# HG changeset patch
# User deba
# Date 1196273149 0
# Node ID e6bc5c0032e970d950d3d17effdb178fb5362264
# Parent  10f3b3286e6393756f49a4dd6e3dc375a8ec4d37
Gomory-Hu tree algorithm

diff -r 10f3b3286e63 -r e6bc5c0032e9 lemon/Makefile.am
--- a/lemon/Makefile.am	Wed Nov 28 18:01:38 2007 +0000
+++ b/lemon/Makefile.am	Wed Nov 28 18:05:49 2007 +0000
@@ -74,6 +74,7 @@
 	lemon/graph_writer.h \
 	lemon/grid_ugraph.h \
 	lemon/goldberg_tarjan.h \
+	lemon/gomory_hu_tree.h \
 	lemon/hao_orlin.h \
 	lemon/hypercube_graph.h \
 	lemon/iterable_maps.h \
diff -r 10f3b3286e63 -r e6bc5c0032e9 lemon/gomory_hu_tree.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/gomory_hu_tree.h	Wed Nov 28 18:05:49 2007 +0000
@@ -0,0 +1,296 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2007
+ * 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 <lemon/preflow.h>
+#include <lemon/concept_check.h>
+#include <lemon/concepts/maps.h>
+
+/// \ingroup min_cut
+/// \file 
+/// \brief Gomory-Hu cut tree in undirected graphs.
+
+namespace lemon {
+
+  /// \ingroup min_cut
+  ///
+  /// \brief Gomory-Hu cut tree algorithm
+  ///
+  /// The Gomory-Hu tree is a tree on the nodeset of the graph, but it
+  /// may contain edges which are not in the original graph. It helps
+  /// to calculate the minimum cut between all pairs of nodes, because
+  /// the minimum capacity edge on the tree path between two nodes has
+  /// the same weight as the minimum cut in the graph between these
+  /// nodes. Moreover this edge separates the nodes to two parts which
+  /// determine this minimum cut.
+  /// 
+  /// The algorithm calculates \e n-1 distinict minimum cuts with
+  /// preflow algorithm, therefore the algorithm has
+  /// \f$(O(n^3\sqrt{e})\f$ overall time complexity. It calculates a
+  /// rooted Gomory-Hu tree, the structure of the tree and the weights
+  /// can be obtained with \c predNode() and \c predValue()
+  /// functions. The \c minCutValue() and \c minCutMap() calculates
+  /// the minimum cut and the minimum cut value between any two node
+  /// in the graph.
+  template <typename _UGraph, 
+	    typename _Capacity = typename _UGraph::template UEdgeMap<int> >
+  class GomoryHuTree {
+  public:
+
+    /// The undirected graph type
+    typedef _UGraph UGraph;
+    /// The capacity on undirected edges
+    typedef _Capacity Capacity;
+    /// The value type of capacities
+    typedef typename Capacity::Value Value;
+    
+  private:
+
+    UGRAPH_TYPEDEFS(typename UGraph);
+
+    const UGraph& _ugraph;
+    const Capacity& _capacity;
+
+    Node _root;
+    typename UGraph::template NodeMap<Node>* _pred;
+    typename UGraph::template NodeMap<Value>* _weight;
+    typename UGraph::template NodeMap<int>* _order;
+
+    void createStructures() {
+      if (!_pred) {
+	_pred = new typename UGraph::template NodeMap<Node>(_ugraph);
+      }
+      if (!_weight) {
+	_weight = new typename UGraph::template NodeMap<Value>(_ugraph);
+      }
+      if (!_order) {
+	_order = new typename UGraph::template NodeMap<int>(_ugraph);
+      }
+    }
+
+    void destroyStructures() {
+      if (_pred) {
+	delete _pred;
+      }
+      if (_weight) {
+	delete _weight;
+      }
+      if (_order) {
+	delete _order;
+      }
+    }
+  
+  public:
+
+    /// \brief Constructor
+    ///
+    /// Constructor
+    /// \param ugraph The undirected graph type.
+    /// \param capacity The capacity map.
+    GomoryHuTree(const UGraph& ugraph, const Capacity& capacity) 
+      : _ugraph(ugraph), _capacity(capacity),
+	_pred(0), _weight(0), _order(0) 
+    {
+      checkConcept<concepts::ReadMap<UEdge, Value>, Capacity>();
+    }
+
+
+    /// \brief Destructor
+    ///
+    /// Destructor
+    ~GomoryHuTree() {
+      destroyStructures();
+    }
+
+    /// \brief Initializes the internal data structures.
+    ///
+    /// Initializes the internal data structures.
+    ///
+    void init() {
+      createStructures();
+
+      _root = NodeIt(_ugraph);
+      for (NodeIt n(_ugraph); n != INVALID; ++n) {
+	_pred->set(n, _root);
+	_order->set(n, -1);
+      }
+      _pred->set(_root, INVALID);
+      _weight->set(_root, std::numeric_limits<Value>::max()); 
+    }
+
+
+    /// \brief Starts the algorithm
+    ///
+    /// Starts the algorithm.
+    void start() {
+      Preflow<UGraph, Capacity> fa(_ugraph, _capacity, _root, INVALID);
+
+      for (NodeIt n(_ugraph); 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(_ugraph); 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(_ugraph); 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();
+	}
+      }
+    }
+
+    /// \brief Runs the Gomory-Hu algorithm.  
+    ///
+    /// Runs the Gomory-Hu algorithm.
+    /// \note gh.run() is just a shortcut of the following code.
+    /// \code
+    ///   ght.init();
+    ///   ght.start();
+    /// \endcode
+    void run() {
+      init();
+      start();
+    }
+
+    /// \brief Returns the predecessor node in the Gomory-Hu tree.
+    ///
+    /// 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 Returns the weight of the predecessor edge in the
+    /// Gomory-Hu tree.
+    ///
+    /// Returns the weight of the predecessor edge in the Gomory-Hu
+    /// tree.  If the node is the root of the Gomory-Hu tree, the
+    /// result is undefined.
+    Value predValue(const Node& node) {
+      return (*_weight)[node];
+    }
+
+    /// \brief Returns the minimum cut value between two nodes
+    ///
+    /// 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 Returns the minimum cut between two nodes
+    ///
+    /// 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. Then it sets all nodes to the cut determined by
+    /// this edge. The \c cutMap should be \ref concepts::ReadWriteMap
+    /// "ReadWriteMap".
+    template <typename CutMap>
+    Value minCutMap(const Node& s, const Node& t, CutMap& cutMap) const {
+      Node sn = s, tn = t;
+
+      Node rn = INVALID;
+      Value value = std::numeric_limits<Value>::max();
+      
+      while (sn != tn) {
+	if ((*_order)[sn] < (*_order)[tn]) {
+	  if ((*_weight)[tn] < value) {
+	    rn = tn;
+	    value = (*_weight)[tn];
+	  }
+	  tn = (*_pred)[tn];
+	} else {
+	  if ((*_weight)[sn] < value) {
+	    rn = sn;
+	    value = (*_weight)[sn];
+	  }
+	  sn = (*_pred)[sn];
+	}
+      }
+
+      typename UGraph::template NodeMap<bool> reached(_ugraph, false);
+      reached.set(_root, true);
+      cutMap.set(_root, false);
+      reached.set(rn, true);
+      cutMap.set(rn, true);
+
+      for (NodeIt n(_ugraph); n != INVALID; ++n) {
+	std::vector<Node> st;
+	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;
+    }
+
+  };
+
+}
+
+#endif