# HG changeset patch
# User Alpar Juttner <alpar@cs.elte.hu>
# Date 1236175785 0
# Node ID d59dcc933e59d63ac26f8af85c03947a32cbd562
# Parent  fc6c7aab4b8d01f2d6ee4eb442b7ee81847319d5# Parent  d6b40ebb26175685ef0bea3cd3a8c01212ba9b5e
Merge

diff -r fc6c7aab4b8d -r d59dcc933e59 lemon/Makefile.am
--- a/lemon/Makefile.am	Wed Mar 04 13:43:05 2009 +0000
+++ b/lemon/Makefile.am	Wed Mar 04 14:09:45 2009 +0000
@@ -68,6 +68,7 @@
 	lemon/euler.h \
 	lemon/full_graph.h \
 	lemon/glpk.h \
+	lemon/gomory_hu.h \
 	lemon/graph_to_eps.h \
 	lemon/grid_graph.h \
 	lemon/hypercube_graph.h \
diff -r fc6c7aab4b8d -r d59dcc933e59 lemon/gomory_hu.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/gomory_hu.h	Wed Mar 04 14:09:45 2009 +0000
@@ -0,0 +1,551 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef LEMON_GOMORY_HU_TREE_H
+#define LEMON_GOMORY_HU_TREE_H
+
+#include <limits>
+
+#include <lemon/core.h>
+#include <lemon/preflow.h>
+#include <lemon/concept_check.h>
+#include <lemon/concepts/maps.h>
+
+/// \ingroup min_cut
+/// \file 
+/// \brief Gomory-Hu cut tree in graphs.
+
+namespace lemon {
+
+  /// \ingroup min_cut
+  ///
+  /// \brief Gomory-Hu cut tree algorithm
+  ///
+  /// The Gomory-Hu tree is a tree on the node set of a given graph, but it
+  /// may contain edges which are not in the original graph. It has the
+  /// property that the minimum capacity edge of the path between two nodes 
+  /// in this tree has the same weight as the minimum cut in the graph
+  /// between these nodes. Moreover the components obtained by removing
+  /// this edge from the tree determine the corresponding minimum cut.
+  ///
+  /// Therefore once this tree is computed, the minimum cut between any pair
+  /// of nodes can easily be obtained.
+  /// 
+  /// The algorithm calculates \e n-1 distinct minimum cuts (currently with
+  /// the \ref Preflow algorithm), therefore the algorithm has
+  /// \f$(O(n^3\sqrt{e})\f$ overall time complexity. It calculates a
+  /// rooted Gomory-Hu tree, its structure and the weights can be obtained
+  /// by \c predNode(), \c predValue() and \c rootDist().
+  /// 
+  /// The members \c minCutMap() and \c minCutValue() calculate
+  /// the minimum cut and the minimum cut value between any two nodes
+  /// in the graph. You can also list (iterate on) the nodes and the
+  /// edges of the cuts using \c MinCutNodeIt and \c MinCutEdgeIt.
+  ///
+  /// \tparam GR The type of the undirected graph the algorithm runs on.
+  /// \tparam CAP The type of the edge map describing the edge capacities.
+  /// It is \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>" by default.
+#ifdef DOXYGEN
+  template <typename GR,
+	    typename CAP>
+#else
+  template <typename GR,
+	    typename CAP = typename GR::template EdgeMap<int> >
+#endif
+  class GomoryHu {
+  public:
+
+    /// The graph type
+    typedef GR Graph;
+    /// The type of the edge capacity map
+    typedef CAP Capacity;
+    /// The value type of capacities
+    typedef typename Capacity::Value Value;
+    
+  private:
+
+    TEMPLATE_GRAPH_TYPEDEFS(Graph);
+
+    const Graph& _graph;
+    const Capacity& _capacity;
+
+    Node _root;
+    typename Graph::template NodeMap<Node>* _pred;
+    typename Graph::template NodeMap<Value>* _weight;
+    typename Graph::template NodeMap<int>* _order;
+
+    void createStructures() {
+      if (!_pred) {
+	_pred = new typename Graph::template NodeMap<Node>(_graph);
+      }
+      if (!_weight) {
+	_weight = new typename Graph::template NodeMap<Value>(_graph);
+      }
+      if (!_order) {
+	_order = new typename Graph::template NodeMap<int>(_graph);
+      }
+    }
+
+    void destroyStructures() {
+      if (_pred) {
+	delete _pred;
+      }
+      if (_weight) {
+	delete _weight;
+      }
+      if (_order) {
+	delete _order;
+      }
+    }
+  
+  public:
+
+    /// \brief Constructor
+    ///
+    /// Constructor
+    /// \param graph The undirected graph the algorithm runs on.
+    /// \param capacity The edge capacity map.
+    GomoryHu(const Graph& graph, const Capacity& capacity) 
+      : _graph(graph), _capacity(capacity),
+	_pred(0), _weight(0), _order(0) 
+    {
+      checkConcept<concepts::ReadMap<Edge, Value>, Capacity>();
+    }
+
+
+    /// \brief Destructor
+    ///
+    /// Destructor
+    ~GomoryHu() {
+      destroyStructures();
+    }
+
+  private:
+  
+    // Initialize the internal data structures
+    void init() {
+      createStructures();
+
+      _root = NodeIt(_graph);
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+	_pred->set(n, _root);
+	_order->set(n, -1);
+      }
+      _pred->set(_root, INVALID);
+      _weight->set(_root, std::numeric_limits<Value>::max()); 
+    }
+
+
+    // Start the algorithm
+    void start() {
+      Preflow<Graph, Capacity> fa(_graph, _capacity, _root, INVALID);
+
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+	if (n == _root) continue;
+
+	Node pn = (*_pred)[n];
+	fa.source(n);
+	fa.target(pn);
+
+	fa.runMinCut();
+
+	_weight->set(n, fa.flowValue());
+
+	for (NodeIt nn(_graph); nn != INVALID; ++nn) {
+	  if (nn != n && fa.minCut(nn) && (*_pred)[nn] == pn) {
+	    _pred->set(nn, n);
+	  }
+	}
+	if ((*_pred)[pn] != INVALID && fa.minCut((*_pred)[pn])) {
+	  _pred->set(n, (*_pred)[pn]);
+	  _pred->set(pn, n);
+	  _weight->set(n, (*_weight)[pn]);
+	  _weight->set(pn, fa.flowValue());	
+	}
+      }
+
+      _order->set(_root, 0);
+      int index = 1;
+
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+	std::vector<Node> st;
+	Node nn = n;
+	while ((*_order)[nn] == -1) {
+	  st.push_back(nn);
+	  nn = (*_pred)[nn];
+	}
+	while (!st.empty()) {
+	  _order->set(st.back(), index++);
+	  st.pop_back();
+	}
+      }
+    }
+
+  public:
+
+    ///\name Execution Control
+ 
+    ///@{
+
+    /// \brief Run the Gomory-Hu algorithm.
+    ///
+    /// This function runs the Gomory-Hu algorithm.
+    void run() {
+      init();
+      start();
+    }
+    
+    /// @}
+
+    ///\name Query Functions
+    ///The results of the algorithm can be obtained using these
+    ///functions.\n
+    ///\ref run() "run()" should be called before using them.\n
+    ///See also \ref MinCutNodeIt and \ref MinCutEdgeIt.
+
+    ///@{
+
+    /// \brief Return the predecessor node in the Gomory-Hu tree.
+    ///
+    /// This function returns the predecessor node in the Gomory-Hu tree.
+    /// If the node is
+    /// the root of the Gomory-Hu tree, then it returns \c INVALID.
+    Node predNode(const Node& node) {
+      return (*_pred)[node];
+    }
+
+    /// \brief Return the distance from the root node in the Gomory-Hu tree.
+    ///
+    /// This function returns the distance of \c node from the root node
+    /// in the Gomory-Hu tree.
+    int rootDist(const Node& node) {
+      return (*_order)[node];
+    }
+
+    /// \brief Return the weight of the predecessor edge in the
+    /// Gomory-Hu tree.
+    ///
+    /// This function returns the weight of the predecessor edge in the
+    /// Gomory-Hu tree.  If the node is the root, the result is undefined.
+    Value predValue(const Node& node) {
+      return (*_weight)[node];
+    }
+
+    /// \brief Return the minimum cut value between two nodes
+    ///
+    /// This function returns the minimum cut value between two nodes. The
+    /// algorithm finds the nearest common ancestor in the Gomory-Hu
+    /// tree and calculates the minimum weight edge on the paths to
+    /// the ancestor.
+    Value minCutValue(const Node& s, const Node& t) const {
+      Node sn = s, tn = t;
+      Value value = std::numeric_limits<Value>::max();
+      
+      while (sn != tn) {
+	if ((*_order)[sn] < (*_order)[tn]) {
+	  if ((*_weight)[tn] <= value) value = (*_weight)[tn];
+	  tn = (*_pred)[tn];
+	} else {
+	  if ((*_weight)[sn] <= value) value = (*_weight)[sn];
+	  sn = (*_pred)[sn];
+	}
+      }
+      return value;
+    }
+
+    /// \brief Return the minimum cut between two nodes
+    ///
+    /// This function returns the minimum cut between the nodes \c s and \c t
+    /// in the \c cutMap parameter by setting the nodes in the component of
+    /// \c s to \c true and the other nodes to \c false.
+    ///
+    /// For higher level interfaces, see MinCutNodeIt and MinCutEdgeIt.
+    template <typename CutMap>
+    Value minCutMap(const Node& s, ///< The base node.
+                    const Node& t,
+                    ///< The node you want to separate from node \c s.
+                    CutMap& cutMap
+                    ///< The cut will be returned in this map.
+                    /// It must be a \c bool (or convertible) 
+                    /// \ref concepts::ReadWriteMap "ReadWriteMap"
+                    /// on the graph nodes.
+                    ) const {
+      Node sn = s, tn = t;
+      bool s_root=false;
+      Node rn = INVALID;
+      Value value = std::numeric_limits<Value>::max();
+      
+      while (sn != tn) {
+	if ((*_order)[sn] < (*_order)[tn]) {
+	  if ((*_weight)[tn] <= value) {
+	    rn = tn;
+            s_root = false;
+	    value = (*_weight)[tn];
+	  }
+	  tn = (*_pred)[tn];
+	} else {
+	  if ((*_weight)[sn] <= value) {
+	    rn = sn;
+            s_root = true;
+	    value = (*_weight)[sn];
+	  }
+	  sn = (*_pred)[sn];
+	}
+      }
+
+      typename Graph::template NodeMap<bool> reached(_graph, false);
+      reached.set(_root, true);
+      cutMap.set(_root, !s_root);
+      reached.set(rn, true);
+      cutMap.set(rn, s_root);
+
+      std::vector<Node> st;
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+	st.clear();
+        Node nn = n;
+	while (!reached[nn]) {
+	  st.push_back(nn);
+	  nn = (*_pred)[nn];
+	}
+	while (!st.empty()) {
+	  cutMap.set(st.back(), cutMap[nn]);
+	  st.pop_back();
+	}
+      }
+      
+      return value;
+    }
+
+    ///@}
+
+    friend class MinCutNodeIt;
+
+    /// Iterate on the nodes of a minimum cut
+    
+    /// This iterator class lists the nodes of a minimum cut found by
+    /// GomoryHu. Before using it, you must allocate a GomoryHu class,
+    /// and call its \ref GomoryHu::run() "run()" method.
+    ///
+    /// This example counts the nodes in the minimum cut separating \c s from
+    /// \c t.
+    /// \code
+    /// GomoruHu<Graph> gom(g, capacities);
+    /// gom.run();
+    /// int cnt=0;
+    /// for(GomoruHu<Graph>::MinCutNodeIt n(gom,s,t); n!=INVALID; ++n) ++cnt;
+    /// \endcode
+    class MinCutNodeIt
+    {
+      bool _side;
+      typename Graph::NodeIt _node_it;
+      typename Graph::template NodeMap<bool> _cut;
+    public:
+      /// Constructor
+
+      /// Constructor.
+      ///
+      MinCutNodeIt(GomoryHu const &gomory,
+                   ///< The GomoryHu class. You must call its
+                   ///  run() method
+                   ///  before initializing this iterator.
+                   const Node& s, ///< The base node.
+                   const Node& t,
+                   ///< The node you want to separate from node \c s.
+                   bool side=true
+                   ///< If it is \c true (default) then the iterator lists
+                   ///  the nodes of the component containing \c s,
+                   ///  otherwise it lists the other component.
+                   /// \note As the minimum cut is not always unique,
+                   /// \code
+                   /// MinCutNodeIt(gomory, s, t, true);
+                   /// \endcode
+                   /// and
+                   /// \code
+                   /// MinCutNodeIt(gomory, t, s, false);
+                   /// \endcode
+                   /// does not necessarily give the same set of nodes.
+                   /// However it is ensured that
+                   /// \code
+                   /// MinCutNodeIt(gomory, s, t, true);
+                   /// \endcode
+                   /// and
+                   /// \code
+                   /// MinCutNodeIt(gomory, s, t, false);
+                   /// \endcode
+                   /// together list each node exactly once.
+                   )
+        : _side(side), _cut(gomory._graph)
+      {
+        gomory.minCutMap(s,t,_cut);
+        for(_node_it=typename Graph::NodeIt(gomory._graph);
+            _node_it!=INVALID && _cut[_node_it]!=_side;
+            ++_node_it) {}
+      }
+      /// Conversion to \c Node
+
+      /// Conversion to \c Node.
+      ///
+      operator typename Graph::Node() const
+      {
+        return _node_it;
+      }
+      bool operator==(Invalid) { return _node_it==INVALID; }
+      bool operator!=(Invalid) { return _node_it!=INVALID; }
+      /// Next node
+
+      /// Next node.
+      ///
+      MinCutNodeIt &operator++()
+      {
+        for(++_node_it;_node_it!=INVALID&&_cut[_node_it]!=_side;++_node_it) {}
+        return *this;
+      }
+      /// Postfix incrementation
+
+      /// Postfix incrementation.
+      ///
+      /// \warning This incrementation
+      /// returns a \c Node, not a \c MinCutNodeIt, as one may
+      /// expect.
+      typename Graph::Node operator++(int)
+      {
+        typename Graph::Node n=*this;
+        ++(*this);
+        return n;
+      }
+    };
+    
+    friend class MinCutEdgeIt;
+    
+    /// Iterate on the edges of a minimum cut
+    
+    /// This iterator class lists the edges of a minimum cut found by
+    /// GomoryHu. Before using it, you must allocate a GomoryHu class,
+    /// and call its \ref GomoryHu::run() "run()" method.
+    ///
+    /// This example computes the value of the minimum cut separating \c s from
+    /// \c t.
+    /// \code
+    /// GomoruHu<Graph> gom(g, capacities);
+    /// gom.run();
+    /// int value=0;
+    /// for(GomoruHu<Graph>::MinCutEdgeIt e(gom,s,t); e!=INVALID; ++e)
+    ///   value+=capacities[e];
+    /// \endcode
+    /// the result will be the same as it is returned by
+    /// \ref GomoryHu::minCutValue() "gom.minCutValue(s,t)"
+    class MinCutEdgeIt
+    {
+      bool _side;
+      const Graph &_graph;
+      typename Graph::NodeIt _node_it;
+      typename Graph::OutArcIt _arc_it;
+      typename Graph::template NodeMap<bool> _cut;
+      void step()
+      {
+        ++_arc_it;
+        while(_node_it!=INVALID && _arc_it==INVALID)
+          {
+            for(++_node_it;_node_it!=INVALID&&!_cut[_node_it];++_node_it) {}
+            if(_node_it!=INVALID)
+              _arc_it=typename Graph::OutArcIt(_graph,_node_it);
+          }
+      }
+      
+    public:
+      MinCutEdgeIt(GomoryHu const &gomory,
+                   ///< The GomoryHu class. You must call its
+                   ///  run() method
+                   ///  before initializing this iterator.
+                   const Node& s,  ///< The base node.
+                   const Node& t,
+                   ///< The node you want to separate from node \c s.
+                   bool side=true
+                   ///< If it is \c true (default) then the listed arcs
+                   ///  will be oriented from the
+                   ///  the nodes of the component containing \c s,
+                   ///  otherwise they will be oriented in the opposite
+                   ///  direction.
+                   )
+        : _graph(gomory._graph), _cut(_graph)
+      {
+        gomory.minCutMap(s,t,_cut);
+        if(!side)
+          for(typename Graph::NodeIt n(_graph);n!=INVALID;++n)
+            _cut[n]=!_cut[n];
+
+        for(_node_it=typename Graph::NodeIt(_graph);
+            _node_it!=INVALID && !_cut[_node_it];
+            ++_node_it) {}
+        _arc_it = _node_it!=INVALID ?
+          typename Graph::OutArcIt(_graph,_node_it) : INVALID;
+        while(_node_it!=INVALID && _arc_it == INVALID)
+          {
+            for(++_node_it; _node_it!=INVALID&&!_cut[_node_it]; ++_node_it) {}
+            if(_node_it!=INVALID)
+              _arc_it= typename Graph::OutArcIt(_graph,_node_it);
+          }
+        while(_arc_it!=INVALID && _cut[_graph.target(_arc_it)]) step();
+      }
+      /// Conversion to \c Arc
+
+      /// Conversion to \c Arc.
+      ///
+      operator typename Graph::Arc() const
+      {
+        return _arc_it;
+      }
+      /// Conversion to \c Edge
+
+      /// Conversion to \c Edge.
+      ///
+      operator typename Graph::Edge() const
+      {
+        return _arc_it;
+      }
+      bool operator==(Invalid) { return _node_it==INVALID; }
+      bool operator!=(Invalid) { return _node_it!=INVALID; }
+      /// Next edge
+
+      /// Next edge.
+      ///
+      MinCutEdgeIt &operator++()
+      {
+        step();
+        while(_arc_it!=INVALID && _cut[_graph.target(_arc_it)]) step();
+        return *this;
+      }
+      /// Postfix incrementation
+      
+      /// Postfix incrementation.
+      ///
+      /// \warning This incrementation
+      /// returns an \c Arc, not a \c MinCutEdgeIt, as one may expect.
+      typename Graph::Arc operator++(int)
+      {
+        typename Graph::Arc e=*this;
+        ++(*this);
+        return e;
+      }
+    };
+
+  };
+
+}
+
+#endif
diff -r fc6c7aab4b8d -r d59dcc933e59 test/CMakeLists.txt
--- a/test/CMakeLists.txt	Wed Mar 04 13:43:05 2009 +0000
+++ b/test/CMakeLists.txt	Wed Mar 04 14:09:45 2009 +0000
@@ -21,6 +21,7 @@
   edge_set_test
   error_test
   euler_test
+  gomory_hu_test
   graph_copy_test
   graph_test
   graph_utils_test
diff -r fc6c7aab4b8d -r d59dcc933e59 test/Makefile.am
--- a/test/Makefile.am	Wed Mar 04 13:43:05 2009 +0000
+++ b/test/Makefile.am	Wed Mar 04 14:09:45 2009 +0000
@@ -17,6 +17,7 @@
 	test/edge_set_test \
 	test/error_test \
 	test/euler_test \
+	test/gomory_hu_test \
 	test/graph_copy_test \
 	test/graph_test \
 	test/graph_utils_test \
@@ -57,6 +58,7 @@
 test_edge_set_test_SOURCES = test/edge_set_test.cc
 test_error_test_SOURCES = test/error_test.cc
 test_euler_test_SOURCES = test/euler_test.cc
+test_gomory_hu_test_SOURCES = test/gomory_hu_test.cc
 test_graph_copy_test_SOURCES = test/graph_copy_test.cc
 test_graph_test_SOURCES = test/graph_test.cc
 test_graph_utils_test_SOURCES = test/graph_utils_test.cc
diff -r fc6c7aab4b8d -r d59dcc933e59 test/gomory_hu_test.cc
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/gomory_hu_test.cc	Wed Mar 04 14:09:45 2009 +0000
@@ -0,0 +1,92 @@
+#include <iostream>
+
+#include "test_tools.h"
+#include <lemon/smart_graph.h>
+#include <lemon/lgf_reader.h>
+#include <lemon/gomory_hu.h>
+#include <cstdlib>
+
+using namespace std;
+using namespace lemon;
+
+typedef SmartGraph Graph;
+
+char test_lgf[] =
+  "@nodes\n"
+  "label\n"
+  "0\n"
+  "1\n"
+  "2\n"
+  "3\n"
+  "4\n"
+  "@arcs\n"
+  "     label capacity\n"
+  "0 1  0     1\n"
+  "1 2  1     1\n"
+  "2 3  2     1\n"
+  "0 3  4     5\n"
+  "0 3  5     10\n"
+  "0 3  6     7\n"
+  "4 2  7     1\n"
+  "@attributes\n"
+  "source 0\n"
+  "target 3\n";
+  
+GRAPH_TYPEDEFS(Graph);
+typedef Graph::EdgeMap<int> IntEdgeMap;
+typedef Graph::NodeMap<bool> BoolNodeMap;
+
+int cutValue(const Graph& graph, const BoolNodeMap& cut,
+	     const IntEdgeMap& capacity) {
+
+  int sum = 0;
+  for (EdgeIt e(graph); e != INVALID; ++e) {
+    Node s = graph.u(e);
+    Node t = graph.v(e);
+
+    if (cut[s] != cut[t]) {
+      sum += capacity[e];
+    }
+  }
+  return sum;
+}
+
+
+int main() {
+  Graph graph;
+  IntEdgeMap capacity(graph);
+
+  std::istringstream input(test_lgf);
+  GraphReader<Graph>(graph, input).
+    edgeMap("capacity", capacity).run();
+
+  GomoryHu<Graph> ght(graph, capacity);
+  ght.run();
+
+  for (NodeIt u(graph); u != INVALID; ++u) {
+    for (NodeIt v(graph); v != u; ++v) {
+      Preflow<Graph, IntEdgeMap> pf(graph, capacity, u, v);
+      pf.runMinCut();
+      BoolNodeMap cm(graph);
+      ght.minCutMap(u, v, cm);
+      check(pf.flowValue() == ght.minCutValue(u, v), "Wrong cut 1");
+      check(cm[u] != cm[v], "Wrong cut 3");
+      check(pf.flowValue() == cutValue(graph, cm, capacity), "Wrong cut 2");
+
+      int sum=0;
+      for(GomoryHu<Graph>::MinCutEdgeIt a(ght, u, v);a!=INVALID;++a)
+        sum+=capacity[a]; 
+      check(sum == ght.minCutValue(u, v), "Problem with MinCutEdgeIt");
+
+      sum=0;
+      for(GomoryHu<Graph>::MinCutNodeIt n(ght, u, v,true);n!=INVALID;++n)
+        sum++;
+      for(GomoryHu<Graph>::MinCutNodeIt n(ght, u, v,false);n!=INVALID;++n)
+        sum++;
+      check(sum == countNodes(graph), "Problem with MinCutNodeIt");
+      
+    }
+  }
+  
+  return 0;
+}