# HG changeset patch
# User Janos Tapolcai <tapolcai@tmit.bme.hu>
# Date 2009-02-20 17:17:17
# Node ID 924887566bf2e375c896f7b955bea6b6adb9ac2e
# Parent  97674155c135e55dcba5116cf01cce8df3d7ebe9

Porting Gomory-Hu algorithm (#66)

diff --git a/lemon/Makefile.am b/lemon/Makefile.am
--- a/lemon/Makefile.am
+++ b/lemon/Makefile.am
@@ -68,6 +68,7 @@
 	lemon/euler.h \
 	lemon/full_graph.h \
 	lemon/glpk.h \
+	lemon/gomory_hu_tree.h \
 	lemon/graph_to_eps.h \
 	lemon/grid_graph.h \
 	lemon/hypercube_graph.h \
diff --git a/lemon/gomory_hu_tree.h b/lemon/gomory_hu_tree.h
new file mode 100644
--- /dev/null
+++ b/lemon/gomory_hu_tree.h
@@ -0,0 +1,298 @@
+/* -*- 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/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 nodeset of the digraph, but it
+  /// may contain arcs which are not in the original digraph. It helps
+  /// to calculate the minimum cut between all pairs of nodes, because
+  /// the minimum capacity arc on the tree path between two nodes has
+  /// the same weight as the minimum cut in the digraph between these
+  /// nodes. Moreover this arc 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 digraph.
+  template <typename _Graph, 
+	    typename _Capacity = typename _Graph::template EdgeMap<int> >
+  class GomoryHuTree {
+  public:
+
+    /// The graph type
+    typedef _Graph Graph;
+    /// The capacity on edges
+    typedef _Capacity 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 graph type.
+    /// \param capacity The capacity map.
+    GomoryHuTree(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
+    ~GomoryHuTree() {
+      destroyStructures();
+    }
+
+    /// \brief Initializes the internal data structures.
+    ///
+    /// Initializes 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()); 
+    }
+
+
+    /// \brief Starts the algorithm
+    ///
+    /// Starts 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();
+	}
+      }
+    }
+
+    /// \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 arc in the
+    /// Gomory-Hu tree.
+    ///
+    /// Returns the weight of the predecessor arc 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 arc 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 arc on the paths to
+    /// the ancestor. Then it sets all nodes to the cut determined by
+    /// this arc. 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 Graph::template NodeMap<bool> reached(_graph, false);
+      reached.set(_root, true);
+      cutMap.set(_root, false);
+      reached.set(rn, true);
+      cutMap.set(rn, true);
+
+      for (NodeIt n(_graph); 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
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -21,6 +21,7 @@
   edge_set_test
   error_test
   euler_test
+  gomory_hu_test
   graph_copy_test
   graph_test
   graph_utils_test
diff --git a/test/Makefile.am b/test/Makefile.am
--- a/test/Makefile.am
+++ b/test/Makefile.am
@@ -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 --git a/test/gomory_hu_test.cc b/test/gomory_hu_test.cc
new file mode 100644
--- /dev/null
+++ b/test/gomory_hu_test.cc
@@ -0,0 +1,85 @@
+#include <iostream>
+
+#include "test_tools.h"
+#include <lemon/smart_graph.h>
+#include <lemon/adaptors.h>
+#include <lemon/lgf_reader.h>
+#include <lemon/lgf_writer.h>
+#include <lemon/dimacs.h>
+#include <lemon/time_measure.h>
+#include <lemon/gomory_hu_tree.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();
+
+  GomoryHuTree<Graph> ght(graph, capacity);
+  ght.init();
+  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");
+      
+    }
+  }
+  
+  return 0;
+}