba@327:     BlossomSet* _blossom_set;
deba@327:     NodeIntMap* _blossom_rep;
deba@327: 
deba@327:     IntNodeMap* _tree_set_index;
deba@327:     TreeSet* _tree_set;
deba@327: 
deba@327:     NodeQueue _node_queue;
deba@327:     int _process, _postpone, _last;
deba@327: 
deba@1203:     int _node_num, _unmatched;
deba@327: 
deba@327:   private:
deba@327: 
deba@327:     void createStructures() {
deba@327:       _node_num = countNodes(_graph);
deba@327:       if (!_matching) {
deba@327:         _matching = new MatchingMap(_graph);
deba@327:       }
deba@327:       if (!_status) {
deba@327:         _status = new StatusMap(_graph);
deba@327:       }
deba@327:       if (!_ear) {
deba@327:         _ear = new EarMap(_graph);
deba@327:       }
deba@327:       if (!_blossom_set) {
deba@327:         _blossom_set_index = new IntNodeMap(_graph);
deba@327:         _blossom_set = new BlossomSet(*_blossom_set_index);
deba@327:       }
deba@327:       if (!_blossom_rep) {
deba@327:         _blossom_rep = new NodeIntMap(_node_num);
deba@327:       }
deba@327:       if (!_tree_set) {
deba@327:         _tree_set_index = new IntNodeMap(_graph);
deba@327:         _tree_set = new TreeSet(*_tree_set_index);
deba@327:       }
deba@327:       _node_queue.resize(_node_num);
deba@327:     }
deba@327: 
deba@327:     void destroyStructures() {
deba@327:       if (_matching) {
deba@327:         delete _matching;
deba@327:       }
deba@327:       if (_status) {
deba@327:         delete _status;
deba@327:       }
deba@327:       if (_ear) {
deba@327:         delete _ear;
deba@327:       }
deba@327:       if (_blossom_set) {
deba@327:         delete _blossom_set;
deba@327:         delete _blossom_set_index;
deba@327:       }
deba@327:       if (_blossom_rep) {
deba@327:         delete _blossom_rep;
deba@327:       }
deba@327:       if (_tree_set) {
deba@327:         delete _tree_set_index;
deba@327:         delete _tree_set;
deba@327:       }
deba@327:     }
deba@327: 
deba@327:     void processDense(const Node& n) {
deba@327:       _process = _postpone = _last = 0;
deba@327:       _node_queue[_last++] = n;
deba@327: 
deba@327:       while (_process != _last) {
deba@327:         Node u = _node_queue[_process++];
deba@327:         for (OutArcIt a(_graph, u); a != INVALID; ++a) {
deba@327:           Node v = _graph.target(a);
deba@327:           if ((*_status)[v] == MATCHED) {
deba@327:             extendOnArc(a);
deba@327:           } else if ((*_status)[v] == UNMATCHED) {
deba@327:             augmentOnArc(a);
deba@1203:             --_unmatched;
deba@327:             return;
deba@327:           }
deba@327:         }
deba@327:       }
deba@327: 
deba@327:       while (_postpone != _last) {
deba@327:         Node u = _node_queue[_postpone++];
deba@327: 
deba@327:         for (OutArcIt a(_graph, u); a != INVALID ; ++a) {
deba@327:           Node v = _graph.target(a);
deba@327: 
deba@327:           if ((*_status)[v] == EVEN) {
deba@327:             if (_blossom_set->find(u) != _blossom_set->find(v)) {
deba@327:               shrinkOnEdge(a);
deba@327:             }
deba@327:           }
deba@327: 
deba@327:           while (_process != _last) {
deba@327:             Node w = _node_queue[_process++];
deba@327:             for (OutArcIt b(_graph, w); b != INVALID; ++b) {
deba@327:               Node x = _graph.target(b);
deba@327:               if ((*_status)[x] == MATCHED) {
deba@327:                 extendOnArc(b);
deba@327:               } else if ((*_status)[x] == UNMATCHED) {
deba@327:                 augmentOnArc(b);
deba@1203:                 --_unmatched;
deba@327:                 return;
deba@327:               }
deba@327:             }
deba@327:           }
deba@327:         }
deba@327:       }
deba@327:     }
deba@327: 
deba@327:     void processSparse(const Node& n) {
deba@327:       _process = _last = 0;
deba@327:       _node_queue[_last++] = n;
deba@327:       while (_process != _last) {
deba@327:         Node u = _node_queue[_process++];
deba@327:         for (OutArcIt a(_graph, u); a != INVALID; ++a) {
deba@327:           Node v = _graph.target(a);
deba@327: 
deba@327:           if ((*_status)[v] == EVEN) {
deba@327:             if (_blossom_set->find(u) != _blossom_set->find(v)) {
deba@327:               shrinkOnEdge(a);
deba@327:             }
deba@327:           } else if ((*_status)[v] == MATCHED) {
deba@327:             extendOnArc(a);
deba@327:           } else if ((*_status)[v] == UNMATCHED) {
deba@327:             augmentOnArc(a);
deba@1203:             --_unmatched;
deba@327:             return;
deba@327:           }
deba@327:         }
deba@327:       }
deba@327:     }
deba@327: 
deba@327:     void shrinkOnEdge(const Edge& e) {
deba@327:       Node nca = INVALID;
deba@327: 
deba@327:       {
deba@327:         std::set<Node> left_set, right_set;
deba@327: 
deba@327:         Node left = (*_blossom_rep)[_blossom_set->find(_graph.u(e))];
deba@327:         left_set.insert(left);
deba@327: 
deba@327:         Node right = (*_blossom_rep)[_blossom_set->find(_graph.v(e))];
deba@327:         right_set.insert(right);
deba@327: 
deba@327:         while (true) {
deba@327:           if ((*_matching)[left] == INVALID) break;
deba@327:           left = _graph.target((*_matching)[left]);
deba@327:           left = (*_blossom_rep)[_blossom_set->
deba@327:                                  find(_graph.target((*_ear)[left]))];
deba@327:           if (right_set.find(left) != right_set.end()) {
deba@327:             nca = left;
deba@327:             break;
deba@327:           }
deba@327:           left_set.insert(left);
deba@327: 
deba@327:           if ((*_matching)[right] == INVALID) break;
deba@327:           right = _graph.target((*_matching)[right]);
deba@327:           right = (*_blossom_rep)[_blossom_set->
deba@327:                                   find(_graph.target((*_ear)[right]))];
deba@327:           if (left_set.find(right) != left_set.end()) {
deba@327:             nca = right;
deba@327:             break;
deba@327:           }
deba@327:           right_set.insert(right);
deba@327:         }
deba@327: 
deba@327:         if (nca == INVALID) {
deba@327:           if ((*_matching)[left] == INVALID) {
deba@327:             nca = right;
deba@327:             while (left_set.find(nca) == left_set.end()) {
deba@327:               nca = _graph.target((*_matching)[nca]);
deba@327:               nca =(*_blossom_rep)[_blossom_set->
deba@327:                                    find(_graph.target((*_ear)[nca]))];
deba@327:             }
deba@327:           } else {
deba@327:             nca = left;
deba@327:             while (right_set.find(nca) == right_set.end()) {
deba@327:               nca = _graph.target((*_matching)[nca]);
deba@327:               nca = (*_blossom_rep)[_blossom_set->
deba@327:                                    find(_graph.target((*_ear)[nca]))];
deba@327:             }
deba@327:           }
deba@327:         }
deba@327:       }
deba@327: 
deba@327:       {
deba@327: 
deba@327:         Node node = _graph.u(e);
deba@327:         Arc arc = _graph.direct(e, true);
deba@327:         Node base = (*_blossom_rep)[_blossom_set->find(node)];
deba@327: 
deba@327:         while (base != nca) {
kpeter@581:           (*_ear)[node] = arc;
deba@327: 
deba@327:           Node n = node;
deba@327:           while (n != base) {
deba@327:             n = _graph.target((*_matching)[n]);
deba@327:             Arc a = (*_ear)[n];
deba@327:             n = _graph.target(a);
kpeter@581:             (*_ear)[n] = _graph.oppositeArc(a);
deba@327:           }
deba@327:           node = _graph.target((*_matching)[base]);
deba@327:           _tree_set->erase(base);
deba@327:           _tree_set->erase(node);
deba@327:           _blossom_set->insert(node, _blossom_set->find(base));
kpeter@581:           (*_status)[node] = EVEN;
deba@327:           _node_queue[_last++] = node;
deba@327:           arc = _graph.oppositeArc((*_ear)[node]);
deba@327:           node = _graph.target((*_ear)[node]);
deba@327:           base = (*_blossom_rep)[_blossom_set->find(node)];
deba@327:           _blossom_set->join(_graph.target(arc), base);
deba@327:         }
deba@327:       }
deba@327: 
kpeter@581:       (*_blossom_rep)[_blossom_set->find(nca)] = nca;
deba@327: 
deba@327:       {
deba@327: 
deba@327:         Node node = _graph.v(e);
deba@327:         Arc arc = _graph.direct(e, false);
deba@327:         Node base = (*_blossom_rep)[_blossom_set->find(node)];
deba@327: 
deba@327:         while (base != nca) {
kpeter@581:           (*_ear)[node] = arc;
deba@327: 
deba@327:           Node n = node;
deba@327:           while (n != base) {
deba@327:             n = _graph.target((*_matching)[n]);
deba@327:             Arc a = (*_ear)[n];
deba@327:             n = _graph.target(a);
kpeter@581:             (*_ear)[n] = _graph.oppositeArc(a);
deba@327:           }
deba@327:           node = _graph.target((*_matching)[base]);
deba@327:           _tree_set->erase(base);
deba@327:           _tree_set->erase(node);
deba@327:           _blossom_set->insert(node, _blossom_set->find(base));
kpeter@581:           (*_status)[node] = EVEN;
deba@327:           _node_queue[_last++] = node;
deba@327:           arc = _graph.oppositeArc((*_ear)[node]);
deba@327:           node = _graph.target((*_ear)[node]);
deba@327:           base = (*_blossom_rep)[_blossom_set->find(node)];
deba@327:           _blossom_set->join(_graph.target(arc), base);
deba@327:         }
deba@327:       }
deba@327: 
kpeter@581:       (*_blossom_rep)[_blossom_set->find(nca)] = nca;
deba@327:     }
deba@327: 
deba@327:     void extendOnArc(const Arc& a) {
deba@327:       Node base = _graph.source(a);
deba@327:       Node odd = _graph.target(a);
deba@327: 
kpeter@581:       (*_ear)[odd] = _graph.oppositeArc(a);
deba@327:       Node even = _graph.target((*_matching)[odd]);
kpeter@581:       (*_blossom_rep)[_blossom_set->insert(even)] = even;
kpeter@581:       (*_status)[odd] = ODD;
kpeter@581:       (*_status)[even] = EVEN;
deba@327:       int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(base)]);
deba@327:       _tree_set->insert(odd, tree);
deba@327:       _tree_set->insert(even, tree);
deba@327:       _node_queue[_last++] = even;
deba@327: 
deba@327:     }
deba@327: 
deba@327:     void augmentOnArc(const Arc& a) {
deba@327:       Node even = _graph.source(a);
deba@327:       Node odd = _graph.target(a);
deba@327: 
deba@327:       int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(even)]);
deba@327: 
kpeter@581:       (*_matching)[odd] = _graph.oppositeArc(a);
kpeter@581:       (*_status)[odd] = MATCHED;
deba@327: 
deba@327:       Arc arc = (*_matching)[even];
kpeter@581:       (*_matching)[even] = a;
deba@327: 
deba@327:       while (arc != INVALID) {
deba@327:         odd = _graph.target(arc);
deba@327:         arc = (*_ear)[odd];
deba@327:         even = _graph.target(arc);
kpeter@581:         (*_matching)[odd] = arc;
deba@327:         arc = (*_matching)[even];
kpeter@581:         (*_matching)[even] = _graph.oppositeArc((*_matching)[odd]);
deba@327:       }
deba@327: 
deba@327:       for (typename TreeSet::ItemIt it(*_tree_set, tree);
deba@327:            it != INVALID; ++it) {
deba@327:         if ((*_status)[it] == ODD) {
kpeter@581:           (*_status)[it] = MATCHED;
deba@327:         } else {
deba@327:           int blossom = _blossom_set->find(it);
deba@327:           for (typename BlossomSet::ItemIt jt(*_blossom_set, blossom);
deba@327:                jt != INVALID; ++jt) {
kpeter@581:             (*_status)[jt] = MATCHED;
deba@327:           }
deba@327:           _blossom_set->eraseClass(blossom);
deba@327:         }
deba@327:       }
deba@327:       _tree_set->eraseClass(tree);
deba@327: 
deba@327:     }
deba@326: 
deba@326:   public:
deba@326: 
deba@327:     /// \brief Constructor
deba@326:     ///
deba@327:     /// Constructor.
deba@327:     MaxMatching(const Graph& graph)
deba@327:       : _graph(graph), _matching(0), _status(0), _ear(0),
deba@327:         _blossom_set_index(0), _blossom_set(0), _blossom_rep(0),
deba@327:         _tree_set_index(0), _tree_set(0) {}
deba@327: 
deba@327:     ~MaxMatching() {
deba@327:       destroyStructures();
deba@327:     }
deba@327: 
kpeter@590:     /// \name Execution Control
alpar@330:     /// The simplest way to execute the algorithm is to use the
kpeter@590:     /// \c run() member function.\n
kpeter@590:     /// If you need better control on the execution, you have to call
kpeter@590:     /// one of the functions \ref init(), \ref greedyInit() or
kpeter@590:     /// \ref matchingInit() first, then you can start the algorithm with
kpeter@590:     /// \ref startSparse() or \ref startDense().
deba@327: 
deba@327:     ///@{
deba@327: 
kpeter@590:     /// \brief Set the initial matching to the empty matching.
deba@326:     ///
kpeter@590:     /// This function sets the initial matching to the empty matching.
deba@326:     void init() {
deba@327:       createStructures();
deba@327:       for(NodeIt n(_graph); n != INVALID; ++n) {
kpeter@581:         (*_matching)[n] = INVALID;
kpeter@581:         (*_status)[n] = UNMATCHED;
deba@326:       }
deba@1203:       _unmatched = _node_num;
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Find an initial matching in a greedy way.
deba@326:     ///
kpeter@590:     /// This function finds an initial matching in a greedy way.
deba@326:     void greedyInit() {
deba@327:       createStructures();
deba@327:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@581:         (*_matching)[n] = INVALID;
kpeter@581:         (*_status)[n] = UNMATCHED;
deba@326:       }
deba@1203:       _unmatched = _node_num;
deba@327:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@327:         if ((*_matching)[n] == INVALID) {
deba@327:           for (OutArcIt a(_graph, n); a != INVALID ; ++a) {
deba@327:             Node v = _graph.target(a);
deba@327:             if ((*_matching)[v] == INVALID && v != n) {
kpeter@581:               (*_matching)[n] = a;
kpeter@581:               (*_status)[n] = MATCHED;
kpeter@581:               (*_matching)[v] = _graph.oppositeArc(a);
kpeter@581:               (*_status)[v] = MATCHED;
deba@1203:               _unmatched -= 2;
deba@326:               break;
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@327: 
kpeter@590:     /// \brief Initialize the matching from a map.
deba@326:     ///
kpeter@590:     /// This function initializes the matching from a \c bool valued edge
kpeter@590:     /// map. This map should have the property that there are no two incident
kpeter@590:     /// edges with \c true value, i.e. it really contains a matching.
kpeter@559:     /// \return \c true if the map contains a matching.
deba@327:     template <typename MatchingMap>
deba@327:     bool matchingInit(const MatchingMap& matching) {
deba@327:       createStructures();
deba@327: 
deba@327:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@581:         (*_matching)[n] = INVALID;
kpeter@581:         (*_status)[n] = UNMATCHED;
deba@326:       }
deba@1203:       _unmatched = _node_num;
deba@327:       for(EdgeIt e(_graph); e!=INVALID; ++e) {
deba@327:         if (matching[e]) {
deba@327: 
deba@327:           Node u = _graph.u(e);
deba@327:           if ((*_matching)[u] != INVALID) return false;
kpeter@581:           (*_matching)[u] = _graph.direct(e, true);
kpeter@581:           (*_status)[u] = MATCHED;
deba@327: 
deba@327:           Node v = _graph.v(e);
deba@327:           if ((*_matching)[v] != INVALID) return false;
kpeter@581:           (*_matching)[v] = _graph.direct(e, false);
kpeter@581:           (*_status)[v] = MATCHED;
deba@1203: 
deba@1203:           _unmatched -= 2;
deba@327:         }
deba@327:       }
deba@327:       return true;
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Start Edmonds' algorithm
deba@326:     ///
deba@1203:     /// This function runs the original Edmonds' algorithm. If the
deba@1203:     /// \c decomposition parameter is set to false, then the Gallai-Edmonds
deba@1203:     /// decomposition is not computed.
kpeter@590:     ///
kpeter@651:     /// \pre \ref init(), \ref greedyInit() or \ref matchingInit() must be
kpeter@590:     /// called before using this function.
deba@1203:     void startSparse(bool decomposition = true) {
deba@1203:       int _unmatched_limit = decomposition ? 0 : 1;
deba@1203:       for(NodeIt n(_graph); _unmatched > _unmatched_limit; ++n) {
deba@327:         if ((*_status)[n] == UNMATCHED) {
deba@327:           (*_blossom_rep)[_blossom_set->insert(n)] = n;
deba@327:           _tree_set->insert(n);
kpeter@581:           (*_status)[n] = EVEN;
deba@1203:           --_unmatched;
deba@327:           processSparse(n);
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@868:     /// \brief Start Edmonds' algorithm with a heuristic improvement
kpeter@590:     /// for dense graphs
deba@326:     ///
kpeter@590:     /// This function runs Edmonds' algorithm with a heuristic of postponing
deba@1203:     /// shrinks, therefore resulting in a faster algorithm for dense graphs.  If
deba@1203:     /// the \c decomposition parameter is set to false, then the Gallai-Edmonds
deba@1203:     /// decomposition is not computed.
kpeter@590:     ///
kpeter@651:     /// \pre \ref init(), \ref greedyInit() or \ref matchingInit() must be
kpeter@590:     /// called before using this function.
deba@1203:     void startDense(bool decomposition = true) {
deba@1203:       int _unmatched_limit = decomposition ? 0 : 1;
deba@1203:       for(NodeIt n(_graph); _unmatched > _unmatched_limit; ++n) {
deba@327:         if ((*_status)[n] == UNMATCHED) {
deba@327:           (*_blossom_rep)[_blossom_set->insert(n)] = n;
deba@327:           _tree_set->insert(n);
kpeter@581:           (*_status)[n] = EVEN;
deba@1203:           --_unmatched;
deba@327:           processDense(n);
deba@327:         }
deba@327:       }
deba@327:     }
deba@327: 
deba@327: 
kpeter@590:     /// \brief Run Edmonds' algorithm
deba@327:     ///
deba@868:     /// This function runs Edmonds' algorithm. An additional heuristic of
deba@1203:     /// postponing shrinks is used for relatively dense graphs (for which
deba@1203:     /// <tt>m>=2*n</tt> holds). If the \c decomposition parameter is set to
deba@1203:     /// false, then the Gallai-Edmonds decomposition is not computed. In some
deba@1203:     /// cases, this can speed up the algorithm significantly, especially when a
deba@1203:     /// maximum matching is computed in a dense graph with odd number of nodes.
deba@1203:     void run(bool decomposition = true) {
deba@327:       if (countEdges(_graph) < 2 * countNodes(_graph)) {
deba@326:         greedyInit();
deba@1203:         startSparse(decomposition);
deba@326:       } else {
deba@326:         init();
deba@1203:         startDense(decomposition);
deba@326:       }
deba@326:     }
deba@326: 
deba@327:     /// @}
deba@327: 
kpeter@590:     /// \name Primal Solution
kpeter@590:     /// Functions to get the primal solution, i.e. the maximum matching.
deba@327: 
deba@327:     /// @{
deba@326: 
kpeter@590:     /// \brief Return the size (cardinality) of the matching.
deba@326:     ///
deba@868:     /// This function returns the size (cardinality) of the current matching.
kpeter@590:     /// After run() it returns the size of the maximum matching in the graph.
deba@327:     int matchingSize() const {
deba@327:       int size = 0;
deba@327:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@327:         if ((*_matching)[n] != INVALID) {
deba@327:           ++size;
deba@326:         }
deba@326:       }
deba@327:       return size / 2;
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Return \c true if the given edge is in the matching.
deba@327:     ///
deba@868:     /// This function returns \c true if the given edge is in the current
kpeter@590:     /// matching.
deba@327:     bool matching(const Edge& edge) const {
deba@327:       return edge == (*_matching)[_graph.u(edge)];
deba@327:     }
deba@327: 
kpeter@590:     /// \brief Return the matching arc (or edge) incident to the given node.
deba@327:     ///
kpeter@590:     /// This function returns the matching arc (or edge) incident to the
deba@868:     /// given node in the current matching or \c INVALID if the node is
kpeter@590:     /// not covered by the matching.
deba@327:     Arc matching(const Node& n) const {
deba@327:       return (*_matching)[n];
deba@327:     }
deba@326: 
kpeter@593:     /// \brief Return a const reference to the matching map.
kpeter@593:     ///
kpeter@593:     /// This function returns a const reference to a node map that stores
kpeter@593:     /// the matching arc (or edge) incident to each node.
kpeter@593:     const MatchingMap& matchingMap() const {
kpeter@593:       return *_matching;
kpeter@593:     }
kpeter@593: 
kpeter@590:     /// \brief Return the mate of the given node.
deba@326:     ///
deba@868:     /// This function returns the mate of the given node in the current
kpeter@590:     /// matching or \c INVALID if the node is not covered by the matching.
deba@327:     Node mate(const Node& n) const {
deba@327:       return (*_matching)[n] != INVALID ?
deba@327:         _graph.target((*_matching)[n]) : INVALID;
deba@326:     }
deba@326: 
deba@327:     /// @}
deba@327: 
kpeter@590:     /// \name Dual Solution
deba@868:     /// Functions to get the dual solution, i.e. the Gallai-Edmonds
kpeter@590:     /// decomposition.
deba@327: 
deba@327:     /// @{
deba@326: 
kpeter@590:     /// \brief Return the status of the given node in the Edmonds-Gallai
deba@326:     /// decomposition.
deba@326:     ///
kpeter@590:     /// This function returns the \ref Status "status" of the given node
kpeter@590:     /// in the Edmonds-Gallai decomposition.
kpeter@593:     Status status(const Node& n) const {
deba@327:       return (*_status)[n];
deba@326:     }
deba@326: 
kpeter@593:     /// \brief Return a const reference to the status map, which stores
kpeter@593:     /// the Edmonds-Gallai decomposition.
kpeter@593:     ///
kpeter@593:     /// This function returns a const reference to a node map that stores the
kpeter@593:     /// \ref Status "status" of each node in the Edmonds-Gallai decomposition.
kpeter@593:     const StatusMap& statusMap() const {
kpeter@593:       return *_status;
kpeter@593:     }
kpeter@593: 
kpeter@590:     /// \brief Return \c true if the given node is in the barrier.
deba@326:     ///
kpeter@590:     /// This function returns \c true if the given node is in the barrier.
deba@327:     bool barrier(const Node& n) const {
deba@327:       return (*_status)[n] == ODD;
deba@326:     }
deba@326: 
deba@327:     /// @}
deba@326: 
deba@326:   };
deba@326: 
deba@326:   /// \ingroup matching
deba@326:   ///
deba@326:   /// \brief Weighted matching in general graphs
deba@326:   ///
deba@326:   /// This class provides an efficient implementation of Edmond's
deba@326:   /// maximum weighted matching algorithm. The implementation is based
deba@326:   /// on extensive use of priority queues and provides
kpeter@559:   /// \f$O(nm\log n)\f$ time complexity.
deba@326:   ///
deba@868:   /// The maximum weighted matching problem is to find a subset of the
deba@868:   /// edges in an undirected graph with maximum overall weight for which
kpeter@590:   /// each node has at most one incident edge.
kpeter@590:   /// It can be formulated with the following linear program.
deba@326:   /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]
deba@327:   /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
deba@327:       \quad \forall B\in\mathcal{O}\f] */
deba@326:   /// \f[x_e \ge 0\quad \forall e\in E\f]
deba@326:   /// \f[\max \sum_{e\in E}x_ew_e\f]
deba@327:   /// where \f$\delta(X)\f$ is the set of edges incident to a node in
deba@327:   /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
deba@327:   /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
deba@327:   /// subsets of the nodes.
deba@326:   ///
deba@326:   /// The algorithm calculates an optimal matching and a proof of the
deba@326:   /// optimality. The solution of the dual problem can be used to check
deba@327:   /// the result of the algorithm. The dual linear problem is the
kpeter@590:   /// following.
deba@327:   /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}
deba@327:       z_B \ge w_{uv} \quad \forall uv\in E\f] */
deba@326:   /// \f[y_u \ge 0 \quad \forall u \in V\f]
deba@326:   /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
deba@327:   /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
deba@327:       \frac{\vert B \vert - 1}{2}z_B\f] */
deba@326:   ///
deba@868:   /// The algorithm can be executed with the run() function.
kpeter@590:   /// After it the matching (the primal solution) and the dual solution
deba@868:   /// can be obtained using the query functions and the
deba@868:   /// \ref MaxWeightedMatching::BlossomIt "BlossomIt" nested class,
deba@868:   /// which is able to iterate on the nodes of a blossom.
kpeter@590:   /// If the value type is integer, then the dual solution is multiplied
kpeter@590:   /// by \ref MaxWeightedMatching::dualScale "4".
kpeter@590:   ///
kpeter@593:   /// \tparam GR The undirected graph type the algorithm runs on.
deba@868:   /// \tparam WM The type edge weight map. The default type is
kpeter@590:   /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".
kpeter@590: #ifdef DOXYGEN
kpeter@590:   template <typename GR, typename WM>
kpeter@590: #else
kpeter@559:   template <typename GR,
kpeter@559:             typename WM = typename GR::template EdgeMap<int> >
kpeter@590: #endif
deba@326:   class MaxWeightedMatching {
deba@326:   public:
deba@326: 
kpeter@590:     /// The graph type of the algorithm
kpeter@559:     typedef GR Graph;
kpeter@590:     /// The type of the edge weight map
kpeter@559:     typedef WM WeightMap;
kpeter@590:     /// The value type of the edge weights
deba@326:     typedef typename WeightMap::Value Value;
deba@326: 
kpeter@593:     /// The type of the matching map
kpeter@590:     typedef typename Graph::template NodeMap<typename Graph::Arc>
kpeter@590:     MatchingMap;
kpeter@590: 
deba@326:     /// \brief Scaling factor for dual solution
deba@326:     ///
kpeter@590:     /// Scaling factor for dual solution. It is equal to 4 or 1
deba@326:     /// according to the value type.
deba@326:     static const int dualScale =
deba@326:       std::numeric_limits<Value>::is_integer ? 4 : 1;
deba@326: 
deba@326:   private:
deba@326: 
deba@326:     TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@326: 
deba@326:     typedef typename Graph::template NodeMap<Value> NodePotential;
deba@326:     typedef std::vector<Node> BlossomNodeList;
deba@326: 
deba@326:     struct BlossomVariable {
deba@326:       int begin, end;
deba@326:       Value value;
deba@326: 
deba@326:       BlossomVariable(int _begin, int _end, Value _value)
deba@326:         : begin(_begin), end(_end), value(_value) {}
deba@326: 
deba@326:     };
deba@326: 
deba@326:     typedef std::vector<BlossomVariable> BlossomPotential;
deba@326: 
deba@326:     const Graph& _graph;
deba@326:     const WeightMap& _weight;
deba@326: 
deba@326:     MatchingMap* _matching;
deba@326: 
deba@326:     NodePotential* _node_potential;
deba@326: 
deba@326:     BlossomPotential _blossom_potential;
deba@326:     BlossomNodeList _blossom_node_list;
deba@326: 
deba@326:     int _node_num;
deba@326:     int _blossom_num;
deba@326: 
deba@326:     typedef RangeMap<int> IntIntMap;
deba@326: 
deba@326:     enum Status {
deba@868:       EVEN = -1, MATCHED = 0, ODD = 1
deba@326:     };
deba@326: 
deba@327:     typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
deba@326:     struct BlossomData {
deba@326:       int tree;
deba@326:       Status status;
deba@326:       Arc pred, next;
deba@326:       Value pot, offset;
deba@326:       Node base;
deba@326:     };
deba@326: 
deba@327:     IntNodeMap *_blossom_index;
deba@326:     BlossomSet *_blossom_set;
deba@326:     RangeMap<BlossomData>* _blossom_data;
deba@326: 
deba@327:     IntNodeMap *_node_index;
deba@327:     IntArcMap *_node_heap_index;
deba@326: 
deba@326:     struct NodeData {
deba@326: 
deba@327:       NodeData(IntArcMap& node_heap_index)
deba@326:         : heap(node_heap_index) {}
deba@326: 
deba@326:       int blossom;
deba@326:       Value pot;
deba@327:       BinHeap<Value, IntArcMap> heap;
deba@326:       std::map<int, Arc> heap_index;
deba@326: 
deba@326:       int tree;
deba@326:     };
deba@326: 
deba@326:     RangeMap<NodeData>* _node_data;
deba@326: 
deba@326:     typedef ExtendFindEnum<IntIntMap> TreeSet;
deba@326: 
deba@326:     IntIntMap *_tree_set_index;
deba@326:     TreeSet *_tree_set;
deba@326: 
deba@327:     IntNodeMap *_delta1_index;
deba@327:     BinHeap<Value, IntNodeMap> *_delta1;
deba@326: 
deba@326:     IntIntMap *_delta2_index;
deba@326:     BinHeap<Value, IntIntMap> *_delta2;
deba@326: 
deba@327:     IntEdgeMap *_delta3_index;
deba@327:     BinHeap<Value, IntEdgeMap> *_delta3;
deba@326: 
deba@326:     IntIntMap *_delta4_index;
deba@326:     BinHeap<Value, IntIntMap> *_delta4;
deba@326: 
deba@326:     Value _delta_sum;
deba@870:     int _unmatched;
deba@870: 
deba@870:     typedef MaxWeightedFractionalMatching<Graph, WeightMap> FractionalMatching;
deba@870:     FractionalMatching *_fractional;
deba@326: 
deba@326:     void createStructures() {
deba@326:       _node_num = countNodes(_graph);
deba@326:       _blossom_num = _node_num * 3 / 2;
deba@326: 
deba@326:       if (!_matching) {
deba@326:         _matching = new MatchingMap(_graph);
deba@326:       }
deba@867: 
deba@326:       if (!_node_potential) {
deba@326:         _node_potential = new NodePotential(_graph);
deba@326:       }
deba@867: 
deba@326:       if (!_blossom_set) {
deba@327:         _blossom_index = new IntNodeMap(_graph);
deba@326:         _blossom_set = new BlossomSet(*_blossom_index);
deba@326:         _blossom_data = new RangeMap<BlossomData>(_blossom_num);
deba@867:       } else if (_blossom_data->size() != _blossom_num) {
deba@867:         delete _blossom_data;
deba@867:         _blossom_data = new RangeMap<BlossomData>(_blossom_num);
deba@326:       }
deba@326: 
deba@326:       if (!_node_index) {
deba@327:         _node_index = new IntNodeMap(_graph);
deba@327:         _node_heap_index = new IntArcMap(_graph);
deba@326:         _node_data = new RangeMap<NodeData>(_node_num,
deba@867:                                             NodeData(*_node_heap_index));
deba@867:       } else {
deba@867:         delete _node_data;
deba@867:         _node_data = new RangeMap<NodeData>(_node_num,
deba@867:                                             NodeData(*_node_heap_index));
deba@326:       }
deba@326: 
deba@326:       if (!_tree_set) {
deba@326:         _tree_set_index = new IntIntMap(_blossom_num);
deba@326:         _tree_set = new TreeSet(*_tree_set_index);
deba@867:       } else {
deba@867:         _tree_set_index->resize(_blossom_num);
deba@326:       }
deba@867: 
deba@326:       if (!_delta1) {
deba@327:         _delta1_index = new IntNodeMap(_graph);
deba@327:         _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index);
deba@326:       }
deba@867: 
deba@326:       if (!_delta2) {
deba@326:         _delta2_index = new IntIntMap(_blossom_num);
deba@326:         _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
deba@867:       } else {
deba@867:         _delta2_index->resize(_blossom_num);
deba@326:       }
deba@867: 
deba@326:       if (!_delta3) {
deba@327:         _delta3_index = new IntEdgeMap(_graph);
deba@327:         _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
deba@326:       }
deba@867: 
deba@326:       if (!_delta4) {
deba@326:         _delta4_index = new IntIntMap(_blossom_num);
deba@326:         _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
deba@867:       } else {
deba@867:         _delta4_index->resize(_blossom_num);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void destroyStructures() {
deba@326:       if (_matching) {
deba@326:         delete _matching;
deba@326:       }
deba@326:       if (_node_potential) {
deba@326:         delete _node_potential;
deba@326:       }
deba@326:       if (_blossom_set) {
deba@326:         delete _blossom_index;
deba@326:         delete _blossom_set;
deba@326:         delete _blossom_data;
deba@326:       }
deba@326: 
deba@326:       if (_node_index) {
deba@326:         delete _node_index;
deba@326:         delete _node_heap_index;
deba@326:         delete _node_data;
deba@326:       }
deba@326: 
deba@326:       if (_tree_set) {
deba@326:         delete _tree_set_index;
deba@326:         delete _tree_set;
deba@326:       }
deba@326:       if (_delta1) {
deba@326:         delete _delta1_index;
deba@326:         delete _delta1;
deba@326:       }
deba@326:       if (_delta2) {
deba@326:         delete _delta2_index;
deba@326:         delete _delta2;
deba@326:       }
deba@326:       if (_delta3) {
deba@326:         delete _delta3_index;
deba@326:         delete _delta3;
deba@326:       }
deba@326:       if (_delta4) {
deba@326:         delete _delta4_index;
deba@326:         delete _delta4;
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void matchedToEven(int blossom, int tree) {
deba@326:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326:         _delta2->erase(blossom);
deba@326:       }
deba@326: 
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         (*_blossom_data)[blossom].pot -=
deba@326:           2 * (_delta_sum - (*_blossom_data)[blossom].offset);
deba@326:       }
deba@326: 
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326: 
deba@326:         _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326:         int ni = (*_node_index)[n];
deba@326: 
deba@326:         (*_node_data)[ni].heap.clear();
deba@326:         (*_node_data)[ni].heap_index.clear();
deba@326: 
deba@326:         (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
deba@326: 
deba@326:         _delta1->push(n, (*_node_data)[ni].pot);
deba@326: 
deba@326:         for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           Node v = _graph.source(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@326:           if ((*_blossom_data)[vb].status == EVEN) {
deba@326:             if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326:               _delta3->push(e, rw / 2);
deba@326:             }
deba@326:           } else {
deba@326:             typename std::map<int, Arc>::iterator it =
deba@326:               (*_node_data)[vi].heap_index.find(tree);
deba@326: 
deba@326:             if (it != (*_node_data)[vi].heap_index.end()) {
deba@326:               if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326:                 (*_node_data)[vi].heap.replace(it->second, e);
deba@326:                 (*_node_data)[vi].heap.decrease(e, rw);
deba@326:                 it->second = e;
deba@326:               }
deba@326:             } else {
deba@326:               (*_node_data)[vi].heap.push(e, rw);
deba@326:               (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326:             }
deba@326: 
deba@326:             if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326:               _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326: 
deba@326:               if ((*_blossom_data)[vb].status == MATCHED) {
deba@326:                 if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326:                   _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326:                                (*_blossom_data)[vb].offset);
deba@326:                 } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326:                            (*_blossom_data)[vb].offset) {
deba@326:                   _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326:                                    (*_blossom_data)[vb].offset);
deba@326:                 }
deba@326:               }
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:       (*_blossom_data)[blossom].offset = 0;
deba@326:     }
deba@326: 
deba@868:     void matchedToOdd(int blossom) {
deba@326:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326:         _delta2->erase(blossom);
deba@326:       }
deba@868:       (*_blossom_data)[blossom].offset += _delta_sum;
deba@868:       if (!_blossom_set->trivial(blossom)) {
deba@868:         _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
deba@868:                       (*_blossom_data)[blossom].offset);
deba@868:       }
deba@868:     }
deba@868: 
deba@868:     void evenToMatched(int blossom, int tree) {
deba@868:       if (!_blossom_set->trivial(blossom)) {
deba@868:         (*_blossom_data)[blossom].pot += 2 * _delta_sum;
deba@868:       }
deba@326: 
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326:         int ni = (*_node_index)[n];
deba@868:         (*_node_data)[ni].pot -= _delta_sum;
deba@868: 
deba@868:         _delta1->erase(n);
deba@868: 
deba@868:         for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@868:           Node v = _graph.source(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@868:           if (vb == blossom) {
deba@868:             if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@868:               _delta3->erase(e);
deba@868:             }
deba@868:           } else if ((*_blossom_data)[vb].status == EVEN) {
deba@868: 
deba@868:             if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@868:               _delta3->erase(e);
deba@868:             }
deba@868: 
deba@868:             int vt = _tree_set->find(vb);
deba@868: 
deba@868:             if (vt != tree) {
deba@868: 
deba@868:               Arc r = _graph.oppositeArc(e);
deba@868: 
deba@868:               typename std::map<int, Arc>::iterator it =
deba@868:                 (*_node_data)[ni].heap_index.find(vt);
deba@868: 
deba@868:               if (it != (*_node_data)[ni].heap_index.end()) {
deba@868:                 if ((*_node_data)[ni].heap[it->second] > rw) {
deba@868:                   (*_node_data)[ni].heap.replace(it->second, r);
deba@868:                   (*_node_data)[ni].heap.decrease(r, rw);
deba@868:                   it->second = r;
deba@868:                 }
deba@868:               } else {
deba@868:                 (*_node_data)[ni].heap.push(r, rw);
deba@868:                 (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@868:               }
deba@868: 
deba@868:               if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@868:                 _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@868: 
deba@868:                 if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@868:                   _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@868:                                (*_blossom_data)[blossom].offset);
deba@868:                 } else if ((*_delta2)[blossom] >
deba@868:                            _blossom_set->classPrio(blossom) -
deba@868:                            (*_blossom_data)[blossom].offset){
deba@868:                   _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@868:                                    (*_blossom_data)[blossom].offset);
deba@868:                 }
deba@868:               }
deba@868:             }
deba@868:           } else {
deba@868: 
deba@868:             typename std::map<int, Arc>::iterator it =
deba@868:               (*_node_data)[vi].heap_index.find(tree);
deba@868: 
deba@868:             if (it != (*_node_data)[vi].heap_index.end()) {
deba@868:               (*_node_data)[vi].heap.erase(it->second);
deba@868:               (*_node_data)[vi].heap_index.erase(it);
deba@868:               if ((*_node_data)[vi].heap.empty()) {
deba@868:                 _blossom_set->increase(v, std::numeric_limits<Value>::max());
deba@868:               } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
deba@868:                 _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
deba@868:               }
deba@868: 
deba@868:               if ((*_blossom_data)[vb].status == MATCHED) {
deba@868:                 if (_blossom_set->classPrio(vb) ==
deba@868:                     std::numeric_limits<Value>::max()) {
deba@868:                   _delta2->erase(vb);
deba@868:                 } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
deba@868:                            (*_blossom_data)[vb].offset) {
deba@868:                   _delta2->increase(vb, _blossom_set->classPrio(vb) -
deba@868:                                    (*_blossom_data)[vb].offset);
deba@868:                 }
deba@868:               }
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@868:     void oddToMatched(int blossom) {
deba@868:       (*_blossom_data)[blossom].offset -= _delta_sum;
deba@868: 
deba@868:       if (_blossom_set->classPrio(blossom) !=
deba@868:           std::numeric_limits<Value>::max()) {
deba@868:         _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@868:                       (*_blossom_data)[blossom].offset);
deba@868:       }
deba@868: 
deba@868:       if (!_blossom_set->trivial(blossom)) {
deba@868:         _delta4->erase(blossom);
deba@868:       }
deba@868:     }
deba@868: 
deba@868:     void oddToEven(int blossom, int tree) {
deba@868:       if (!_blossom_set->trivial(blossom)) {
deba@868:         _delta4->erase(blossom);
deba@868:         (*_blossom_data)[blossom].pot -=
deba@868:           2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
deba@868:       }
deba@868: 
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326:         int ni = (*_node_index)[n];
deba@326: 
deba@868:         _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@868: 
deba@868:         (*_node_data)[ni].heap.clear();
deba@868:         (*_node_data)[ni].heap_index.clear();
deba@868:         (*_node_data)[ni].pot +=
deba@868:           2 * _delta_sum - (*_blossom_data)[blossom].offset;
deba@868: 
deba@868:         _delta1->push(n, (*_node_data)[ni].pot);
deba@868: 
deba@326:         for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           Node v = _graph.source(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@868:           if ((*_blossom_data)[vb].status == EVEN) {
deba@868:             if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@868:               _delta3->push(e, rw / 2);
deba@326:             }
deba@868:           } else {
deba@326: 
deba@326:             typename std::map<int, Arc>::iterator it =
deba@868:               (*_node_data)[vi].heap_index.find(tree);
deba@868: 
deba@868:             if (it != (*_node_data)[vi].heap_index.end()) {
deba@868:               if ((*_node_data)[vi].heap[it->second] > rw) {
deba@868:                 (*_node_data)[vi].heap.replace(it->second, e);
deba@868:                 (*_node_data)[vi].heap.decrease(e, rw);
deba@868:                 it->second = e;
deba@326:               }
deba@326:             } else {
deba@868:               (*_node_data)[vi].heap.push(e, rw);
deba@868:               (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326:             }
deba@326: 
deba@868:             if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@868:               _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@868: 
deba@868:               if ((*_blossom_data)[vb].status == MATCHED) {
deba@868:                 if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@868:                   _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@868:                                (*_blossom_data)[vb].offset);
deba@868:                 } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@868:                            (*_blossom_data)[vb].offset) {
deba@868:                   _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@868:                                    (*_blossom_data)[vb].offset);
deba@868:                 }
deba@326:               }
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@868:       (*_blossom_data)[blossom].offset = 0;
deba@326:     }
deba@326: 
deba@326:     void alternatePath(int even, int tree) {
deba@326:       int odd;
deba@326: 
deba@326:       evenToMatched(even, tree);
deba@326:       (*_blossom_data)[even].status = MATCHED;
deba@326: 
deba@326:       while ((*_blossom_data)[even].pred != INVALID) {
deba@326:         odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
deba@326:         (*_blossom_data)[odd].status = MATCHED;
deba@326:         oddToMatched(odd);
deba@326:         (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
deba@326: 
deba@326:         even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
deba@326:         (*_blossom_data)[even].status = MATCHED;
deba@326:         evenToMatched(even, tree);
deba@326:         (*_blossom_data)[even].next =
deba@326:           _graph.oppositeArc((*_blossom_data)[odd].pred);
deba@326:       }
deba@326: 
deba@326:     }
deba@326: 
deba@326:     void destroyTree(int tree) {
deba@326:       for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
deba@326:         if ((*_blossom_data)[b].status == EVEN) {
deba@326:           (*_blossom_data)[b].status = MATCHED;
deba@326:           evenToMatched(b, tree);
deba@326:         } else if ((*_blossom_data)[b].status == ODD) {
deba@326:           (*_blossom_data)[b].status = MATCHED;
deba@326:           oddToMatched(b);
deba@326:         }
deba@326:       }
deba@326:       _tree_set->eraseClass(tree);
deba@326:     }
deba@326: 
deba@326: 
deba@326:     void unmatchNode(const Node& node) {
deba@326:       int blossom = _blossom_set->find(node);
deba@326:       int tree = _tree_set->find(blossom);
deba@326: 
deba@326:       alternatePath(blossom, tree);
deba@326:       destroyTree(tree);
deba@326: 
deba@326:       (*_blossom_data)[blossom].base = node;
deba@868:       (*_blossom_data)[blossom].next = INVALID;
deba@326:     }
deba@326: 
deba@327:     void augmentOnEdge(const Edge& edge) {
deba@327: 
deba@327:       int left = _blossom_set->find(_graph.u(edge));
deba@327:       int right = _blossom_set->find(_graph.v(edge));
deba@326: 
deba@868:       int left_tree = _tree_set->find(left);
deba@868:       alternatePath(left, left_tree);
deba@868:       destroyTree(left_tree);
deba@868: 
deba@868:       int right_tree = _tree_set->find(right);
deba@868:       alternatePath(right, right_tree);
deba@868:       destroyTree(right_tree);
deba@326: 
deba@327:       (*_blossom_data)[left].next = _graph.direct(edge, true);
deba@327:       (*_blossom_data)[right].next = _graph.direct(edge, false);
deba@326:     }
deba@326: 
deba@868:     void augmentOnArc(const Arc& arc) {
deba@868: 
deba@868:       int left = _blossom_set->find(_graph.source(arc));
deba@868:       int right = _blossom_set->find(_graph.target(arc));
deba@868: 
deba@868:       (*_blossom_data)[left].status = MATCHED;
deba@868: 
deba@868:       int right_tree = _tree_set->find(right);
deba@868:       alternatePath(right, right_tree);
deba@868:       destroyTree(right_tree);
deba@868: 
deba@868:       (*_blossom_data)[left].next = arc;
deba@868:       (*_blossom_data)[right].next = _graph.oppositeArc(arc);
deba@868:     }
deba@868: 
deba@326:     void extendOnArc(const Arc& arc) {
deba@326:       int base = _blossom_set->find(_graph.target(arc));
deba@326:       int tree = _tree_set->find(base);
deba@326: 
deba@326:       int odd = _blossom_set->find(_graph.source(arc));
deba@326:       _tree_set->insert(odd, tree);
deba@326:       (*_blossom_data)[odd].status = ODD;
deba@326:       matchedToOdd(odd);
deba@326:       (*_blossom_data)[odd].pred = arc;
deba@326: 
deba@326:       int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
deba@326:       (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
deba@326:       _tree_set->insert(even, tree);
deba@326:       (*_blossom_data)[even].status = EVEN;
deba@326:       matchedToEven(even, tree);
deba@326:     }
deba@326: 
deba@327:     void shrinkOnEdge(const Edge& edge, int tree) {
deba@326:       int nca = -1;
deba@326:       std::vector<int> left_path, right_path;
deba@326: 
deba@326:       {
deba@326:         std::set<int> left_set, right_set;
deba@326:         int left = _blossom_set->find(_graph.u(edge));
deba@326:         left_path.push_back(left);
deba@326:         left_set.insert(left);
deba@326: 
deba@326:         int right = _blossom_set->find(_graph.v(edge));
deba@326:         right_path.push_back(right);
deba@326:         right_set.insert(right);
deba@326: 
deba@326:         while (true) {
deba@326: 
deba@326:           if ((*_blossom_data)[left].pred == INVALID) break;
deba@326: 
deba@326:           left =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326:           left_path.push_back(left);
deba@326:           left =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326:           left_path.push_back(left);
deba@326: 
deba@326:           left_set.insert(left);
deba@326: 
deba@326:           if (right_set.find(left) != right_set.end()) {
deba@326:             nca = left;
deba@326:             break;
deba@326:           }
deba@326: 
deba@326:           if ((*_blossom_data)[right].pred == INVALID) break;
deba@326: 
deba@326:           right =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326:           right_path.push_back(right);
deba@326:           right =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326:           right_path.push_back(right);
deba@326: 
deba@326:           right_set.insert(right);
deba@326: 
deba@326:           if (left_set.find(right) != left_set.end()) {
deba@326:             nca = right;
deba@326:             break;
deba@326:           }
deba@326: 
deba@326:         }
deba@326: 
deba@326:         if (nca == -1) {
deba@326:           if ((*_blossom_data)[left].pred == INVALID) {
deba@326:             nca = right;
deba@326:             while (left_set.find(nca) == left_set.end()) {
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               right_path.push_back(nca);
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               right_path.push_back(nca);
deba@326:             }
deba@326:           } else {
deba@326:             nca = left;
deba@326:             while (right_set.find(nca) == right_set.end()) {
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               left_path.push_back(nca);
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               left_path.push_back(nca);
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326: 
deba@326:       std::vector<int> subblossoms;
deba@326:       Arc prev;
deba@326: 
deba@326:       prev = _graph.direct(edge, true);
deba@326:       for (int i = 0; left_path[i] != nca; i += 2) {
deba@326:         subblossoms.push_back(left_path[i]);
deba@326:         (*_blossom_data)[left_path[i]].next = prev;
deba@326:         _tree_set->erase(left_path[i]);
deba@326: 
deba@326:         subblossoms.push_back(left_path[i + 1]);
deba@326:         (*_blossom_data)[left_path[i + 1]].status = EVEN;
deba@326:         oddToEven(left_path[i + 1], tree);
deba@326:         _tree_set->erase(left_path[i + 1]);
deba@326:         prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
deba@326:       }
deba@326: 
deba@326:       int k = 0;
deba@326:       while (right_path[k] != nca) ++k;
deba@326: 
deba@326:       subblossoms.push_back(nca);
deba@326:       (*_blossom_data)[nca].next = prev;
deba@326: 
deba@326:       for (int i = k - 2; i >= 0; i -= 2) {
deba@326:         subblossoms.push_back(right_path[i + 1]);
deba@326:         (*_blossom_data)[right_path[i + 1]].status = EVEN;
deba@326:         oddToEven(right_path[i + 1], tree);
deba@326:         _tree_set->erase(right_path[i + 1]);
deba@326: 
deba@326:         (*_blossom_data)[right_path[i + 1]].next =
deba@326:           (*_blossom_data)[right_path[i + 1]].pred;
deba@326: 
deba@326:         subblossoms.push_back(right_path[i]);
deba@326:         _tree_set->erase(right_path[i]);
deba@326:       }
deba@326: 
deba@326:       int surface =
deba@326:         _blossom_set->join(subblossoms.begin(), subblossoms.end());
deba@326: 
deba@326:       for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326:         if (!_blossom_set->trivial(subblossoms[i])) {
deba@326:           (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
deba@326:         }
deba@326:         (*_blossom_data)[subblossoms[i]].status = MATCHED;
deba@326:       }
deba@326: 
deba@326:       (*_blossom_data)[surface].pot = -2 * _delta_sum;
deba@326:       (*_blossom_data)[surface].offset = 0;
deba@326:       (*_blossom_data)[surface].status = EVEN;
deba@326:       (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
deba@326:       (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
deba@326: 
deba@326:       _tree_set->insert(surface, tree);
deba@326:       _tree_set->erase(nca);
deba@326:     }
deba@326: 
deba@326:     void splitBlossom(int blossom) {
deba@326:       Arc next = (*_blossom_data)[blossom].next;
deba@326:       Arc pred = (*_blossom_data)[blossom].pred;
deba@326: 
deba@326:       int tree = _tree_set->find(blossom);
deba@326: 
deba@326:       (*_blossom_data)[blossom].status = MATCHED;
deba@326:       oddToMatched(blossom);
deba@326:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326:         _delta2->erase(blossom);
deba@326:       }
deba@326: 
deba@326:       std::vector<int> subblossoms;
deba@326:       _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326: 
deba@326:       Value offset = (*_blossom_data)[blossom].offset;
deba@326:       int b = _blossom_set->find(_graph.source(pred));
deba@326:       int d = _blossom_set->find(_graph.source(next));
deba@326: 
deba@326:       int ib = -1, id = -1;
deba@326:       for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326:         if (subblossoms[i] == b) ib = i;
deba@326:         if (subblossoms[i] == d) id = i;
deba@326: 
deba@326:         (*_blossom_data)[subblossoms[i]].offset = offset;
deba@326:         if (!_blossom_set->trivial(subblossoms[i])) {
deba@326:           (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
deba@326:         }
deba@326:         if (_blossom_set->classPrio(subblossoms[i]) !=
deba@326:             std::numeric_limits<Value>::max()) {
deba@326:           _delta2->push(subblossoms[i],
deba@326:                         _blossom_set->classPrio(subblossoms[i]) -
deba@326:                         (*_blossom_data)[subblossoms[i]].offset);
deba@326:         }
deba@326:       }
deba@326: 
deba@326:       if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
deba@326:         for (int i = (id + 1) % subblossoms.size();
deba@326:              i != ib; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           (*_blossom_data)[sb].next =
deba@326:             _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326:         }
deba@326: 
deba@326:         for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326: 
deba@326:           (*_blossom_data)[sb].status = ODD;
deba@326:           matchedToOdd(sb);
deba@326:           _tree_set->insert(sb, tree);
deba@326:           (*_blossom_data)[sb].pred = pred;
deba@326:           (*_blossom_data)[sb].next =
deba@868:             _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326: 
deba@326:           pred = (*_blossom_data)[ub].next;
deba@326: 
deba@326:           (*_blossom_data)[tb].status = EVEN;
deba@326:           matchedToEven(tb, tree);
deba@326:           _tree_set->insert(tb, tree);
deba@326:           (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
deba@326:         }
deba@326: 
deba@326:         (*_blossom_data)[subblossoms[id]].status = ODD;
deba@326:         matchedToOdd(subblossoms[id]);
deba@326:         _tree_set->insert(subblossoms[id], tree);
deba@326:         (*_blossom_data)[subblossoms[id]].next = next;
deba@326:         (*_blossom_data)[subblossoms[id]].pred = pred;
deba@326: 
deba@326:       } else {
deba@326: 
deba@326:         for (int i = (ib + 1) % subblossoms.size();
deba@326:              i != id; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           (*_blossom_data)[sb].next =
deba@326:             _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326:         }
deba@326: 
deba@326:         for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326: 
deba@326:           (*_blossom_data)[sb].status = ODD;
deba@326:           matchedToOdd(sb);
deba@326:           _tree_set->insert(sb, tree);
deba@326:           (*_blossom_data)[sb].next = next;
deba@326:           (*_blossom_data)[sb].pred =
deba@326:             _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326: 
deba@326:           (*_blossom_data)[tb].status = EVEN;
deba@326:           matchedToEven(tb, tree);
deba@326:           _tree_set->insert(tb, tree);
deba@326:           (*_blossom_data)[tb].pred =
deba@326:             (*_blossom_data)[tb].next =
deba@326:             _graph.oppositeArc((*_blossom_data)[ub].next);
deba@326:           next = (*_blossom_data)[ub].next;
deba@326:         }
deba@326: 
deba@326:         (*_blossom_data)[subblossoms[ib]].status = ODD;
deba@326:         matchedToOdd(subblossoms[ib]);
deba@326:         _tree_set->insert(subblossoms[ib], tree);
deba@326:         (*_blossom_data)[subblossoms[ib]].next = next;
deba@326:         (*_blossom_data)[subblossoms[ib]].pred = pred;
deba@326:       }
deba@326:       _tree_set->erase(blossom);
deba@326:     }
deba@326: 
deba@326:     void extractBlossom(int blossom, const Node& base, const Arc& matching) {
deba@326:       if (_blossom_set->trivial(blossom)) {
deba@326:         int bi = (*_node_index)[base];
deba@326:         Value pot = (*_node_data)[bi].pot;
deba@326: 
kpeter@581:         (*_matching)[base] = matching;
deba@326:         _blossom_node_list.push_back(base);
kpeter@581:         (*_node_potential)[base] = pot;
deba@326:       } else {
deba@326: 
deba@326:         Value pot = (*_blossom_data)[blossom].pot;
deba@326:         int bn = _blossom_node_list.size();
deba@326: 
deba@326:         std::vector<int> subblossoms;
deba@326:         _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326:         int b = _blossom_set->find(base);
deba@326:         int ib = -1;
deba@326:         for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326:           if (subblossoms[i] == b) { ib = i; break; }
deba@326:         }
deba@326: 
deba@326:         for (int i = 1; i < int(subblossoms.size()); i += 2) {
deba@326:           int sb = subblossoms[(ib + i) % subblossoms.size()];
deba@326:           int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
deba@326: 
deba@326:           Arc m = (*_blossom_data)[tb].next;
deba@326:           extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
deba@326:           extractBlossom(tb, _graph.source(m), m);
deba@326:         }
deba@326:         extractBlossom(subblossoms[ib], base, matching);
deba@326: 
deba@326:         int en = _blossom_node_list.size();
deba@326: 
deba@326:         _blossom_potential.push_back(BlossomVariable(bn, en, pot));
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void extractMatching() {
deba@326:       std::vector<int> blossoms;
deba@326:       for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
deba@326:         blossoms.push_back(c);
deba@326:       }
deba@326: 
deba@326:       for (int i = 0; i < int(blossoms.size()); ++i) {
deba@868:         if ((*_blossom_data)[blossoms[i]].next != INVALID) {
deba@326: 
deba@326:           Value offset = (*_blossom_data)[blossoms[i]].offset;
deba@326:           (*_blossom_data)[blossoms[i]].pot += 2 * offset;
deba@326:           for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
deba@326:                n != INVALID; ++n) {
deba@326:             (*_node_data)[(*_node_index)[n]].pot -= offset;
deba@326:           }
deba@326: 
deba@326:           Arc matching = (*_blossom_data)[blossoms[i]].next;
deba@326:           Node base = _graph.source(matching);
deba@326:           extractBlossom(blossoms[i], base, matching);
deba@326:         } else {
deba@326:           Node base = (*_blossom_data)[blossoms[i]].base;
deba@326:           extractBlossom(blossoms[i], base, INVALID);
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326:   public:
deba@326: 
deba@326:     /// \brief Constructor
deba@326:     ///
deba@326:     /// Constructor.
deba@326:     MaxWeightedMatching(const Graph& graph, const WeightMap& weight)
deba@326:       : _graph(graph), _weight(weight), _matching(0),
deba@326:         _node_potential(0), _blossom_potential(), _blossom_node_list(),
deba@326:         _node_num(0), _blossom_num(0),
deba@326: 
deba@326:         _blossom_index(0), _blossom_set(0), _blossom_data(0),
deba@326:         _node_index(0), _node_heap_index(0), _node_data(0),
deba@326:         _tree_set_index(0), _tree_set(0),
deba@326: 
deba@326:         _delta1_index(0), _delta1(0),
deba@326:         _delta2_index(0), _delta2(0),
deba@326:         _delta3_index(0), _delta3(0),
deba@326:         _delta4_index(0), _delta4(0),
deba@326: 
deba@870:         _delta_sum(), _unmatched(0),
deba@870: 
deba@870:         _fractional(0)
deba@870:     {}
deba@326: 
deba@326:     ~MaxWeightedMatching() {
deba@326:       destroyStructures();
deba@870:       if (_fractional) {
deba@870:         delete _fractional;
deba@870:       }
deba@326:     }
deba@326: 
kpeter@590:     /// \name Execution Control
alpar@330:     /// The simplest way to execute the algorithm is to use the
kpeter@590:     /// \ref run() member function.
deba@326: 
deba@326:     ///@{
deba@326: 
deba@326:     /// \brief Initialize the algorithm
deba@326:     ///
kpeter@590:     /// This function initializes the algorithm.
deba@326:     void init() {
deba@326:       createStructures();
deba@326: 
deba@867:       _blossom_node_list.clear();
deba@867:       _blossom_potential.clear();
deba@867: 
deba@326:       for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@581:         (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
deba@326:       }
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@581:         (*_delta1_index)[n] = _delta1->PRE_HEAP;
deba@326:       }
deba@326:       for (EdgeIt e(_graph); e != INVALID; ++e) {
kpeter@581:         (*_delta3_index)[e] = _delta3->PRE_HEAP;
deba@326:       }
deba@326:       for (int i = 0; i < _blossom_num; ++i) {
kpeter@581:         (*_delta2_index)[i] = _delta2->PRE_HEAP;
kpeter@581:         (*_delta4_index)[i] = _delta4->PRE_HEAP;
deba@326:       }
alpar@877: 
deba@870:       _unmatched = _node_num;
deba@870: 
deba@867:       _delta1->clear();
deba@867:       _delta2->clear();
deba@867:       _delta3->clear();
deba@867:       _delta4->clear();
deba@867:       _blossom_set->clear();
deba@867:       _tree_set->clear();
deba@326: 
deba@326:       int index = 0;
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326:         Value max = 0;
deba@326:         for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           if (_graph.target(e) == n) continue;
deba@326:           if ((dualScale * _weight[e]) / 2 > max) {
deba@326:             max = (dualScale * _weight[e]) / 2;
deba@326:           }
deba@326:         }
kpeter@581:         (*_node_index)[n] = index;
deba@867:         (*_node_data)[index].heap_index.clear();
deba@867:         (*_node_data)[index].heap.clear();
deba@326:         (*_node_data)[index].pot = max;
deba@326:         _delta1->push(n, max);
deba@326:         int blossom =
deba@326:           _blossom_set->insert(n, std::numeric_limits<Value>::max());
deba@326: 
deba@326:         _tree_set->insert(blossom);
deba@326: 
deba@326:         (*_blossom_data)[blossom].status = EVEN;
deba@326:         (*_blossom_data)[blossom].pred = INVALID;
deba@326:         (*_blossom_data)[blossom].next = INVALID;
deba@326:         (*_blossom_data)[blossom].pot = 0;
deba@326:         (*_blossom_data)[blossom].offset = 0;
deba@326:         ++index;
deba@326:       }
deba@326:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@326:         int si = (*_node_index)[_graph.u(e)];
deba@326:         int ti = (*_node_index)[_graph.v(e)];
deba@326:         if (_graph.u(e) != _graph.v(e)) {
deba@326:           _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
deba@326:                             dualScale * _weight[e]) / 2);
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@870:     /// \brief Initialize the algorithm with fractional matching
deba@870:     ///
deba@870:     /// This function initializes the algorithm with a fractional
deba@870:     /// matching. This initialization is also called jumpstart heuristic.
deba@870:     void fractionalInit() {
deba@870:       createStructures();
deba@876: 
deba@876:       _blossom_node_list.clear();
deba@876:       _blossom_potential.clear();
alpar@877: 
deba@870:       if (_fractional == 0) {
deba@870:         _fractional = new FractionalMatching(_graph, _weight, false);
deba@870:       }
deba@870:       _fractional->run();
deba@870: 
deba@870:       for (ArcIt e(_graph); e != INVALID; ++e) {
deba@870:         (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
deba@870:       }
deba@870:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@870:         (*_delta1_index)[n] = _delta1->PRE_HEAP;
deba@870:       }
deba@870:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@870:         (*_delta3_index)[e] = _delta3->PRE_HEAP;
deba@870:       }
deba@870:       for (int i = 0; i < _blossom_num; ++i) {
deba@870:         (*_delta2_index)[i] = _delta2->PRE_HEAP;
deba@870:         (*_delta4_index)[i] = _delta4->PRE_HEAP;
deba@870:       }
deba@870: 
deba@870:       _unmatched = 0;
deba@870: 
deba@876:       _delta1->clear();
deba@876:       _delta2->clear();
deba@876:       _delta3->clear();
deba@876:       _delta4->clear();
deba@876:       _blossom_set->clear();
deba@876:       _tree_set->clear();
deba@876: 
deba@870:       int index = 0;
deba@870:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@870:         Value pot = _fractional->nodeValue(n);
deba@870:         (*_node_index)[n] = index;
deba@870:         (*_node_data)[index].pot = pot;
deba@876:         (*_node_data)[index].heap_index.clear();
deba@876:         (*_node_data)[index].heap.clear();
deba@870:         int blossom =
deba@870:           _blossom_set->insert(n, std::numeric_limits<Value>::max());
deba@870: 
deba@870:         (*_blossom_data)[blossom].status = MATCHED;
deba@870:         (*_blossom_data)[blossom].pred = INVALID;
deba@870:         (*_blossom_data)[blossom].next = _fractional->matching(n);
deba@870:         if (_fractional->matching(n) == INVALID) {
deba@870:           (*_blossom_data)[blossom].base = n;
deba@870:         }
deba@870:         (*_blossom_data)[blossom].pot = 0;
deba@870:         (*_blossom_data)[blossom].offset = 0;
deba@870:         ++index;
deba@870:       }
deba@870: 
deba@870:       typename Graph::template NodeMap<bool> processed(_graph, false);
deba@870:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@870:         if (processed[n]) continue;
deba@870:         processed[n] = true;
deba@870:         if (_fractional->matching(n) == INVALID) continue;
deba@870:         int num = 1;
deba@870:         Node v = _graph.target(_fractional->matching(n));
deba@870:         while (n != v) {
deba@870:           processed[v] = true;
deba@870:           v = _graph.target(_fractional->matching(v));
deba@870:           ++num;
deba@870:         }
deba@870: 
deba@870:         if (num % 2 == 1) {
deba@870:           std::vector<int> subblossoms(num);
deba@870: 
deba@870:           subblossoms[--num] = _blossom_set->find(n);
deba@870:           _delta1->push(n, _fractional->nodeValue(n));
deba@870:           v = _graph.target(_fractional->matching(n));
deba@870:           while (n != v) {
deba@870:             subblossoms[--num] = _blossom_set->find(v);
deba@870:             _delta1->push(v, _fractional->nodeValue(v));
alpar@877:             v = _graph.target(_fractional->matching(v));
deba@870:           }
alpar@877: 
alpar@877:           int surface =
deba@870:             _blossom_set->join(subblossoms.begin(), subblossoms.end());
deba@870:           (*_blossom_data)[surface].status = EVEN;
deba@870:           (*_blossom_data)[surface].pred = INVALID;
deba@870:           (*_blossom_data)[surface].next = INVALID;
deba@870:           (*_blossom_data)[surface].pot = 0;
deba@870:           (*_blossom_data)[surface].offset = 0;
alpar@877: 
deba@870:           _tree_set->insert(surface);
deba@870:           ++_unmatched;
deba@870:         }
deba@870:       }
deba@870: 
deba@870:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@870:         int si = (*_node_index)[_graph.u(e)];
deba@870:         int sb = _blossom_set->find(_graph.u(e));
deba@870:         int ti = (*_node_index)[_graph.v(e)];
deba@870:         int tb = _blossom_set->find(_graph.v(e));
deba@870:         if ((*_blossom_data)[sb].status == EVEN &&
deba@870:             (*_blossom_data)[tb].status == EVEN && sb != tb) {
deba@870:           _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
deba@870:                             dualScale * _weight[e]) / 2);
deba@870:         }
deba@870:       }
deba@870: 
deba@870:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@870:         int nb = _blossom_set->find(n);
deba@870:         if ((*_blossom_data)[nb].status != MATCHED) continue;
deba@870:         int ni = (*_node_index)[n];
deba@870: 
deba@870:         for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@870:           Node v = _graph.target(e);
deba@870:           int vb = _blossom_set->find(v);
deba@870:           int vi = (*_node_index)[v];
deba@870: 
deba@870:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@870:             dualScale * _weight[e];
deba@870: 
deba@870:           if ((*_blossom_data)[vb].status == EVEN) {
deba@870: 
deba@870:             int vt = _tree_set->find(vb);
deba@870: 
deba@870:             typename std::map<int, Arc>::iterator it =
deba@870:               (*_node_data)[ni].heap_index.find(vt);
deba@870: 
deba@870:             if (it != (*_node_data)[ni].heap_index.end()) {
deba@870:               if ((*_node_data)[ni].heap[it->second] > rw) {
deba@870:                 (*_node_data)[ni].heap.replace(it->second, e);
deba@870:                 (*_node_data)[ni].heap.decrease(e, rw);
deba@870:                 it->second = e;
deba@870:               }
deba@870:             } else {
deba@870:               (*_node_data)[ni].heap.push(e, rw);
deba@870:               (*_node_data)[ni].heap_index.insert(std::make_pair(vt, e));
deba@870:             }
deba@870:           }
deba@870:         }
alpar@877: 
deba@870:         if (!(*_node_data)[ni].heap.empty()) {
deba@870:           _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@870:           _delta2->push(nb, _blossom_set->classPrio(nb));
deba@870:         }
deba@870:       }
deba@870:     }
deba@870: 
kpeter@590:     /// \brief Start the algorithm
deba@326:     ///
kpeter@590:     /// This function starts the algorithm.
kpeter@590:     ///
deba@870:     /// \pre \ref init() or \ref fractionalInit() must be called
deba@870:     /// before using this function.
deba@326:     void start() {
deba@326:       enum OpType {
deba@326:         D1, D2, D3, D4
deba@326:       };
deba@326: 
deba@870:       while (_unmatched > 0) {
deba@326:         Value d1 = !_delta1->empty() ?
deba@326:           _delta1->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@326:         Value d2 = !_delta2->empty() ?
deba@326:           _delta2->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@326:         Value d3 = !_delta3->empty() ?
deba@326:           _delta3->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@326:         Value d4 = !_delta4->empty() ?
deba@326:           _delta4->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@868:         _delta_sum = d3; OpType ot = D3;
deba@868:         if (d1 < _delta_sum) { _delta_sum = d1; ot = D1; }
deba@326:         if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
deba@326:         if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
deba@326: 
deba@326:         switch (ot) {
deba@326:         case D1:
deba@326:           {
deba@326:             Node n = _delta1->top();
deba@326:             unmatchNode(n);
deba@870:             --_unmatched;
deba@326:           }
deba@326:           break;
deba@326:         case D2:
deba@326:           {
deba@326:             int blossom = _delta2->top();
deba@326:             Node n = _blossom_set->classTop(blossom);
deba@868:             Arc a = (*_node_data)[(*_node_index)[n]].heap.top();
deba@868:             if ((*_blossom_data)[blossom].next == INVALID) {
deba@868:               augmentOnArc(a);
deba@870:               --_unmatched;
deba@868:             } else {
deba@868:               extendOnArc(a);
deba@868:             }
deba@326:           }
deba@326:           break;
deba@326:         case D3:
deba@326:           {
deba@326:             Edge e = _delta3->top();
deba@326: 
deba@326:             int left_blossom = _blossom_set->find(_graph.u(e));
deba@326:             int right_blossom = _blossom_set->find(_graph.v(e));
deba@326: 
deba@326:             if (left_blossom == right_blossom) {
deba@326:               _delta3->pop();
deba@326:             } else {
deba@868:               int left_tree = _tree_set->find(left_blossom);
deba@868:               int right_tree = _tree_set->find(right_blossom);
deba@326: 
deba@326:               if (left_tree == right_tree) {
deba@327:                 shrinkOnEdge(e, left_tree);
deba@326:               } else {
deba@327:                 augmentOnEdge(e);
deba@870:                 _unmatched -= 2;
deba@326:               }
deba@326:             }
deba@326:           } break;
deba@326:         case D4:
deba@326:           splitBlossom(_delta4->top());
deba@326:           break;
deba@326:         }
deba@326:       }
deba@326:       extractMatching();
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Run the algorithm.
deba@326:     ///
kpeter@590:     /// This method runs the \c %MaxWeightedMatching algorithm.
deba@326:     ///
deba@326:     /// \note mwm.run() is just a shortcut of the following code.
deba@326:     /// \code
deba@870:     ///   mwm.fractionalInit();
deba@326:     ///   mwm.start();
deba@326:     /// \endcode
deba@326:     void run() {
deba@870:       fractionalInit();
deba@326:       start();
deba@326:     }
deba@326: 
deba@326:     /// @}
deba@326: 
kpeter@590:     /// \name Primal Solution
deba@868:     /// Functions to get the primal solution, i.e. the maximum weighted
kpeter@590:     /// matching.\n
kpeter@590:     /// Either \ref run() or \ref start() function should be called before
kpeter@590:     /// using them.
deba@326: 
deba@326:     /// @{
deba@326: 
kpeter@590:     /// \brief Return the weight of the matching.
deba@326:     ///
kpeter@590:     /// This function returns the weight of the found matching.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
kpeter@593:     Value matchingWeight() const {
deba@326:       Value sum = 0;
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326:         if ((*_matching)[n] != INVALID) {
deba@326:           sum += _weight[(*_matching)[n]];
deba@326:         }
deba@326:       }
deba@868:       return sum / 2;
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Return the size (cardinality) of the matching.
deba@326:     ///
kpeter@590:     /// This function returns the size (cardinality) of the found matching.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@327:     int matchingSize() const {
deba@327:       int num = 0;
deba@327:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@327:         if ((*_matching)[n] != INVALID) {
deba@327:           ++num;
deba@327:         }
deba@327:       }
deba@327:       return num /= 2;
deba@327:     }
deba@327: 
kpeter@590:     /// \brief Return \c true if the given edge is in the matching.
deba@327:     ///
deba@868:     /// This function returns \c true if the given edge is in the found
kpeter@590:     /// matching.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@327:     bool matching(const Edge& edge) const {
deba@327:       return edge == (*_matching)[_graph.u(edge)];
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Return the matching arc (or edge) incident to the given node.
deba@326:     ///
kpeter@590:     /// This function returns the matching arc (or edge) incident to the
deba@868:     /// given node in the found matching or \c INVALID if the node is
kpeter@590:     /// not covered by the matching.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@326:     Arc matching(const Node& node) const {
deba@326:       return (*_matching)[node];
deba@326:     }
deba@326: 
kpeter@593:     /// \brief Return a const reference to the matching map.
kpeter@593:     ///
kpeter@593:     /// This function returns a const reference to a node map that stores
kpeter@593:     /// the matching arc (or edge) incident to each node.
kpeter@593:     const MatchingMap& matchingMap() const {
kpeter@593:       return *_matching;
kpeter@593:     }
kpeter@593: 
kpeter@590:     /// \brief Return the mate of the given node.
deba@326:     ///
deba@868:     /// This function returns the mate of the given node in the found
kpeter@590:     /// matching or \c INVALID if the node is not covered by the matching.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@326:     Node mate(const Node& node) const {
deba@326:       return (*_matching)[node] != INVALID ?
deba@326:         _graph.target((*_matching)[node]) : INVALID;
deba@326:     }
deba@326: 
deba@326:     /// @}
deba@326: 
kpeter@590:     /// \name Dual Solution
kpeter@590:     /// Functions to get the dual solution.\n
kpeter@590:     /// Either \ref run() or \ref start() function should be called before
kpeter@590:     /// using them.
deba@326: 
deba@326:     /// @{
deba@326: 
kpeter@590:     /// \brief Return the value of the dual solution.
deba@326:     ///
deba@868:     /// This function returns the value of the dual solution.
deba@868:     /// It should be equal to the primal value scaled by \ref dualScale
kpeter@590:     /// "dual scale".
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@326:     Value dualValue() const {
deba@326:       Value sum = 0;
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326:         sum += nodeValue(n);
deba@326:       }
deba@326:       for (int i = 0; i < blossomNum(); ++i) {
deba@326:         sum += blossomValue(i) * (blossomSize(i) / 2);
deba@326:       }
deba@326:       return sum;
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Return the dual value (potential) of the given node.
deba@326:     ///
kpeter@590:     /// This function returns the dual value (potential) of the given node.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@326:     Value nodeValue(const Node& n) const {
deba@326:       return (*_node_potential)[n];
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Return the number of the blossoms in the basis.
deba@326:     ///
kpeter@590:     /// This function returns the number of the blossoms in the basis.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@326:     /// \see BlossomIt
deba@326:     int blossomNum() const {
deba@326:       return _blossom_potential.size();
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Return the number of the nodes in the given blossom.
deba@326:     ///
kpeter@590:     /// This function returns the number of the nodes in the given blossom.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
kpeter@590:     /// \see BlossomIt
deba@326:     int blossomSize(int k) const {
deba@326:       return _blossom_potential[k].end - _blossom_potential[k].begin;
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Return the dual value (ptential) of the given blossom.
deba@326:     ///
kpeter@590:     /// This function returns the dual value (ptential) of the given blossom.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@326:     Value blossomValue(int k) const {
deba@326:       return _blossom_potential[k].value;
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Iterator for obtaining the nodes of a blossom.
deba@326:     ///
deba@868:     /// This class provides an iterator for obtaining the nodes of the
kpeter@590:     /// given blossom. It lists a subset of the nodes.
deba@868:     /// Before using this iterator, you must allocate a
kpeter@590:     /// MaxWeightedMatching class and execute it.
deba@326:     class BlossomIt {
deba@326:     public:
deba@326: 
deba@326:       /// \brief Constructor.
deba@326:       ///
kpeter@590:       /// Constructor to get the nodes of the given variable.
kpeter@590:       ///
deba@868:       /// \pre Either \ref MaxWeightedMatching::run() "algorithm.run()" or
deba@868:       /// \ref MaxWeightedMatching::start() "algorithm.start()" must be
kpeter@590:       /// called before initializing this iterator.
deba@326:       BlossomIt(const MaxWeightedMatching& algorithm, int variable)
deba@326:         : _algorithm(&algorithm)
deba@326:       {
deba@326:         _index = _algorithm->_blossom_potential[variable].begin;
deba@326:         _last = _algorithm->_blossom_potential[variable].end;
deba@326:       }
deba@326: 
kpeter@590:       /// \brief Conversion to \c Node.
deba@326:       ///
kpeter@590:       /// Conversion to \c Node.
deba@326:       operator Node() const {
deba@327:         return _algorithm->_blossom_node_list[_index];
deba@326:       }
deba@326: 
deba@326:       /// \brief Increment operator.
deba@326:       ///
deba@326:       /// Increment operator.
deba@326:       BlossomIt& operator++() {
deba@326:         ++_index;
deba@326:         return *this;
deba@326:       }
deba@326: 
deba@327:       /// \brief Validity checking
deba@327:       ///
deba@327:       /// Checks whether the iterator is invalid.
deba@327:       bool operator==(Invalid) const { return _index == _last; }
deba@327: 
deba@327:       /// \brief Validity checking
deba@327:       ///
deba@327:       /// Checks whether the iterator is valid.
deba@327:       bool operator!=(Invalid) const { return _index != _last; }
deba@326: 
deba@326:     private:
deba@326:       const MaxWeightedMatching* _algorithm;
deba@326:       int _last;
deba@326:       int _index;
deba@326:     };
deba@326: 
deba@326:     /// @}
deba@326: 
deba@326:   };
deba@326: 
deba@326:   /// \ingroup matching
deba@326:   ///
deba@326:   /// \brief Weighted perfect matching in general graphs
deba@326:   ///
deba@326:   /// This class provides an efficient implementation of Edmond's
deba@327:   /// maximum weighted perfect matching algorithm. The implementation
deba@326:   /// is based on extensive use of priority queues and provides
kpeter@559:   /// \f$O(nm\log n)\f$ time complexity.
deba@326:   ///
deba@868:   /// The maximum weighted perfect matching problem is to find a subset of
deba@868:   /// the edges in an undirected graph with maximum overall weight for which
kpeter@590:   /// each node has exactly one incident edge.
kpeter@590:   /// It can be formulated with the following linear program.
deba@326:   /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f]
deba@327:   /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
deba@327:       \quad \forall B\in\mathcal{O}\f] */
deba@326:   /// \f[x_e \ge 0\quad \forall e\in E\f]
deba@326:   /// \f[\max \sum_{e\in E}x_ew_e\f]
deba@327:   /// where \f$\delta(X)\f$ is the set of edges incident to a node in
deba@327:   /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
deba@327:   /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
deba@327:   /// subsets of the nodes.
deba@326:   ///
deba@326:   /// The algorithm calculates an optimal matching and a proof of the
deba@326:   /// optimality. The solution of the dual problem can be used to check
deba@327:   /// the result of the algorithm. The dual linear problem is the
kpeter@590:   /// following.
deba@327:   /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge
deba@327:       w_{uv} \quad \forall uv\in E\f] */
deba@326:   /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
deba@327:   /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
deba@327:       \frac{\vert B \vert - 1}{2}z_B\f] */
deba@326:   ///
deba@868:   /// The algorithm can be executed with the run() function.
kpeter@590:   /// After it the matching (the primal solution) and the dual solution
deba@868:   /// can be obtained using the query functions and the
deba@868:   /// \ref MaxWeightedPerfectMatching::BlossomIt "BlossomIt" nested class,
deba@868:   /// which is able to iterate on the nodes of a blossom.
kpeter@590:   /// If the value type is integer, then the dual solution is multiplied
kpeter@590:   /// by \ref MaxWeightedMatching::dualScale "4".
kpeter@590:   ///
kpeter@593:   /// \tparam GR The undirected graph type the algorithm runs on.
deba@868:   /// \tparam WM The type edge weight map. The default type is
kpeter@590:   /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".
kpeter@590: #ifdef DOXYGEN
kpeter@590:   template <typename GR, typename WM>
kpeter@590: #else
kpeter@559:   template <typename GR,
kpeter@559:             typename WM = typename GR::template EdgeMap<int> >
kpeter@590: #endif
deba@326:   class MaxWeightedPerfectMatching {
deba@326:   public:
deba@326: 
kpeter@590:     /// The graph type of the algorithm
kpeter@559:     typedef GR Graph;
kpeter@590:     /// The type of the edge weight map
kpeter@559:     typedef WM WeightMap;
kpeter@590:     /// The value type of the edge weights
deba@326:     typedef typename WeightMap::Value Value;
deba@326: 
deba@326:     /// \brief Scaling factor for dual solution
deba@326:     ///
deba@326:     /// Scaling factor for dual solution, it is equal to 4 or 1
deba@326:     /// according to the value type.
deba@326:     static const int dualScale =
deba@326:       std::numeric_limits<Value>::is_integer ? 4 : 1;
deba@326: 
kpeter@593:     /// The type of the matching map
deba@326:     typedef typename Graph::template NodeMap<typename Graph::Arc>
deba@326:     MatchingMap;
deba@326: 
deba@326:   private:
deba@326: 
deba@326:     TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@326: 
deba@326:     typedef typename Graph::template NodeMap<Value> NodePotential;
deba@326:     typedef std::vector<Node> BlossomNodeList;
deba@326: 
deba@326:     struct BlossomVariable {
deba@326:       int begin, end;
deba@326:       Value value;
deba@326: 
deba@326:       BlossomVariable(int _begin, int _end, Value _value)
deba@326:         : begin(_begin), end(_end), value(_value) {}
deba@326: 
deba@326:     };
deba@326: 
deba@326:     typedef std::vector<BlossomVariable> BlossomPotential;
deba@326: 
deba@326:     const Graph& _graph;
deba@326:     const WeightMap& _weight;
deba@326: 
deba@326:     MatchingMap* _matching;
deba@326: 
deba@326:     NodePotential* _node_potential;
deba@326: 
deba@326:     BlossomPotential _blossom_potential;
deba@326:     BlossomNodeList _blossom_node_list;
deba@326: 
deba@326:     int _node_num;
deba@326:     int _blossom_num;
deba@326: 
deba@326:     typedef RangeMap<int> IntIntMap;
deba@326: 
deba@326:     enum Status {
deba@326:       EVEN = -1, MATCHED = 0, ODD = 1
deba@326:     };
deba@326: 
deba@327:     typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
deba@326:     struct BlossomData {
deba@326:       int tree;
deba@326:       Status status;
deba@326:       Arc pred, next;
deba@326:       Value pot, offset;
deba@326:     };
deba@326: 
deba@327:     IntNodeMap *_blossom_index;
deba@326:     BlossomSet *_blossom_set;
deba@326:     RangeMap<BlossomData>* _blossom_data;
deba@326: 
deba@327:     IntNodeMap *_node_index;
deba@327:     IntArcMap *_node_heap_index;
deba@326: 
deba@326:     struct NodeData {
deba@326: 
deba@327:       NodeData(IntArcMap& node_heap_index)
deba@326:         : heap(node_heap_index) {}
deba@326: 
deba@326:       int blossom;
deba@326:       Value pot;
deba@327:       BinHeap<Value, IntArcMap> heap;
deba@326:       std::map<int, Arc> heap_index;
deba@326: 
deba@326:       int tree;
deba@326:     };
deba@326: 
deba@326:     RangeMap<NodeData>* _node_data;
deba@326: 
deba@326:     typedef ExtendFindEnum<IntIntMap> TreeSet;
deba@326: 
deba@326:     IntIntMap *_tree_set_index;
deba@326:     TreeSet *_tree_set;
deba@326: 
deba@326:     IntIntMap *_delta2_index;
deba@326:     BinHeap<Value, IntIntMap> *_delta2;
deba@326: 
deba@327:     IntEdgeMap *_delta3_index;
deba@327:     BinHeap<Value, IntEdgeMap> *_delta3;
deba@326: 
deba@326:     IntIntMap *_delta4_index;
deba@326:     BinHeap<Value, IntIntMap> *_delta4;
deba@326: 
deba@326:     Value _delta_sum;
deba@870:     int _unmatched;
deba@870: 
alpar@877:     typedef MaxWeightedPerfectFractionalMatching<Graph, WeightMap>
deba@870:     FractionalMatching;
deba@870:     FractionalMatching *_fractional;
deba@326: 
deba@326:     void createStructures() {
deba@326:       _node_num = countNodes(_graph);
deba@326:       _blossom_num = _node_num * 3 / 2;
deba@326: 
deba@326:       if (!_matching) {
deba@326:         _matching = new MatchingMap(_graph);
deba@326:       }
deba@867: 
deba@326:       if (!_node_potential) {
deba@326:         _node_potential = new NodePotential(_graph);
deba@326:       }
deba@867: 
deba@326:       if (!_blossom_set) {
deba@327:         _blossom_index = new IntNodeMap(_graph);
deba@326:         _blossom_set = new BlossomSet(*_blossom_index);
deba@326:         _blossom_data = new RangeMap<BlossomData>(_blossom_num);
deba@867:       } else if (_blossom_data->size() != _blossom_num) {
deba@867:         delete _blossom_data;
deba@867:         _blossom_data = new RangeMap<BlossomData>(_blossom_num);
deba@326:       }
deba@326: 
deba@326:       if (!_node_index) {
deba@327:         _node_index = new IntNodeMap(_graph);
deba@327:         _node_heap_index = new IntArcMap(_graph);
deba@326:         _node_data = new RangeMap<NodeData>(_node_num,
deba@327:                                             NodeData(*_node_heap_index));
deba@867:       } else if (_node_data->size() != _node_num) {
deba@867:         delete _node_data;
deba@867:         _node_data = new RangeMap<NodeData>(_node_num,
deba@867:                                             NodeData(*_node_heap_index));
deba@326:       }
deba@326: 
deba@326:       if (!_tree_set) {
deba@326:         _tree_set_index = new IntIntMap(_blossom_num);
deba@326:         _tree_set = new TreeSet(*_tree_set_index);
deba@867:       } else {
deba@867:         _tree_set_index->resize(_blossom_num);
deba@326:       }
deba@867: 
deba@326:       if (!_delta2) {
deba@326:         _delta2_index = new IntIntMap(_blossom_num);
deba@326:         _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
deba@867:       } else {
deba@867:         _delta2_index->resize(_blossom_num);
deba@326:       }
deba@867: 
deba@326:       if (!_delta3) {
deba@327:         _delta3_index = new IntEdgeMap(_graph);
deba@327:         _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
deba@326:       }
deba@867: 
deba@326:       if (!_delta4) {
deba@326:         _delta4_index = new IntIntMap(_blossom_num);
deba@326:         _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
deba@867:       } else {
deba@867:         _delta4_index->resize(_blossom_num);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void destroyStructures() {
deba@326:       if (_matching) {
deba@326:         delete _matching;
deba@326:       }
deba@326:       if (_node_potential) {
deba@326:         delete _node_potential;
deba@326:       }
deba@326:       if (_blossom_set) {
deba@326:         delete _blossom_index;
deba@326:         delete _blossom_set;
deba@326:         delete _blossom_data;
deba@326:       }
deba@326: 
deba@326:       if (_node_index) {
deba@326:         delete _node_index;
deba@326:         delete _node_heap_index;
deba@326:         delete _node_data;
deba@326:       }
deba@326: 
deba@326:       if (_tree_set) {
deba@326:         delete _tree_set_index;
deba@326:         delete _tree_set;
deba@326:       }
deba@326:       if (_delta2) {
deba@326:         delete _delta2_index;
deba@326:         delete _delta2;
deba@326:       }
deba@326:       if (_delta3) {
deba@326:         delete _delta3_index;
deba@326:         delete _delta3;
deba@326:       }
deba@326:       if (_delta4) {
deba@326:         delete _delta4_index;
deba@326:         delete _delta4;
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void matchedToEven(int blossom, int tree) {
deba@326:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326:         _delta2->erase(blossom);
deba@326:       }
deba@326: 
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         (*_blossom_data)[blossom].pot -=
deba@326:           2 * (_delta_sum - (*_blossom_data)[blossom].offset);
deba@326:       }
deba@326: 
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326: 
deba@326:         _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326:         int ni = (*_node_index)[n];
deba@326: 
deba@326:         (*_node_data)[ni].heap.clear();
deba@326:         (*_node_data)[ni].heap_index.clear();
deba@326: 
deba@326:         (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
deba@326: 
deba@326:         for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           Node v = _graph.source(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@326:           if ((*_blossom_data)[vb].status == EVEN) {
deba@326:             if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326:               _delta3->push(e, rw / 2);
deba@326:             }
deba@326:           } else {
deba@326:             typename std::map<int, Arc>::iterator it =
deba@326:               (*_node_data)[vi].heap_index.find(tree);
deba@326: 
deba@326:             if (it != (*_node_data)[vi].heap_index.end()) {
deba@326:               if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326:                 (*_node_data)[vi].heap.replace(it->second, e);
deba@326:                 (*_node_data)[vi].heap.decrease(e, rw);
deba@326:                 it->second = e;
deba@326:               }
deba@326:             } else {
deba@326:               (*_node_data)[vi].heap.push(e, rw);
deba@326:               (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326:             }
deba@326: 
deba@326:             if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326:               _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326: 
deba@326:               if ((*_blossom_data)[vb].status == MATCHED) {
deba@326:                 if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326:                   _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326:                                (*_blossom_data)[vb].offset);
deba@326:                 } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326:                            (*_blossom_data)[vb].offset){
deba@326:                   _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326:                                    (*_blossom_data)[vb].offset);
deba@326:                 }
deba@326:               }
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:       (*_blossom_data)[blossom].offset = 0;
deba@326:     }
deba@326: 
deba@326:     void matchedToOdd(int blossom) {
deba@326:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326:         _delta2->erase(blossom);
deba@326:       }
deba@326:       (*_blossom_data)[blossom].offset += _delta_sum;
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
deba@326:                      (*_blossom_data)[blossom].offset);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void evenToMatched(int blossom, int tree) {
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         (*_blossom_data)[blossom].pot += 2 * _delta_sum;
deba@326:       }
deba@326: 
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326:         int ni = (*_node_index)[n];
deba@326:         (*_node_data)[ni].pot -= _delta_sum;
deba@326: 
deba@326:         for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           Node v = _graph.source(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@326:           if (vb == blossom) {
deba@326:             if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326:               _delta3->erase(e);
deba@326:             }
deba@326:           } else if ((*_blossom_data)[vb].status == EVEN) {
deba@326: 
deba@326:             if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326:               _delta3->erase(e);
deba@326:             }
deba@326: 
deba@326:             int vt = _tree_set->find(vb);
deba@326: 
deba@326:             if (vt != tree) {
deba@326: 
deba@326:               Arc r = _graph.oppositeArc(e);
deba@326: 
deba@326:               typename std::map<int, Arc>::iterator it =
deba@326:                 (*_node_data)[ni].heap_index.find(vt);
deba@326: 
deba@326:               if (it != (*_node_data)[ni].heap_index.end()) {
deba@326:                 if ((*_node_data)[ni].heap[it->second] > rw) {
deba@326:                   (*_node_data)[ni].heap.replace(it->second, r);
deba@326:                   (*_node_data)[ni].heap.decrease(r, rw);
deba@326:                   it->second = r;
deba@326:                 }
deba@326:               } else {
deba@326:                 (*_node_data)[ni].heap.push(r, rw);
deba@326:                 (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@326:               }
deba@326: 
deba@326:               if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@326:                 _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@326: 
deba@326:                 if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@326:                   _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326:                                (*_blossom_data)[blossom].offset);
deba@326:                 } else if ((*_delta2)[blossom] >
deba@326:                            _blossom_set->classPrio(blossom) -
deba@326:                            (*_blossom_data)[blossom].offset){
deba@326:                   _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@326:                                    (*_blossom_data)[blossom].offset);
deba@326:                 }
deba@326:               }
deba@326:             }
deba@326:           } else {
deba@326: 
deba@326:             typename std::map<int, Arc>::iterator it =
deba@326:               (*_node_data)[vi].heap_index.find(tree);
deba@326: 
deba@326:             if (it != (*_node_data)[vi].heap_index.end()) {
deba@326:               (*_node_data)[vi].heap.erase(it->second);
deba@326:               (*_node_data)[vi].heap_index.erase(it);
deba@326:               if ((*_node_data)[vi].heap.empty()) {
deba@326:                 _blossom_set->increase(v, std::numeric_limits<Value>::max());
deba@326:               } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
deba@326:                 _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
deba@326:               }
deba@326: 
deba@326:               if ((*_blossom_data)[vb].status == MATCHED) {
deba@326:                 if (_blossom_set->classPrio(vb) ==
deba@326:                     std::numeric_limits<Value>::max()) {
deba@326:                   _delta2->erase(vb);
deba@326:                 } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
deba@326:                            (*_blossom_data)[vb].offset) {
deba@326:                   _delta2->increase(vb, _blossom_set->classPrio(vb) -
deba@326:                                    (*_blossom_data)[vb].offset);
deba@326:                 }
deba@326:               }
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void oddToMatched(int blossom) {
deba@326:       (*_blossom_data)[blossom].offset -= _delta_sum;
deba@326: 
deba@326:       if (_blossom_set->classPrio(blossom) !=
deba@326:           std::numeric_limits<Value>::max()) {
deba@326:         _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326:                        (*_blossom_data)[blossom].offset);
deba@326:       }
deba@326: 
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         _delta4->erase(blossom);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void oddToEven(int blossom, int tree) {
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         _delta4->erase(blossom);
deba@326:         (*_blossom_data)[blossom].pot -=
deba@326:           2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
deba@326:       }
deba@326: 
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326:         int ni = (*_node_index)[n];
deba@326: 
deba@326:         _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326: 
deba@326:         (*_node_data)[ni].heap.clear();
deba@326:         (*_node_data)[ni].heap_index.clear();
deba@326:         (*_node_data)[ni].pot +=
deba@326:           2 * _delta_sum - (*_blossom_data)[blossom].offset;
deba@326: 
deba@326:         for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           Node v = _graph.source(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@326:           if ((*_blossom_data)[vb].status == EVEN) {
deba@326:             if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326:               _delta3->push(e, rw / 2);
deba@326:             }
deba@326:           } else {
deba@326: 
deba@326:             typename std::map<int, Arc>::iterator it =
deba@326:               (*_node_data)[vi].heap_index.find(tree);
deba@326: 
deba@326:             if (it != (*_node_data)[vi].heap_index.end()) {
deba@326:               if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326:                 (*_node_data)[vi].heap.replace(it->second, e);
deba@326:                 (*_node_data)[vi].heap.decrease(e, rw);
deba@326:                 it->second = e;
deba@326:               }
deba@326:             } else {
deba@326:               (*_node_data)[vi].heap.push(e, rw);
deba@326:               (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326:             }
deba@326: 
deba@326:             if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326:               _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326: 
deba@326:               if ((*_blossom_data)[vb].status == MATCHED) {
deba@326:                 if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326:                   _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326:                                (*_blossom_data)[vb].offset);
deba@326:                 } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326:                            (*_blossom_data)[vb].offset) {
deba@326:                   _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326:                                    (*_blossom_data)[vb].offset);
deba@326:                 }
deba@326:               }
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:       (*_blossom_data)[blossom].offset = 0;
deba@326:     }
deba@326: 
deba@326:     void alternatePath(int even, int tree) {
deba@326:       int odd;
deba@326: 
deba@326:       evenToMatched(even, tree);
deba@326:       (*_blossom_data)[even].status = MATCHED;
deba@326: 
deba@326:       while ((*_blossom_data)[even].pred != INVALID) {
deba@326:         odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
deba@326:         (*_blossom_data)[odd].status = MATCHED;
deba@326:         oddToMatched(odd);
deba@326:         (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
deba@326: 
deba@326:         even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
deba@326:         (*_blossom_data)[even].status = MATCHED;
deba@326:         evenToMatched(even, tree);
deba@326:         (*_blossom_data)[even].next =
deba@326:           _graph.oppositeArc((*_blossom_data)[odd].pred);
deba@326:       }
deba@326: 
deba@326:     }
deba@326: 
deba@326:     void destroyTree(int tree) {
deba@326:       for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
deba@326:         if ((*_blossom_data)[b].status == EVEN) {
deba@326:           (*_blossom_data)[b].status = MATCHED;
deba@326:           evenToMatched(b, tree);
deba@326:         } else if ((*_blossom_data)[b].status == ODD) {
deba@326:           (*_blossom_data)[b].status = MATCHED;
deba@326:           oddToMatched(b);
deba@326:         }
deba@326:       }
deba@326:       _tree_set->eraseClass(tree);
deba@326:     }
deba@326: 
deba@327:     void augmentOnEdge(const Edge& edge) {
deba@327: 
deba@327:       int left = _blossom_set->find(_graph.u(edge));
deba@327:       int right = _blossom_set->find(_graph.v(edge));
deba@326: 
deba@326:       int left_tree = _tree_set->find(left);
deba@326:       alternatePath(left, left_tree);
deba@326:       destroyTree(left_tree);
deba@326: 
deba@326:       int right_tree = _tree_set->find(right);
deba@326:       alternatePath(right, right_tree);
deba@326:       destroyTree(right_tree);
deba@326: 
deba@327:       (*_blossom_data)[left].next = _graph.direct(edge, true);
deba@327:       (*_blossom_data)[right].next = _graph.direct(edge, false);
deba@326:     }
deba@326: 
deba@326:     void extendOnArc(const Arc& arc) {
deba@326:       int base = _blossom_set->find(_graph.target(arc));
deba@326:       int tree = _tree_set->find(base);
deba@326: 
deba@326:       int odd = _blossom_set->find(_graph.source(arc));
deba@326:       _tree_set->insert(odd, tree);
deba@326:       (*_blossom_data)[odd].status = ODD;
deba@326:       matchedToOdd(odd);
deba@326:       (*_blossom_data)[odd].pred = arc;
deba@326: 
deba@326:       int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
deba@326:       (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
deba@326:       _tree_set->insert(even, tree);
deba@326:       (*_blossom_data)[even].status = EVEN;
deba@326:       matchedToEven(even, tree);
deba@326:     }
deba@326: 
deba@327:     void shrinkOnEdge(const Edge& edge, int tree) {
deba@326:       int nca = -1;
deba@326:       std::vector<int> left_path, right_path;
deba@326: 
deba@326:       {
deba@326:         std::set<int> left_set, right_set;
deba@326:         int left = _blossom_set->find(_graph.u(edge));
deba@326:         left_path.push_back(left);
deba@326:         left_set.insert(left);
deba@326: 
deba@326:         int right = _blossom_set->find(_graph.v(edge));
deba@326:         right_path.push_back(right);
deba@326:         right_set.insert(right);
deba@326: 
deba@326:         while (true) {
deba@326: 
deba@326:           if ((*_blossom_data)[left].pred == INVALID) break;
deba@326: 
deba@326:           left =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326:           left_path.push_back(left);
deba@326:           left =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326:           left_path.push_back(left);
deba@326: 
deba@326:           left_set.insert(left);
deba@326: 
deba@326:           if (right_set.find(left) != right_set.end()) {
deba@326:             nca = left;
deba@326:             break;
deba@326:           }
deba@326: 
deba@326:           if ((*_blossom_data)[right].pred == INVALID) break;
deba@326: 
deba@326:           right =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326:           right_path.push_back(right);
deba@326:           right =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326:           right_path.push_back(right);
deba@326: 
deba@326:           right_set.insert(right);
deba@326: 
deba@326:           if (left_set.find(right) != left_set.end()) {
deba@326:             nca = right;
deba@326:             break;
deba@326:           }
deba@326: 
deba@326:         }
deba@326: 
deba@326:         if (nca == -1) {
deba@326:           if ((*_blossom_data)[left].pred == INVALID) {
deba@326:             nca = right;
deba@326:             while (left_set.find(nca) == left_set.end()) {
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               right_path.push_back(nca);
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               right_path.push_back(nca);
deba@326:             }
deba@326:           } else {
deba@326:             nca = left;
deba@326:             while (right_set.find(nca) == right_set.end()) {
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               left_path.push_back(nca);
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               left_path.push_back(nca);
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326: 
deba@326:       std::vector<int> subblossoms;
deba@326:       Arc prev;
deba@326: 
deba@326:       prev = _graph.direct(edge, true);
deba@326:       for (int i = 0; left_path[i] != nca; i += 2) {
deba@326:         subblossoms.push_back(left_path[i]);
deba@326:         (*_blossom_data)[left_path[i]].next = prev;
deba@326:         _tree_set->erase(left_path[i]);
deba@326: 
deba@326:         subblossoms.push_back(left_path[i + 1]);
deba@326:         (*_blossom_data)[left_path[i + 1]].status = EVEN;
deba@326:         oddToEven(left_path[i + 1], tree);
deba@326:         _tree_set->erase(left_path[i + 1]);
deba@326:         prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
deba@326:       }
deba@326: 
deba@326:       int k = 0;
deba@326:       while (right_path[k] != nca) ++k;
deba@326: 
deba@326:       subblossoms.push_back(nca);
deba@326:       (*_blossom_data)[nca].next = prev;
deba@326: 
deba@326:       for (int i = k - 2; i >= 0; i -= 2) {
deba@326:         subblossoms.push_back(right_path[i + 1]);
deba@326:         (*_blossom_data)[right_path[i + 1]].status = EVEN;
deba@326:         oddToEven(right_path[i + 1], tree);
deba@326:         _tree_set->erase(right_path[i + 1]);
deba@326: 
deba@326:         (*_blossom_data)[right_path[i + 1]].next =
deba@326:           (*_blossom_data)[right_path[i + 1]].pred;
deba@326: 
deba@326:         subblossoms.push_back(right_path[i]);
deba@326:         _tree_set->erase(right_path[i]);
deba@326:       }
deba@326: 
deba@326:       int surface =
deba@326:         _blossom_set->join(subblossoms.begin(), subblossoms.end());
deba@326: 
deba@326:       for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326:         if (!_blossom_set->trivial(subblossoms[i])) {
deba@326:           (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
deba@326:         }
deba@326:         (*_blossom_data)[subblossoms[i]].status = MATCHED;
deba@326:       }
deba@326: 
deba@326:       (*_blossom_data)[surface].pot = -2 * _delta_sum;
deba@326:       (*_blossom_data)[surface].offset = 0;
deba@326:       (*_blossom_data)[surface].status = EVEN;
deba@326:       (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
deba@326:       (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
deba@326: 
deba@326:       _tree_set->insert(surface, tree);
deba@326:       _tree_set->erase(nca);
deba@326:     }
deba@326: 
deba@326:     void splitBlossom(int blossom) {
deba@326:       Arc next = (*_blossom_data)[blossom].next;
deba@326:       Arc pred = (*_blossom_data)[blossom].pred;
deba@326: 
deba@326:       int tree = _tree_set->find(blossom);
deba@326: 
deba@326:       (*_blossom_data)[blossom].status = MATCHED;
deba@326:       oddToMatched(blossom);
deba@326:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326:         _delta2->erase(blossom);
deba@326:       }
deba@326: 
deba@326:       std::vector<int> subblossoms;
deba@326:       _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326: 
deba@326:       Value offset = (*_blossom_data)[blossom].offset;
deba@326:       int b = _blossom_set->find(_graph.source(pred));
deba@326:       int d = _blossom_set->find(_graph.source(next));
deba@326: 
deba@326:       int ib = -1, id = -1;
deba@326:       for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326:         if (subblossoms[i] == b) ib = i;
deba@326:         if (subblossoms[i] == d) id = i;
deba@326: 
deba@326:         (*_blossom_data)[subblossoms[i]].offset = offset;
deba@326:         if (!_blossom_set->trivial(subblossoms[i])) {
deba@326:           (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
deba@326:         }
deba@326:         if (_blossom_set->classPrio(subblossoms[i]) !=
deba@326:             std::numeric_limits<Value>::max()) {
deba@326:           _delta2->push(subblossoms[i],
deba@326:                         _blossom_set->classPrio(subblossoms[i]) -
deba@326:                         (*_blossom_data)[subblossoms[i]].offset);
deba@326:         }
deba@326:       }
deba@326: 
deba@326:       if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
deba@326:         for (int i = (id + 1) % subblossoms.size();
deba@326:              i != ib; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           (*_blossom_data)[sb].next =
deba@326:             _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326:         }
deba@326: 
deba@326:         for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326: 
deba@326:           (*_blossom_data)[sb].status = ODD;
deba@326:           matchedToOdd(sb);
deba@326:           _tree_set->insert(sb, tree);
deba@326:           (*_blossom_data)[sb].pred = pred;
deba@326:           (*_blossom_data)[sb].next =
deba@326:                            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326: 
deba@326:           pred = (*_blossom_data)[ub].next;
deba@326: 
deba@326:           (*_blossom_data)[tb].status = EVEN;
deba@326:           matchedToEven(tb, tree);
deba@326:           _tree_set->insert(tb, tree);
deba@326:           (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
deba@326:         }
deba@326: 
deba@326:         (*_blossom_data)[subblossoms[id]].status = ODD;
deba@326:         matchedToOdd(subblossoms[id]);
deba@326:         _tree_set->insert(subblossoms[id], tree);
deba@326:         (*_blossom_data)[subblossoms[id]].next = next;
deba@326:         (*_blossom_data)[subblossoms[id]].pred = pred;
deba@326: 
deba@326:       } else {
deba@326: 
deba@326:         for (int i = (ib + 1) % subblossoms.size();
deba@326:              i != id; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           (*_blossom_data)[sb].next =
deba@326:             _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326:         }
deba@326: 
deba@326:         for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326: 
deba@326:           (*_blossom_data)[sb].status = ODD;
deba@326:           matchedToOdd(sb);
deba@326:           _tree_set->insert(sb, tree);
deba@326:           (*_blossom_data)[sb].next = next;
deba@326:           (*_blossom_data)[sb].pred =
deba@326:             _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326: 
deba@326:           (*_blossom_data)[tb].status = EVEN;
deba@326:           matchedToEven(tb, tree);
deba@326:           _tree_set->insert(tb, tree);
deba@326:           (*_blossom_data)[tb].pred =
deba@326:             (*_blossom_data)[tb].next =
deba@326:             _graph.oppositeArc((*_blossom_data)[ub].next);
deba@326:           next = (*_blossom_data)[ub].next;
deba@326:         }
deba@326: 
deba@326:         (*_blossom_data)[subblossoms[ib]].status = ODD;
deba@326:         matchedToOdd(subblossoms[ib]);
deba@326:         _tree_set->insert(subblossoms[ib], tree);
deba@326:         (*_blossom_data)[subblossoms[ib]].next = next;
deba@326:         (*_blossom_data)[subblossoms[ib]].pred = pred;
deba@326:       }
deba@326:       _tree_set->erase(blossom);
deba@326:     }
deba@326: 
deba@326:     void extractBlossom(int blossom, const Node& base, const Arc& matching) {
deba@326:       if (_blossom_set->trivial(blossom)) {
deba@326:         int bi = (*_node_index)[base];
deba@326:         Value pot = (*_node_data)[bi].pot;
deba@326: 
kpeter@581:         (*_matching)[base] = matching;
deba@326:         _blossom_node_list.push_back(base);
kpeter@581:         (*_node_potential)[base] = pot;
deba@326:       } else {
deba@326: 
deba@326:         Value pot = (*_blossom_data)[blossom].pot;
deba@326:         int bn = _blossom_node_list.size();
deba@326: 
deba@326:         std::vector<int> subblossoms;
deba@326:         _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326:         int b = _blossom_set->find(base);
deba@326:         int ib = -1;
deba@326:         for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326:           if (subblossoms[i] == b) { ib = i; break; }
deba@326:         }
deba@326: 
deba@326:         for (int i = 1; i < int(subblossoms.size()); i += 2) {
deba@326:           int sb = subblossoms[(ib + i) % subblossoms.size()];
deba@326:           int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
deba@326: 
deba@326:           Arc m = (*_blossom_data)[tb].next;
deba@326:           extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
deba@326:           extractBlossom(tb, _graph.source(m), m);
deba@326:         }
deba@326:         extractBlossom(subblossoms[ib], base, matching);
deba@326: 
deba@326:         int en = _blossom_node_list.size();
deba@326: 
deba@326:         _blossom_potential.push_back(BlossomVariable(bn, en, pot));
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void extractMatching() {
deba@326:       std::vector<int> blossoms;
deba@326:       for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
deba@326:         blossoms.push_back(c);
deba@326:       }
deba@326: 
deba@326:       for (int i = 0; i < int(blossoms.size()); ++i) {
deba@326: 
deba@326:         Value offset = (*_blossom_data)[blossoms[i]].offset;
deba@326:         (*_blossom_data)[blossoms[i]].pot += 2 * offset;
deba@326:         for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
deba@326:              n != INVALID; ++n) {
deba@326:           (*_node_data)[(*_node_index)[n]].pot -= offset;
deba@326:         }
deba@326: 
deba@326:         Arc matching = (*_blossom_data)[blossoms[i]].next;
deba@326:         Node base = _graph.source(matching);
deba@326:         extractBlossom(blossoms[i], base, matching);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:   public:
deba@326: 
deba@326:     /// \brief Constructor
deba@326:     ///
deba@326:     /// Constructor.
deba@326:     MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight)
deba@326:       : _graph(graph), _weight(weight), _matching(0),
deba@326:         _node_potential(0), _blossom_potential(), _blossom_node_list(),
deba@326:         _node_num(0), _blossom_num(0),
deba@326: 
deba@326:         _blossom_index(0), _blossom_set(0), _blossom_data(0),
deba@326:         _node_index(0), _node_heap_index(0), _node_data(0),
deba@326:         _tree_set_index(0), _tree_set(0),
deba@326: 
deba@326:         _delta2_index(0), _delta2(0),
deba@326:         _delta3_index(0), _delta3(0),
deba@326:         _delta4_index(0), _delta4(0),
deba@326: 
deba@870:         _delta_sum(), _unmatched(0),
deba@870: 
deba@870:         _fractional(0)
deba@870:     {}
deba@326: 
deba@326:     ~MaxWeightedPerfectMatching() {
deba@326:       destroyStructures();
deba@870:       if (_fractional) {
deba@870:         delete _fractional;
deba@870:       }
deba@326:     }
deba@326: 
kpeter@590:     /// \name Execution Control
alpar@330:     /// The simplest way to execute the algorithm is to use the
kpeter@590:     /// \ref run() member function.
deba@326: 
deba@326:     ///@{
deba@326: 
deba@326:     /// \brief Initialize the algorithm
deba@326:     ///
kpeter@590:     /// This function initializes the algorithm.
deba@326:     void init() {
deba@326:       createStructures();
deba@326: 
deba@867:       _blossom_node_list.clear();
deba@867:       _blossom_potential.clear();
deba@867: 
deba@326:       for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@581:         (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
deba@326:       }
deba@326:       for (EdgeIt e(_graph); e != INVALID; ++e) {
kpeter@581:         (*_delta3_index)[e] = _delta3->PRE_HEAP;
deba@326:       }
deba@326:       for (int i = 0; i < _blossom_num; ++i) {
kpeter@581:         (*_delta2_index)[i] = _delta2->PRE_HEAP;
kpeter@581:         (*_delta4_index)[i] = _delta4->PRE_HEAP;
deba@326:       }
deba@326: 
deba@870:       _unmatched = _node_num;
deba@870: 
deba@867:       _delta2->clear();
deba@867:       _delta3->clear();
deba@867:       _delta4->clear();
deba@867:       _blossom_set->clear();
deba@867:       _tree_set->clear();
deba@867: 
deba@326:       int index = 0;
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326:         Value max = - std::numeric_limits<Value>::max();
deba@326:         for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           if (_graph.target(e) == n) continue;
deba@326:           if ((dualScale * _weight[e]) / 2 > max) {
deba@326:             max = (dualScale * _weight[e]) / 2;
deba@326:           }
deba@326:         }
kpeter@581:         (*_node_index)[n] = index;
deba@867:         (*_node_data)[index].heap_index.clear();
deba@867:         (*_node_data)[index].heap.clear();
deba@326:         (*_node_data)[index].pot = max;
deba@326:         int blossom =
deba@326:           _blossom_set->insert(n, std::numeric_limits<Value>::max());
deba@326: 
deba@326:         _tree_set->insert(blossom);
deba@326: 
deba@326:         (*_blossom_data)[blossom].status = EVEN;
deba@326:         (*_blossom_data)[blossom].pred = INVALID;
deba@326:         (*_blossom_data)[blossom].next = INVALID;
deba@326:         (*_blossom_data)[blossom].pot = 0;
deba@326:         (*_blossom_data)[blossom].offset = 0;
deba@326:         ++index;
deba@326:       }
deba@326:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@326:         int si = (*_node_index)[_graph.u(e)];
deba@326:         int ti = (*_node_index)[_graph.v(e)];
deba@326:         if (_graph.u(e) != _graph.v(e)) {
deba@326:           _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
deba@326:                             dualScale * _weight[e]) / 2);
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@870:     /// \brief Initialize the algorithm with fractional matching
deba@870:     ///
deba@870:     /// This function initializes the algorithm with a fractional
deba@870:     /// matching. This initialization is also called jumpstart heuristic.
deba@870:     void fractionalInit() {
deba@870:       createStructures();
deba@876: 
deba@876:       _blossom_node_list.clear();
deba@876:       _blossom_potential.clear();
alpar@877: 
deba@870:       if (_fractional == 0) {
deba@870:         _fractional = new FractionalMatching(_graph, _weight, false);
deba@870:       }
deba@870:       if (!_fractional->run()) {
deba@870:         _unmatched = -1;
deba@870:         return;
deba@870:       }
deba@870: 
deba@870:       for (ArcIt e(_graph); e != INVALID; ++e) {
deba@870:         (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
deba@870:       }
deba@870:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@870:         (*_delta3_index)[e] = _delta3->PRE_HEAP;
deba@870:       }
deba@870:       for (int i = 0; i < _blossom_num; ++i) {
deba@870:         (*_delta2_index)[i] = _delta2->PRE_HEAP;
deba@870:         (*_delta4_index)[i] = _delta4->PRE_HEAP;
deba@870:       }
deba@870: 
deba@870:       _unmatched = 0;
deba@870: 
deba@876:       _delta2->clear();
deba@876:       _delta3->clear();
deba@876:       _delta4->clear();
deba@876:       _blossom_set->clear();
deba@876:       _tree_set->clear();
deba@876: 
deba@870:       int index = 0;
deba@870:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@870:         Value pot = _fractional->nodeValue(n);
deba@870:         (*_node_index)[n] = index;
deba@870:         (*_node_data)[index].pot = pot;
deba@876:         (*_node_data)[index].heap_index.clear();
deba@876:         (*_node_data)[index].heap.clear();
deba@870:         int blossom =
deba@870:           _blossom_set->insert(n, std::numeric_limits<Value>::max());
deba@870: 
deba@870:         (*_blossom_data)[blossom].status = MATCHED;
deba@870:         (*_blossom_data)[blossom].pred = INVALID;
deba@870:         (*_blossom_data)[blossom].next = _fractional->matching(n);
deba@870:         (*_blossom_data)[blossom].pot = 0;
deba@870:         (*_blossom_data)[blossom].offset = 0;
deba@870:         ++index;
deba@870:       }
deba@870: 
deba@870:       typename Graph::template NodeMap<bool> processed(_graph, false);
deba@870:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@870:         if (processed[n]) continue;
deba@870:         processed[n] = true;
deba@870:         if (_fractional->matching(n) == INVALID) continue;
deba@870:         int num = 1;
deba@870:         Node v = _graph.target(_fractional->matching(n));
deba@870:         while (n != v) {
deba@870:           processed[v] = true;
deba@870:           v = _graph.target(_fractional->matching(v));
deba@870:           ++num;
deba@870:         }
deba@870: 
deba@870:         if (num % 2 == 1) {
deba@870:           std::vector<int> subblossoms(num);
deba@870: 
deba@870:           subblossoms[--num] = _blossom_set->find(n);
deba@870:           v = _graph.target(_fractional->matching(n));
deba@870:           while (n != v) {
deba@870:             subblossoms[--num] = _blossom_set->find(v);
alpar@877:             v = _graph.target(_fractional->matching(v));
deba@870:           }
alpar@877: 
alpar@877:           int surface =
deba@870:             _blossom_set->join(subblossoms.begin(), subblossoms.end());
deba@870:           (*_blossom_data)[surface].status = EVEN;
deba@870:           (*_blossom_data)[surface].pred = INVALID;
deba@870:           (*_blossom_data)[surface].next = INVALID;
deba@870:           (*_blossom_data)[surface].pot = 0;
deba@870:           (*_blossom_data)[surface].offset = 0;
alpar@877: 
deba@870:           _tree_set->insert(surface);
deba@870:           ++_unmatched;
deba@870:         }
deba@870:       }
deba@870: 
deba@870:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@870:         int si = (*_node_index)[_graph.u(e)];
deba@870:         int sb = _blossom_set->find(_graph.u(e));
deba@870:         int ti = (*_node_index)[_graph.v(e)];
deba@870:         int tb = _blossom_set->find(_graph.v(e));
deba@870:         if ((*_blossom_data)[sb].status == EVEN &&
deba@870:             (*_blossom_data)[tb].status == EVEN && sb != tb) {
deba@870:           _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
deba@870:                             dualScale * _weight[e]) / 2);
deba@870:         }
deba@870:       }
deba@870: 
deba@870:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@870:         int nb = _blossom_set->find(n);
deba@870:         if ((*_blossom_data)[nb].status != MATCHED) continue;
deba@870:         int ni = (*_node_index)[n];
deba@870: 
deba@870:         for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@870:           Node v = _graph.target(e);
deba@870:           int vb = _blossom_set->find(v);
deba@870:           int vi = (*_node_index)[v];
deba@870: 
deba@870:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@870:             dualScale * _weight[e];
deba@870: 
deba@870:           if ((*_blossom_data)[vb].status == EVEN) {
deba@870: 
deba@870:             int vt = _tree_set->find(vb);
deba@870: 
deba@870:             typename std::map<int, Arc>::iterator it =
deba@870:               (*_node_data)[ni].heap_index.find(vt);
deba@870: 
deba@870:             if (it != (*_node_data)[ni].heap_index.end()) {
deba@870:               if ((*_node_data)[ni].heap[it->second] > rw) {
deba@870:                 (*_node_data)[ni].heap.replace(it->second, e);
deba@870:                 (*_node_data)[ni].heap.decrease(e, rw);
deba@870:                 it->second = e;
deba@870:               }
deba@870:             } else {
deba@870:               (*_node_data)[ni].heap.push(e, rw);
deba@870:               (*_node_data)[ni].heap_index.insert(std::make_pair(vt, e));
deba@870:             }
deba@870:           }
deba@870:         }
alpar@877: 
deba@870:         if (!(*_node_data)[ni].heap.empty()) {
deba@870:           _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@870:           _delta2->push(nb, _blossom_set->classPrio(nb));
deba@870:         }
deba@870:       }
deba@870:     }
deba@870: 
kpeter@590:     /// \brief Start the algorithm
deba@326:     ///
kpeter@590:     /// This function starts the algorithm.
kpeter@590:     ///
deba@870:     /// \pre \ref init() or \ref fractionalInit() must be called before
deba@870:     /// using this function.
deba@326:     bool start() {
deba@326:       enum OpType {
deba@326:         D2, D3, D4
deba@326:       };
deba@326: 
deba@870:       if (_unmatched == -1) return false;
deba@870: 
deba@870:       while (_unmatched > 0) {
deba@326:         Value d2 = !_delta2->empty() ?
deba@326:           _delta2->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@326:         Value d3 = !_delta3->empty() ?
deba@326:           _delta3->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@326:         Value d4 = !_delta4->empty() ?
deba@326:           _delta4->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@868:         _delta_sum = d3; OpType ot = D3;
deba@868:         if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
deba@326:         if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
deba@326: 
deba@326:         if (_delta_sum == std::numeric_limits<Value>::max()) {
deba@326:           return false;
deba@326:         }
deba@326: 
deba@326:         switch (ot) {
deba@326:         case D2:
deba@326:           {
deba@326:             int blossom = _delta2->top();
deba@326:             Node n = _blossom_set->classTop(blossom);
deba@326:             Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
deba@326:             extendOnArc(e);
deba@326:           }
deba@326:           break;
deba@326:         case D3:
deba@326:           {
deba@326:             Edge e = _delta3->top();
deba@326: 
deba@326:             int left_blossom = _blossom_set->find(_graph.u(e));
deba@326:             int right_blossom = _blossom_set->find(_graph.v(e));
deba@326: 
deba@326:             if (left_blossom == right_blossom) {
deba@326:               _delta3->pop();
deba@326:             } else {
deba@326:               int left_tree = _tree_set->find(left_blossom);
deba@326:               int right_tree = _tree_set->find(right_blossom);
deba@326: 
deba@326:               if (left_tree == right_tree) {
deba@327:                 shrinkOnEdge(e, left_tree);
deba@326:               } else {
deba@327:                 augmentOnEdge(e);
deba@870:                 _unmatched -= 2;
deba@326:               }
deba@326:             }
deba@326:           } break;
deba@326:         case D4:
deba@326:           splitBlossom(_delta4->top());
deba@326:           break;
deba@326:         }
deba@326:       }
deba@326:       extractMatching();
deba@326:       return true;
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Run the algorithm.
deba@326:     ///
kpeter@590:     /// This method runs the \c %MaxWeightedPerfectMatching algorithm.
deba@326:     ///
kpeter@590:     /// \note mwpm.run() is just a shortcut of the following code.
deba@326:     /// \code
deba@870:     ///   mwpm.fractionalInit();
kpeter@590:     ///   mwpm.start();
deba@326:     /// \endcode
deba@326:     bool run() {
deba@870:       fractionalInit();
deba@326:       return start();
deba@326:     }
deba@326: 
deba@326:     /// @}
deba@326: 
kpeter@590:     /// \name Primal Solution
deba@868:     /// Functions to get the primal solution, i.e. the maximum weighted
kpeter@590:     /// perfect matching.\n
kpeter@590:     /// Either \ref run() or \ref start() function should be called before
kpeter@590:     /// using them.
deba@326: 
deba@326:     /// @{
deba@326: 
kpeter@590:     /// \brief Return the weight of the matching.
deba@326:     ///
kpeter@590:     /// This function returns the weight of the found matching.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
kpeter@593:     Value matchingWeight() const {
deba@326:       Value sum = 0;
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326:         if ((*_matching)[n] != INVALID) {
deba@326:           sum += _weight[(*_matching)[n]];
deba@326:         }
deba@326:       }
deba@868:       return sum / 2;
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Return \c true if the given edge is in the matching.
deba@326:     ///
deba@868:     /// This function returns \c true if the given edge is in the found
kpeter@590:     /// matching.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@327:     bool matching(const Edge& edge) const {
deba@327:       return static_cast<const Edge&>((*_matching)[_graph.u(edge)]) == edge;
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Return the matching arc (or edge) incident to the given node.
deba@326:     ///
kpeter@590:     /// This function returns the matching arc (or edge) incident to the
deba@868:     /// given node in the found matching or \c INVALID if the node is
kpeter@590:     /// not covered by the matching.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@326:     Arc matching(const Node& node) const {
deba@326:       return (*_matching)[node];
deba@326:     }
deba@326: 
kpeter@593:     /// \brief Return a const reference to the matching map.
kpeter@593:     ///
kpeter@593:     /// This function returns a const reference to a node map that stores
kpeter@593:     /// the matching arc (or edge) incident to each node.
kpeter@593:     const MatchingMap& matchingMap() const {
kpeter@593:       return *_matching;
kpeter@593:     }
kpeter@593: 
kpeter@590:     /// \brief Return the mate of the given node.
deba@326:     ///
deba@868:     /// This function returns the mate of the given node in the found
kpeter@590:     /// matching or \c INVALID if the node is not covered by the matching.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@326:     Node mate(const Node& node) const {
deba@326:       return _graph.target((*_matching)[node]);
deba@326:     }
deba@326: 
deba@326:     /// @}
deba@326: 
kpeter@590:     /// \name Dual Solution
kpeter@590:     /// Functions to get the dual solution.\n
kpeter@590:     /// Either \ref run() or \ref start() function should be called before
kpeter@590:     /// using them.
deba@326: 
deba@326:     /// @{
deba@326: 
kpeter@590:     /// \brief Return the value of the dual solution.
deba@326:     ///
deba@868:     /// This function returns the value of the dual solution.
deba@868:     /// It should be equal to the primal value scaled by \ref dualScale
kpeter@590:     /// "dual scale".
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@326:     Value dualValue() const {
deba@326:       Value sum = 0;
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326:         sum += nodeValue(n);
deba@326:       }
deba@326:       for (int i = 0; i < blossomNum(); ++i) {
deba@326:         sum += blossomValue(i) * (blossomSize(i) / 2);
deba@326:       }
deba@326:       return sum;
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Return the dual value (potential) of the given node.
deba@326:     ///
kpeter@590:     /// This function returns the dual value (potential) of the given node.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@326:     Value nodeValue(const Node& n) const {
deba@326:       return (*_node_potential)[n];
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Return the number of the blossoms in the basis.
deba@326:     ///
kpeter@590:     /// This function returns the number of the blossoms in the basis.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@326:     /// \see BlossomIt
deba@326:     int blossomNum() const {
deba@326:       return _blossom_potential.size();
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Return the number of the nodes in the given blossom.
deba@326:     ///
kpeter@590:     /// This function returns the number of the nodes in the given blossom.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
kpeter@590:     /// \see BlossomIt
deba@326:     int blossomSize(int k) const {
deba@326:       return _blossom_potential[k].end - _blossom_potential[k].begin;
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Return the dual value (ptential) of the given blossom.
deba@326:     ///
kpeter@590:     /// This function returns the dual value (ptential) of the given blossom.
kpeter@590:     ///
kpeter@590:     /// \pre Either run() or start() must be called before using this function.
deba@326:     Value blossomValue(int k) const {
deba@326:       return _blossom_potential[k].value;
deba@326:     }
deba@326: 
kpeter@590:     /// \brief Iterator for obtaining the nodes of a blossom.
deba@326:     ///
deba@868:     /// This class provides an iterator for obtaining the nodes of the
kpeter@590:     /// given blossom. It lists a subset of the nodes.
deba@868:     /// Before using this iterator, you must allocate a
kpeter@590:     /// MaxWeightedPerfectMatching class and execute it.
deba@326:     class BlossomIt {
deba@326:     public:
deba@326: 
deba@326:       /// \brief Constructor.
deba@326:       ///
kpeter@590:       /// Constructor to get the nodes of the given variable.
kpeter@590:       ///
deba@868:       /// \pre Either \ref MaxWeightedPerfectMatching::run() "algorithm.run()"
deba@868:       /// or \ref MaxWeightedPerfectMatching::start() "algorithm.start()"
kpeter@590:       /// must be called before initializing this iterator.
deba@326:       BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable)
deba@326:         : _algorithm(&algorithm)
deba@326:       {
deba@326:         _index = _algorithm->_blossom_potential[variable].begin;
deba@326:         _last = _algorithm->_blossom_potential[variable].end;
deba@326:       }
deba@326: 
kpeter@590:       /// \brief Conversion to \c Node.
deba@326:       ///
kpeter@590:       /// Conversion to \c Node.
deba@326:       operator Node() const {
deba@327:         return _algorithm->_blossom_node_list[_index];
deba@326:       }
deba@326: 
deba@326:       /// \brief Increment operator.
deba@326:       ///
deba@326:       /// Increment operator.
deba@326:       BlossomIt& operator++() {
deba@326:         ++_index;
deba@326:         return *this;
deba@326:       }
deba@326: 
deba@327:       /// \brief Validity checking
deba@327:       ///
kpeter@590:       /// This function checks whether the iterator is invalid.
deba@327:       bool operator==(Invalid) const { return _index == _last; }
deba@327: 
deba@327:       /// \brief Validity checking
deba@327:       ///
kpeter@590:       /// This function checks whether the iterator is valid.
deba@327:       bool operator!=(Invalid) const { return _index != _last; }
deba@326: 
deba@326:     private:
deba@326:       const MaxWeightedPerfectMatching* _algorithm;
deba@326:       int _last;
deba@326:       int _index;
deba@326:     };
deba@326: 
deba@326:     /// @}
deba@326: 
deba@326:   };
deba@326: 
deba@326: } //END OF NAMESPACE LEMON
deba@326: 
deba@868: #endif //LEMON_MATCHING_H