# HG changeset patch
# User Peter Kovacs <kpeter@inf.elte.hu>
# Date 1258067375 -3600
# Node ID 0643a9c2c3ae4ff91e8faca9061745c21150e0af
# Parent  25804ef350647df8f6c1f4c6354f525348669910
Port cycle canceling algorithms from SVN -r3524 (#180)

diff -r 25804ef35064 -r 0643a9c2c3ae lemon/Makefile.am
--- a/lemon/Makefile.am	Thu Nov 12 23:52:51 2009 +0100
+++ b/lemon/Makefile.am	Fri Nov 13 00:09:35 2009 +0100
@@ -62,6 +62,7 @@
 	lemon/bin_heap.h \
 	lemon/binom_heap.h \
 	lemon/bucket_heap.h \
+	lemon/cancel_and_tighten.h \
 	lemon/capacity_scaling.h \
 	lemon/cbc.h \
 	lemon/circulation.h \
@@ -73,6 +74,7 @@
 	lemon/cost_scaling.h \
 	lemon/counter.h \
 	lemon/cplex.h \
+	lemon/cycle_canceling.h \
 	lemon/dfs.h \
 	lemon/dijkstra.h \
 	lemon/dim2.h \
diff -r 25804ef35064 -r 0643a9c2c3ae lemon/cancel_and_tighten.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/cancel_and_tighten.h	Fri Nov 13 00:09:35 2009 +0100
@@ -0,0 +1,797 @@
+/* -*- 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_CANCEL_AND_TIGHTEN_H
+#define LEMON_CANCEL_AND_TIGHTEN_H
+
+/// \ingroup min_cost_flow
+///
+/// \file
+/// \brief Cancel and Tighten algorithm for finding a minimum cost flow.
+
+#include <vector>
+
+#include <lemon/circulation.h>
+#include <lemon/bellman_ford.h>
+#include <lemon/howard.h>
+#include <lemon/adaptors.h>
+#include <lemon/tolerance.h>
+#include <lemon/math.h>
+
+#include <lemon/static_graph.h>
+
+namespace lemon {
+
+  /// \addtogroup min_cost_flow
+  /// @{
+
+  /// \brief Implementation of the Cancel and Tighten algorithm for
+  /// finding a minimum cost flow.
+  ///
+  /// \ref CancelAndTighten implements the Cancel and Tighten algorithm for
+  /// finding a minimum cost flow.
+  ///
+  /// \tparam Digraph The digraph type the algorithm runs on.
+  /// \tparam LowerMap The type of the lower bound map.
+  /// \tparam CapacityMap The type of the capacity (upper bound) map.
+  /// \tparam CostMap The type of the cost (length) map.
+  /// \tparam SupplyMap The type of the supply map.
+  ///
+  /// \warning
+  /// - Arc capacities and costs should be \e non-negative \e integers.
+  /// - Supply values should be \e signed \e integers.
+  /// - The value types of the maps should be convertible to each other.
+  /// - \c CostMap::Value must be signed type.
+  ///
+  /// \author Peter Kovacs
+  template < typename Digraph,
+             typename LowerMap = typename Digraph::template ArcMap<int>,
+             typename CapacityMap = typename Digraph::template ArcMap<int>,
+             typename CostMap = typename Digraph::template ArcMap<int>,
+             typename SupplyMap = typename Digraph::template NodeMap<int> >
+  class CancelAndTighten
+  {
+    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
+
+    typedef typename CapacityMap::Value Capacity;
+    typedef typename CostMap::Value Cost;
+    typedef typename SupplyMap::Value Supply;
+    typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap;
+    typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap;
+
+    typedef ResidualDigraph< const Digraph,
+      CapacityArcMap, CapacityArcMap > ResDigraph;
+
+  public:
+
+    /// The type of the flow map.
+    typedef typename Digraph::template ArcMap<Capacity> FlowMap;
+    /// The type of the potential map.
+    typedef typename Digraph::template NodeMap<Cost> PotentialMap;
+
+  private:
+
+    /// \brief Map adaptor class for handling residual arc costs.
+    ///
+    /// Map adaptor class for handling residual arc costs.
+    class ResidualCostMap : public MapBase<typename ResDigraph::Arc, Cost>
+    {
+      typedef typename ResDigraph::Arc Arc;
+      
+    private:
+
+      const CostMap &_cost_map;
+
+    public:
+
+      ///\e
+      ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {}
+
+      ///\e
+      Cost operator[](const Arc &e) const {
+        return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e];
+      }
+
+    }; //class ResidualCostMap
+
+    /// \brief Map adaptor class for handling reduced arc costs.
+    ///
+    /// Map adaptor class for handling reduced arc costs.
+    class ReducedCostMap : public MapBase<Arc, Cost>
+    {
+    private:
+
+      const Digraph &_gr;
+      const CostMap &_cost_map;
+      const PotentialMap &_pot_map;
+
+    public:
+
+      ///\e
+      ReducedCostMap( const Digraph &gr,
+                      const CostMap &cost_map,
+                      const PotentialMap &pot_map ) :
+        _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {}
+
+      ///\e
+      inline Cost operator[](const Arc &e) const {
+        return _cost_map[e] + _pot_map[_gr.source(e)]
+                            - _pot_map[_gr.target(e)];
+      }
+
+    }; //class ReducedCostMap
+
+    struct BFOperationTraits {
+      static double zero() { return 0; }
+
+      static double infinity() {
+        return std::numeric_limits<double>::infinity();
+      }
+
+      static double plus(const double& left, const double& right) {
+        return left + right;
+      }
+
+      static bool less(const double& left, const double& right) {
+        return left + 1e-6 < right;
+      }
+    }; // class BFOperationTraits
+
+  private:
+
+    // The digraph the algorithm runs on
+    const Digraph &_graph;
+    // The original lower bound map
+    const LowerMap *_lower;
+    // The modified capacity map
+    CapacityArcMap _capacity;
+    // The original cost map
+    const CostMap &_cost;
+    // The modified supply map
+    SupplyNodeMap _supply;
+    bool _valid_supply;
+
+    // Arc map of the current flow
+    FlowMap *_flow;
+    bool _local_flow;
+    // Node map of the current potentials
+    PotentialMap *_potential;
+    bool _local_potential;
+
+    // The residual digraph
+    ResDigraph *_res_graph;
+    // The residual cost map
+    ResidualCostMap _res_cost;
+
+  public:
+
+    /// \brief General constructor (with lower bounds).
+    ///
+    /// General constructor (with lower bounds).
+    ///
+    /// \param digraph The digraph the algorithm runs on.
+    /// \param lower The lower bounds of the arcs.
+    /// \param capacity The capacities (upper bounds) of the arcs.
+    /// \param cost The cost (length) values of the arcs.
+    /// \param supply The supply values of the nodes (signed).
+    CancelAndTighten( const Digraph &digraph,
+                      const LowerMap &lower,
+                      const CapacityMap &capacity,
+                      const CostMap &cost,
+                      const SupplyMap &supply ) :
+      _graph(digraph), _lower(&lower), _capacity(digraph), _cost(cost),
+      _supply(digraph), _flow(NULL), _local_flow(false),
+      _potential(NULL), _local_potential(false),
+      _res_graph(NULL), _res_cost(_cost)
+    {
+      // Check the sum of supply values
+      Supply sum = 0;
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        _supply[n] = supply[n];
+        sum += _supply[n];
+      }
+      _valid_supply = sum == 0;
+
+      // Remove non-zero lower bounds
+      for (ArcIt e(_graph); e != INVALID; ++e) {
+        _capacity[e] = capacity[e];
+        if (lower[e] != 0) {
+          _capacity[e] -= lower[e];
+          _supply[_graph.source(e)] -= lower[e];
+          _supply[_graph.target(e)] += lower[e];
+        }
+      }
+    }
+/*
+    /// \brief General constructor (without lower bounds).
+    ///
+    /// General constructor (without lower bounds).
+    ///
+    /// \param digraph The digraph the algorithm runs on.
+    /// \param capacity The capacities (upper bounds) of the arcs.
+    /// \param cost The cost (length) values of the arcs.
+    /// \param supply The supply values of the nodes (signed).
+    CancelAndTighten( const Digraph &digraph,
+                      const CapacityMap &capacity,
+                      const CostMap &cost,
+                      const SupplyMap &supply ) :
+      _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
+      _supply(supply), _flow(NULL), _local_flow(false),
+      _potential(NULL), _local_potential(false),
+      _res_graph(NULL), _res_cost(_cost)
+    {
+      // Check the sum of supply values
+      Supply sum = 0;
+      for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
+      _valid_supply = sum == 0;
+    }
+
+    /// \brief Simple constructor (with lower bounds).
+    ///
+    /// Simple constructor (with lower bounds).
+    ///
+    /// \param digraph The digraph the algorithm runs on.
+    /// \param lower The lower bounds of the arcs.
+    /// \param capacity The capacities (upper bounds) of the arcs.
+    /// \param cost The cost (length) values of the arcs.
+    /// \param s The source node.
+    /// \param t The target node.
+    /// \param flow_value The required amount of flow from node \c s
+    /// to node \c t (i.e. the supply of \c s and the demand of \c t).
+    CancelAndTighten( const Digraph &digraph,
+                      const LowerMap &lower,
+                      const CapacityMap &capacity,
+                      const CostMap &cost,
+                      Node s, Node t,
+                      Supply flow_value ) :
+      _graph(digraph), _lower(&lower), _capacity(capacity), _cost(cost),
+      _supply(digraph, 0), _flow(NULL), _local_flow(false),
+      _potential(NULL), _local_potential(false),
+      _res_graph(NULL), _res_cost(_cost)
+    {
+      // Remove non-zero lower bounds
+      _supply[s] =  flow_value;
+      _supply[t] = -flow_value;
+      for (ArcIt e(_graph); e != INVALID; ++e) {
+        if (lower[e] != 0) {
+          _capacity[e] -= lower[e];
+          _supply[_graph.source(e)] -= lower[e];
+          _supply[_graph.target(e)] += lower[e];
+        }
+      }
+      _valid_supply = true;
+    }
+
+    /// \brief Simple constructor (without lower bounds).
+    ///
+    /// Simple constructor (without lower bounds).
+    ///
+    /// \param digraph The digraph the algorithm runs on.
+    /// \param capacity The capacities (upper bounds) of the arcs.
+    /// \param cost The cost (length) values of the arcs.
+    /// \param s The source node.
+    /// \param t The target node.
+    /// \param flow_value The required amount of flow from node \c s
+    /// to node \c t (i.e. the supply of \c s and the demand of \c t).
+    CancelAndTighten( const Digraph &digraph,
+                      const CapacityMap &capacity,
+                      const CostMap &cost,
+                      Node s, Node t,
+                      Supply flow_value ) :
+      _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
+      _supply(digraph, 0), _flow(NULL), _local_flow(false),
+      _potential(NULL), _local_potential(false),
+      _res_graph(NULL), _res_cost(_cost)
+    {
+      _supply[s] =  flow_value;
+      _supply[t] = -flow_value;
+      _valid_supply = true;
+    }
+*/
+    /// Destructor.
+    ~CancelAndTighten() {
+      if (_local_flow) delete _flow;
+      if (_local_potential) delete _potential;
+      delete _res_graph;
+    }
+
+    /// \brief Set the flow map.
+    ///
+    /// Set the flow map.
+    ///
+    /// \return \c (*this)
+    CancelAndTighten& flowMap(FlowMap &map) {
+      if (_local_flow) {
+        delete _flow;
+        _local_flow = false;
+      }
+      _flow = &map;
+      return *this;
+    }
+
+    /// \brief Set the potential map.
+    ///
+    /// Set the potential map.
+    ///
+    /// \return \c (*this)
+    CancelAndTighten& potentialMap(PotentialMap &map) {
+      if (_local_potential) {
+        delete _potential;
+        _local_potential = false;
+      }
+      _potential = &map;
+      return *this;
+    }
+
+    /// \name Execution control
+
+    /// @{
+
+    /// \brief Run the algorithm.
+    ///
+    /// Run the algorithm.
+    ///
+    /// \return \c true if a feasible flow can be found.
+    bool run() {
+      return init() && start();
+    }
+
+    /// @}
+
+    /// \name Query Functions
+    /// The result of the algorithm can be obtained using these
+    /// functions.\n
+    /// \ref lemon::CancelAndTighten::run() "run()" must be called before
+    /// using them.
+
+    /// @{
+
+    /// \brief Return a const reference to the arc map storing the
+    /// found flow.
+    ///
+    /// Return a const reference to the arc map storing the found flow.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    const FlowMap& flowMap() const {
+      return *_flow;
+    }
+
+    /// \brief Return a const reference to the node map storing the
+    /// found potentials (the dual solution).
+    ///
+    /// Return a const reference to the node map storing the found
+    /// potentials (the dual solution).
+    ///
+    /// \pre \ref run() must be called before using this function.
+    const PotentialMap& potentialMap() const {
+      return *_potential;
+    }
+
+    /// \brief Return the flow on the given arc.
+    ///
+    /// Return the flow on the given arc.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    Capacity flow(const Arc& arc) const {
+      return (*_flow)[arc];
+    }
+
+    /// \brief Return the potential of the given node.
+    ///
+    /// Return the potential of the given node.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    Cost potential(const Node& node) const {
+      return (*_potential)[node];
+    }
+
+    /// \brief Return the total cost of the found flow.
+    ///
+    /// Return the total cost of the found flow. The complexity of the
+    /// function is \f$ O(e) \f$.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    Cost totalCost() const {
+      Cost c = 0;
+      for (ArcIt e(_graph); e != INVALID; ++e)
+        c += (*_flow)[e] * _cost[e];
+      return c;
+    }
+
+    /// @}
+
+  private:
+
+    /// Initialize the algorithm.
+    bool init() {
+      if (!_valid_supply) return false;
+
+      // Initialize flow and potential maps
+      if (!_flow) {
+        _flow = new FlowMap(_graph);
+        _local_flow = true;
+      }
+      if (!_potential) {
+        _potential = new PotentialMap(_graph);
+        _local_potential = true;
+      }
+
+      _res_graph = new ResDigraph(_graph, _capacity, *_flow);
+
+      // Find a feasible flow using Circulation
+      Circulation< Digraph, ConstMap<Arc, Capacity>,
+                   CapacityArcMap, SupplyMap >
+        circulation( _graph, constMap<Arc>(Capacity(0)),
+                     _capacity, _supply );
+      return circulation.flowMap(*_flow).run();
+    }
+
+    bool start() {
+      const double LIMIT_FACTOR = 0.01;
+      const int MIN_LIMIT = 3;
+
+      typedef typename Digraph::template NodeMap<double> FloatPotentialMap;
+      typedef typename Digraph::template NodeMap<int> LevelMap;
+      typedef typename Digraph::template NodeMap<bool> BoolNodeMap;
+      typedef typename Digraph::template NodeMap<Node> PredNodeMap;
+      typedef typename Digraph::template NodeMap<Arc> PredArcMap;
+      typedef typename ResDigraph::template ArcMap<double> ResShiftCostMap;
+      FloatPotentialMap pi(_graph);
+      LevelMap level(_graph);
+      BoolNodeMap reached(_graph);
+      BoolNodeMap processed(_graph);
+      PredNodeMap pred_node(_graph);
+      PredArcMap pred_arc(_graph);
+      int node_num = countNodes(_graph);
+      typedef std::pair<Arc, bool> pair;
+      std::vector<pair> stack(node_num);
+      std::vector<Node> proc_vector(node_num);
+      ResShiftCostMap shift_cost(*_res_graph);
+
+      Tolerance<double> tol;
+      tol.epsilon(1e-6);
+
+      Timer t1, t2, t3;
+      t1.reset();
+      t2.reset();
+      t3.reset();
+
+      // Initialize epsilon and the node potentials
+      double epsilon = 0;
+      for (ArcIt e(_graph); e != INVALID; ++e) {
+        if (_capacity[e] - (*_flow)[e] > 0 && _cost[e] < -epsilon)
+          epsilon = -_cost[e];
+        else if ((*_flow)[e] > 0 && _cost[e] > epsilon)
+          epsilon = _cost[e];
+      }
+      for (NodeIt v(_graph); v != INVALID; ++v) {
+        pi[v] = 0;
+      }
+
+      // Start phases
+      int limit = int(LIMIT_FACTOR * node_num);
+      if (limit < MIN_LIMIT) limit = MIN_LIMIT;
+      int iter = limit;
+      while (epsilon * node_num >= 1) {
+        t1.start();
+        // Find and cancel cycles in the admissible digraph using DFS
+        for (NodeIt n(_graph); n != INVALID; ++n) {
+          reached[n] = false;
+          processed[n] = false;
+        }
+        int stack_head = -1;
+        int proc_head = -1;
+
+        for (NodeIt start(_graph); start != INVALID; ++start) {
+          if (reached[start]) continue;
+
+          // New start node
+          reached[start] = true;
+          pred_arc[start] = INVALID;
+          pred_node[start] = INVALID;
+
+          // Find the first admissible residual outgoing arc
+          double p = pi[start];
+          Arc e;
+          _graph.firstOut(e, start);
+          while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
+                  !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
+            _graph.nextOut(e);
+          if (e != INVALID) {
+            stack[++stack_head] = pair(e, true);
+            goto next_step_1;
+          }
+          _graph.firstIn(e, start);
+          while ( e != INVALID && ((*_flow)[e] == 0 ||
+                  !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
+            _graph.nextIn(e);
+          if (e != INVALID) {
+            stack[++stack_head] = pair(e, false);
+            goto next_step_1;
+          }
+          processed[start] = true;
+          proc_vector[++proc_head] = start;
+          continue;
+        next_step_1:
+
+          while (stack_head >= 0) {
+            Arc se = stack[stack_head].first;
+            bool sf = stack[stack_head].second;
+            Node u, v;
+            if (sf) {
+              u = _graph.source(se);
+              v = _graph.target(se);
+            } else {
+              u = _graph.target(se);
+              v = _graph.source(se);
+            }
+
+            if (!reached[v]) {
+              // A new node is reached
+              reached[v] = true;
+              pred_node[v] = u;
+              pred_arc[v] = se;
+              // Find the first admissible residual outgoing arc
+              double p = pi[v];
+              Arc e;
+              _graph.firstOut(e, v);
+              while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
+                      !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
+                _graph.nextOut(e);
+              if (e != INVALID) {
+                stack[++stack_head] = pair(e, true);
+                goto next_step_2;
+              }
+              _graph.firstIn(e, v);
+              while ( e != INVALID && ((*_flow)[e] == 0 ||
+                      !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
+                _graph.nextIn(e);
+              stack[++stack_head] = pair(e, false);
+            next_step_2: ;
+            } else {
+              if (!processed[v]) {
+                // A cycle is found
+                Node n, w = u;
+                Capacity d, delta = sf ? _capacity[se] - (*_flow)[se] :
+                                         (*_flow)[se];
+                for (n = u; n != v; n = pred_node[n]) {
+                  d = _graph.target(pred_arc[n]) == n ?
+                      _capacity[pred_arc[n]] - (*_flow)[pred_arc[n]] :
+                      (*_flow)[pred_arc[n]];
+                  if (d <= delta) {
+                    delta = d;
+                    w = pred_node[n];
+                  }
+                }
+
+/*
+                std::cout << "CYCLE FOUND: ";
+                if (sf)
+                  std::cout << _cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)];
+                else
+                  std::cout << _graph.id(se) << ":" << -(_cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)]);
+                for (n = u; n != v; n = pred_node[n]) {
+                  if (_graph.target(pred_arc[n]) == n)
+                    std::cout << " " << _cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])];
+                  else
+                    std::cout << " " << -(_cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])]);
+                }
+                std::cout << "\n";
+*/
+                // Augment along the cycle
+                (*_flow)[se] = sf ? (*_flow)[se] + delta :
+                                    (*_flow)[se] - delta;
+                for (n = u; n != v; n = pred_node[n]) {
+                  if (_graph.target(pred_arc[n]) == n)
+                    (*_flow)[pred_arc[n]] += delta;
+                  else
+                    (*_flow)[pred_arc[n]] -= delta;
+                }
+                for (n = u; stack_head > 0 && n != w; n = pred_node[n]) {
+                  --stack_head;
+                  reached[n] = false;
+                }
+                u = w;
+              }
+              v = u;
+
+              // Find the next admissible residual outgoing arc
+              double p = pi[v];
+              Arc e = stack[stack_head].first;
+              if (!stack[stack_head].second) {
+                _graph.nextIn(e);
+                goto in_arc_3;
+              }
+              _graph.nextOut(e);
+              while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
+                      !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
+                _graph.nextOut(e);
+              if (e != INVALID) {
+                stack[stack_head] = pair(e, true);
+                goto next_step_3;
+              }
+              _graph.firstIn(e, v);
+            in_arc_3:
+              while ( e != INVALID && ((*_flow)[e] == 0 ||
+                      !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
+                _graph.nextIn(e);
+              stack[stack_head] = pair(e, false);
+            next_step_3: ;
+            }
+
+            while (stack_head >= 0 && stack[stack_head].first == INVALID) {
+              processed[v] = true;
+              proc_vector[++proc_head] = v;
+              if (--stack_head >= 0) {
+                v = stack[stack_head].second ?
+                    _graph.source(stack[stack_head].first) :
+                    _graph.target(stack[stack_head].first);
+                // Find the next admissible residual outgoing arc
+                double p = pi[v];
+                Arc e = stack[stack_head].first;
+                if (!stack[stack_head].second) {
+                  _graph.nextIn(e);
+                  goto in_arc_4;
+                }
+                _graph.nextOut(e);
+                while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
+                        !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
+                  _graph.nextOut(e);
+                if (e != INVALID) {
+                  stack[stack_head] = pair(e, true);
+                  goto next_step_4;
+                }
+                _graph.firstIn(e, v);
+              in_arc_4:
+                while ( e != INVALID && ((*_flow)[e] == 0 ||
+                        !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
+                  _graph.nextIn(e);
+                stack[stack_head] = pair(e, false);
+              next_step_4: ;
+              }
+            }
+          }
+        }
+        t1.stop();
+
+        // Tighten potentials and epsilon
+        if (--iter > 0) {
+          // Compute levels
+          t2.start();
+          for (int i = proc_head; i >= 0; --i) {
+            Node v = proc_vector[i];
+            double p = pi[v];
+            int l = 0;
+            for (InArcIt e(_graph, v); e != INVALID; ++e) {
+              Node u = _graph.source(e);
+              if ( _capacity[e] - (*_flow)[e] > 0 &&
+                   tol.negative(_cost[e] + pi[u] - p) &&
+                   level[u] + 1 > l ) l = level[u] + 1;
+            }
+            for (OutArcIt e(_graph, v); e != INVALID; ++e) {
+              Node u = _graph.target(e);
+              if ( (*_flow)[e] > 0 &&
+                   tol.negative(-_cost[e] + pi[u] - p) &&
+                   level[u] + 1 > l ) l = level[u] + 1;
+            }
+            level[v] = l;
+          }
+
+          // Modify potentials
+          double p, q = -1;
+          for (ArcIt e(_graph); e != INVALID; ++e) {
+            Node u = _graph.source(e);
+            Node v = _graph.target(e);
+            if (_capacity[e] - (*_flow)[e] > 0 && level[u] - level[v] > 0) {
+              p = (_cost[e] + pi[u] - pi[v] + epsilon) /
+                  (level[u] - level[v] + 1);
+              if (q < 0 || p < q) q = p;
+            }
+            else if ((*_flow)[e] > 0 && level[v] - level[u] > 0) {
+              p = (-_cost[e] - pi[u] + pi[v] + epsilon) /
+                  (level[v] - level[u] + 1);
+              if (q < 0 || p < q) q = p;
+            }
+          }
+          for (NodeIt v(_graph); v != INVALID; ++v) {
+            pi[v] -= q * level[v];
+          }
+
+          // Modify epsilon
+          epsilon = 0;
+          for (ArcIt e(_graph); e != INVALID; ++e) {
+            double curr = _cost[e] + pi[_graph.source(e)]
+                                   - pi[_graph.target(e)];
+            if (_capacity[e] - (*_flow)[e] > 0 && curr < -epsilon)
+              epsilon = -curr;
+            else if ((*_flow)[e] > 0 && curr > epsilon)
+              epsilon = curr;
+          }
+          t2.stop();
+        } else {
+          // Set epsilon to the minimum cycle mean
+          t3.start();
+
+/**/
+          StaticDigraph static_graph;
+          typename ResDigraph::template NodeMap<typename StaticDigraph::Node> node_ref(*_res_graph);
+          typename ResDigraph::template ArcMap<typename StaticDigraph::Arc> arc_ref(*_res_graph);
+          static_graph.build(*_res_graph, node_ref, arc_ref);
+          typename StaticDigraph::template NodeMap<double> static_pi(static_graph);
+          typename StaticDigraph::template ArcMap<double> static_cost(static_graph);
+
+          for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e)
+            static_cost[arc_ref[e]] = _res_cost[e];
+
+          Howard<StaticDigraph, typename StaticDigraph::template ArcMap<double> >
+            mmc(static_graph, static_cost);
+          mmc.findMinMean();
+          epsilon = -mmc.cycleMean();
+/**/
+
+/*
+          Howard<ResDigraph, ResidualCostMap> mmc(*_res_graph, _res_cost);
+          mmc.findMinMean();
+          epsilon = -mmc.cycleMean();
+*/
+
+          // Compute feasible potentials for the current epsilon
+          for (typename StaticDigraph::ArcIt e(static_graph); e != INVALID; ++e)
+            static_cost[e] += epsilon;
+          typename BellmanFord<StaticDigraph, typename StaticDigraph::template ArcMap<double> >::
+            template SetDistMap<typename StaticDigraph::template NodeMap<double> >::
+            template SetOperationTraits<BFOperationTraits>::Create
+              bf(static_graph, static_cost);
+          bf.distMap(static_pi).init(0);
+          bf.start();
+          for (NodeIt n(_graph); n != INVALID; ++n)
+            pi[n] = static_pi[node_ref[n]];
+          
+/*
+          for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e)
+            shift_cost[e] = _res_cost[e] + epsilon;
+          typename BellmanFord<ResDigraph, ResShiftCostMap>::
+            template SetDistMap<FloatPotentialMap>::
+            template SetOperationTraits<BFOperationTraits>::Create
+              bf(*_res_graph, shift_cost);
+          bf.distMap(pi).init(0);
+          bf.start();
+*/
+
+          iter = limit;
+          t3.stop();
+        }
+      }
+
+//      std::cout << t1.realTime() << " " << t2.realTime() << " " << t3.realTime() << "\n";
+
+      // Handle non-zero lower bounds
+      if (_lower) {
+        for (ArcIt e(_graph); e != INVALID; ++e)
+          (*_flow)[e] += (*_lower)[e];
+      }
+      return true;
+    }
+
+  }; //class CancelAndTighten
+
+  ///@}
+
+} //namespace lemon
+
+#endif //LEMON_CANCEL_AND_TIGHTEN_H
diff -r 25804ef35064 -r 0643a9c2c3ae lemon/cycle_canceling.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/cycle_canceling.h	Fri Nov 13 00:09:35 2009 +0100
@@ -0,0 +1,559 @@
+/* -*- 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_CYCLE_CANCELING_H
+#define LEMON_CYCLE_CANCELING_H
+
+/// \ingroup min_cost_flow
+///
+/// \file
+/// \brief Cycle-canceling algorithm for finding a minimum cost flow.
+
+#include <vector>
+#include <lemon/adaptors.h>
+#include <lemon/path.h>
+
+#include <lemon/circulation.h>
+#include <lemon/bellman_ford.h>
+#include <lemon/howard.h>
+
+namespace lemon {
+
+  /// \addtogroup min_cost_flow
+  /// @{
+
+  /// \brief Implementation of a cycle-canceling algorithm for
+  /// finding a minimum cost flow.
+  ///
+  /// \ref CycleCanceling implements a cycle-canceling algorithm for
+  /// finding a minimum cost flow.
+  ///
+  /// \tparam Digraph The digraph type the algorithm runs on.
+  /// \tparam LowerMap The type of the lower bound map.
+  /// \tparam CapacityMap The type of the capacity (upper bound) map.
+  /// \tparam CostMap The type of the cost (length) map.
+  /// \tparam SupplyMap The type of the supply map.
+  ///
+  /// \warning
+  /// - Arc capacities and costs should be \e non-negative \e integers.
+  /// - Supply values should be \e signed \e integers.
+  /// - The value types of the maps should be convertible to each other.
+  /// - \c CostMap::Value must be signed type.
+  ///
+  /// \note By default the \ref BellmanFord "Bellman-Ford" algorithm is
+  /// used for negative cycle detection with limited iteration number.
+  /// However \ref CycleCanceling also provides the "Minimum Mean
+  /// Cycle-Canceling" algorithm, which is \e strongly \e polynomial,
+  /// but rather slower in practice.
+  /// To use this version of the algorithm, call \ref run() with \c true
+  /// parameter.
+  ///
+  /// \author Peter Kovacs
+  template < typename Digraph,
+             typename LowerMap = typename Digraph::template ArcMap<int>,
+             typename CapacityMap = typename Digraph::template ArcMap<int>,
+             typename CostMap = typename Digraph::template ArcMap<int>,
+             typename SupplyMap = typename Digraph::template NodeMap<int> >
+  class CycleCanceling
+  {
+    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
+
+    typedef typename CapacityMap::Value Capacity;
+    typedef typename CostMap::Value Cost;
+    typedef typename SupplyMap::Value Supply;
+    typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap;
+    typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap;
+
+    typedef ResidualDigraph< const Digraph,
+      CapacityArcMap, CapacityArcMap > ResDigraph;
+    typedef typename ResDigraph::Node ResNode;
+    typedef typename ResDigraph::NodeIt ResNodeIt;
+    typedef typename ResDigraph::Arc ResArc;
+    typedef typename ResDigraph::ArcIt ResArcIt;
+
+  public:
+
+    /// The type of the flow map.
+    typedef typename Digraph::template ArcMap<Capacity> FlowMap;
+    /// The type of the potential map.
+    typedef typename Digraph::template NodeMap<Cost> PotentialMap;
+
+  private:
+
+    /// \brief Map adaptor class for handling residual arc costs.
+    ///
+    /// Map adaptor class for handling residual arc costs.
+    class ResidualCostMap : public MapBase<ResArc, Cost>
+    {
+    private:
+
+      const CostMap &_cost_map;
+
+    public:
+
+      ///\e
+      ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {}
+
+      ///\e
+      Cost operator[](const ResArc &e) const {
+        return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e];
+      }
+
+    }; //class ResidualCostMap
+
+  private:
+
+    // The maximum number of iterations for the first execution of the
+    // Bellman-Ford algorithm. It should be at least 2.
+    static const int BF_FIRST_LIMIT  = 2;
+    // The iteration limit for the Bellman-Ford algorithm is multiplied
+    // by BF_LIMIT_FACTOR/100 in every round.
+    static const int BF_LIMIT_FACTOR = 150;
+
+  private:
+
+    // The digraph the algorithm runs on
+    const Digraph &_graph;
+    // The original lower bound map
+    const LowerMap *_lower;
+    // The modified capacity map
+    CapacityArcMap _capacity;
+    // The original cost map
+    const CostMap &_cost;
+    // The modified supply map
+    SupplyNodeMap _supply;
+    bool _valid_supply;
+
+    // Arc map of the current flow
+    FlowMap *_flow;
+    bool _local_flow;
+    // Node map of the current potentials
+    PotentialMap *_potential;
+    bool _local_potential;
+
+    // The residual digraph
+    ResDigraph *_res_graph;
+    // The residual cost map
+    ResidualCostMap _res_cost;
+
+  public:
+
+    /// \brief General constructor (with lower bounds).
+    ///
+    /// General constructor (with lower bounds).
+    ///
+    /// \param digraph The digraph the algorithm runs on.
+    /// \param lower The lower bounds of the arcs.
+    /// \param capacity The capacities (upper bounds) of the arcs.
+    /// \param cost The cost (length) values of the arcs.
+    /// \param supply The supply values of the nodes (signed).
+    CycleCanceling( const Digraph &digraph,
+                    const LowerMap &lower,
+                    const CapacityMap &capacity,
+                    const CostMap &cost,
+                    const SupplyMap &supply ) :
+      _graph(digraph), _lower(&lower), _capacity(digraph), _cost(cost),
+      _supply(digraph), _flow(NULL), _local_flow(false),
+      _potential(NULL), _local_potential(false),
+      _res_graph(NULL), _res_cost(_cost)
+    {
+      // Check the sum of supply values
+      Supply sum = 0;
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        _supply[n] = supply[n];
+        sum += _supply[n];
+      }
+      _valid_supply = sum == 0;
+
+      // Remove non-zero lower bounds
+      for (ArcIt e(_graph); e != INVALID; ++e) {
+        _capacity[e] = capacity[e];
+        if (lower[e] != 0) {
+          _capacity[e] -= lower[e];
+          _supply[_graph.source(e)] -= lower[e];
+          _supply[_graph.target(e)] += lower[e];
+        }
+      }
+    }
+/*
+    /// \brief General constructor (without lower bounds).
+    ///
+    /// General constructor (without lower bounds).
+    ///
+    /// \param digraph The digraph the algorithm runs on.
+    /// \param capacity The capacities (upper bounds) of the arcs.
+    /// \param cost The cost (length) values of the arcs.
+    /// \param supply The supply values of the nodes (signed).
+    CycleCanceling( const Digraph &digraph,
+                    const CapacityMap &capacity,
+                    const CostMap &cost,
+                    const SupplyMap &supply ) :
+      _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
+      _supply(supply), _flow(NULL), _local_flow(false),
+      _potential(NULL), _local_potential(false), _res_graph(NULL),
+      _res_cost(_cost)
+    {
+      // Check the sum of supply values
+      Supply sum = 0;
+      for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
+      _valid_supply = sum == 0;
+    }
+
+    /// \brief Simple constructor (with lower bounds).
+    ///
+    /// Simple constructor (with lower bounds).
+    ///
+    /// \param digraph The digraph the algorithm runs on.
+    /// \param lower The lower bounds of the arcs.
+    /// \param capacity The capacities (upper bounds) of the arcs.
+    /// \param cost The cost (length) values of the arcs.
+    /// \param s The source node.
+    /// \param t The target node.
+    /// \param flow_value The required amount of flow from node \c s
+    /// to node \c t (i.e. the supply of \c s and the demand of \c t).
+    CycleCanceling( const Digraph &digraph,
+                    const LowerMap &lower,
+                    const CapacityMap &capacity,
+                    const CostMap &cost,
+                    Node s, Node t,
+                    Supply flow_value ) :
+      _graph(digraph), _lower(&lower), _capacity(capacity), _cost(cost),
+      _supply(digraph, 0), _flow(NULL), _local_flow(false),
+      _potential(NULL), _local_potential(false), _res_graph(NULL),
+      _res_cost(_cost)
+    {
+      // Remove non-zero lower bounds
+      _supply[s] =  flow_value;
+      _supply[t] = -flow_value;
+      for (ArcIt e(_graph); e != INVALID; ++e) {
+        if (lower[e] != 0) {
+          _capacity[e] -= lower[e];
+          _supply[_graph.source(e)] -= lower[e];
+          _supply[_graph.target(e)] += lower[e];
+        }
+      }
+      _valid_supply = true;
+    }
+
+    /// \brief Simple constructor (without lower bounds).
+    ///
+    /// Simple constructor (without lower bounds).
+    ///
+    /// \param digraph The digraph the algorithm runs on.
+    /// \param capacity The capacities (upper bounds) of the arcs.
+    /// \param cost The cost (length) values of the arcs.
+    /// \param s The source node.
+    /// \param t The target node.
+    /// \param flow_value The required amount of flow from node \c s
+    /// to node \c t (i.e. the supply of \c s and the demand of \c t).
+    CycleCanceling( const Digraph &digraph,
+                    const CapacityMap &capacity,
+                    const CostMap &cost,
+                    Node s, Node t,
+                    Supply flow_value ) :
+      _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
+      _supply(digraph, 0), _flow(NULL), _local_flow(false),
+      _potential(NULL), _local_potential(false), _res_graph(NULL),
+      _res_cost(_cost)
+    {
+      _supply[s] =  flow_value;
+      _supply[t] = -flow_value;
+      _valid_supply = true;
+    }
+*/
+    /// Destructor.
+    ~CycleCanceling() {
+      if (_local_flow) delete _flow;
+      if (_local_potential) delete _potential;
+      delete _res_graph;
+    }
+
+    /// \brief Set the flow map.
+    ///
+    /// Set the flow map.
+    ///
+    /// \return \c (*this)
+    CycleCanceling& flowMap(FlowMap &map) {
+      if (_local_flow) {
+        delete _flow;
+        _local_flow = false;
+      }
+      _flow = &map;
+      return *this;
+    }
+
+    /// \brief Set the potential map.
+    ///
+    /// Set the potential map.
+    ///
+    /// \return \c (*this)
+    CycleCanceling& potentialMap(PotentialMap &map) {
+      if (_local_potential) {
+        delete _potential;
+        _local_potential = false;
+      }
+      _potential = &map;
+      return *this;
+    }
+
+    /// \name Execution control
+
+    /// @{
+
+    /// \brief Run the algorithm.
+    ///
+    /// Run the algorithm.
+    ///
+    /// \param min_mean_cc Set this parameter to \c true to run the
+    /// "Minimum Mean Cycle-Canceling" algorithm, which is strongly
+    /// polynomial, but rather slower in practice.
+    ///
+    /// \return \c true if a feasible flow can be found.
+    bool run(bool min_mean_cc = false) {
+      return init() && start(min_mean_cc);
+    }
+
+    /// @}
+
+    /// \name Query Functions
+    /// The result of the algorithm can be obtained using these
+    /// functions.\n
+    /// \ref lemon::CycleCanceling::run() "run()" must be called before
+    /// using them.
+
+    /// @{
+
+    /// \brief Return a const reference to the arc map storing the
+    /// found flow.
+    ///
+    /// Return a const reference to the arc map storing the found flow.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    const FlowMap& flowMap() const {
+      return *_flow;
+    }
+
+    /// \brief Return a const reference to the node map storing the
+    /// found potentials (the dual solution).
+    ///
+    /// Return a const reference to the node map storing the found
+    /// potentials (the dual solution).
+    ///
+    /// \pre \ref run() must be called before using this function.
+    const PotentialMap& potentialMap() const {
+      return *_potential;
+    }
+
+    /// \brief Return the flow on the given arc.
+    ///
+    /// Return the flow on the given arc.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    Capacity flow(const Arc& arc) const {
+      return (*_flow)[arc];
+    }
+
+    /// \brief Return the potential of the given node.
+    ///
+    /// Return the potential of the given node.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    Cost potential(const Node& node) const {
+      return (*_potential)[node];
+    }
+
+    /// \brief Return the total cost of the found flow.
+    ///
+    /// Return the total cost of the found flow. The complexity of the
+    /// function is \f$ O(e) \f$.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    Cost totalCost() const {
+      Cost c = 0;
+      for (ArcIt e(_graph); e != INVALID; ++e)
+        c += (*_flow)[e] * _cost[e];
+      return c;
+    }
+
+    /// @}
+
+  private:
+
+    /// Initialize the algorithm.
+    bool init() {
+      if (!_valid_supply) return false;
+
+      // Initializing flow and potential maps
+      if (!_flow) {
+        _flow = new FlowMap(_graph);
+        _local_flow = true;
+      }
+      if (!_potential) {
+        _potential = new PotentialMap(_graph);
+        _local_potential = true;
+      }
+
+      _res_graph = new ResDigraph(_graph, _capacity, *_flow);
+
+      // Finding a feasible flow using Circulation
+      Circulation< Digraph, ConstMap<Arc, Capacity>, CapacityArcMap,
+                   SupplyMap >
+        circulation( _graph, constMap<Arc>(Capacity(0)), _capacity,
+                     _supply );
+      return circulation.flowMap(*_flow).run();
+    }
+
+    bool start(bool min_mean_cc) {
+      if (min_mean_cc)
+        startMinMean();
+      else
+        start();
+
+      // Handling non-zero lower bounds
+      if (_lower) {
+        for (ArcIt e(_graph); e != INVALID; ++e)
+          (*_flow)[e] += (*_lower)[e];
+      }
+      return true;
+    }
+
+    /// \brief Execute the algorithm using \ref BellmanFord.
+    ///
+    /// Execute the algorithm using the \ref BellmanFord
+    /// "Bellman-Ford" algorithm for negative cycle detection with
+    /// successively larger limit for the number of iterations.
+    void start() {
+      typename BellmanFord<ResDigraph, ResidualCostMap>::PredMap pred(*_res_graph);
+      typename ResDigraph::template NodeMap<int> visited(*_res_graph);
+      std::vector<ResArc> cycle;
+      int node_num = countNodes(_graph);
+
+      int length_bound = BF_FIRST_LIMIT;
+      bool optimal = false;
+      while (!optimal) {
+        BellmanFord<ResDigraph, ResidualCostMap> bf(*_res_graph, _res_cost);
+        bf.predMap(pred);
+        bf.init(0);
+        int iter_num = 0;
+        bool cycle_found = false;
+        while (!cycle_found) {
+          int curr_iter_num = iter_num + length_bound <= node_num ?
+                              length_bound : node_num - iter_num;
+          iter_num += curr_iter_num;
+          int real_iter_num = curr_iter_num;
+          for (int i = 0; i < curr_iter_num; ++i) {
+            if (bf.processNextWeakRound()) {
+              real_iter_num = i;
+              break;
+            }
+          }
+          if (real_iter_num < curr_iter_num) {
+            // Optimal flow is found
+            optimal = true;
+            // Setting node potentials
+            for (NodeIt n(_graph); n != INVALID; ++n)
+              (*_potential)[n] = bf.dist(n);
+            break;
+          } else {
+            // Searching for node disjoint negative cycles
+            for (ResNodeIt n(*_res_graph); n != INVALID; ++n)
+              visited[n] = 0;
+            int id = 0;
+            for (ResNodeIt n(*_res_graph); n != INVALID; ++n) {
+              if (visited[n] > 0) continue;
+              visited[n] = ++id;
+              ResNode u = pred[n] == INVALID ?
+                          INVALID : _res_graph->source(pred[n]);
+              while (u != INVALID && visited[u] == 0) {
+                visited[u] = id;
+                u = pred[u] == INVALID ?
+                    INVALID : _res_graph->source(pred[u]);
+              }
+              if (u != INVALID && visited[u] == id) {
+                // Finding the negative cycle
+                cycle_found = true;
+                cycle.clear();
+                ResArc e = pred[u];
+                cycle.push_back(e);
+                Capacity d = _res_graph->residualCapacity(e);
+                while (_res_graph->source(e) != u) {
+                  cycle.push_back(e = pred[_res_graph->source(e)]);
+                  if (_res_graph->residualCapacity(e) < d)
+                    d = _res_graph->residualCapacity(e);
+                }
+
+                // Augmenting along the cycle
+                for (int i = 0; i < int(cycle.size()); ++i)
+                  _res_graph->augment(cycle[i], d);
+              }
+            }
+          }
+
+          if (!cycle_found)
+            length_bound = length_bound * BF_LIMIT_FACTOR / 100;
+        }
+      }
+    }
+
+    /// \brief Execute the algorithm using \ref Howard.
+    ///
+    /// Execute the algorithm using \ref Howard for negative
+    /// cycle detection.
+    void startMinMean() {
+      typedef Path<ResDigraph> ResPath;
+      Howard<ResDigraph, ResidualCostMap> mmc(*_res_graph, _res_cost);
+      ResPath cycle;
+
+      mmc.cycle(cycle);
+      if (mmc.findMinMean()) {
+        while (mmc.cycleLength() < 0) {
+          // Finding the cycle
+          mmc.findCycle();
+
+          // Finding the largest flow amount that can be augmented
+          // along the cycle
+          Capacity delta = 0;
+          for (typename ResPath::ArcIt e(cycle); e != INVALID; ++e) {
+            if (delta == 0 || _res_graph->residualCapacity(e) < delta)
+              delta = _res_graph->residualCapacity(e);
+          }
+
+          // Augmenting along the cycle
+          for (typename ResPath::ArcIt e(cycle); e != INVALID; ++e)
+            _res_graph->augment(e, delta);
+
+          // Finding the minimum cycle mean for the modified residual
+          // digraph
+          if (!mmc.findMinMean()) break;
+        }
+      }
+
+      // Computing node potentials
+      BellmanFord<ResDigraph, ResidualCostMap> bf(*_res_graph, _res_cost);
+      bf.init(0); bf.start();
+      for (NodeIt n(_graph); n != INVALID; ++n)
+        (*_potential)[n] = bf.dist(n);
+    }
+
+  }; //class CycleCanceling
+
+  ///@}
+
+} //namespace lemon
+
+#endif //LEMON_CYCLE_CANCELING_H