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