diff -r 3f1c7a6c33cd -r c9218405595b lemon/capacity_scaling.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/capacity_scaling.h	Mon May 07 11:42:18 2007 +0000
@@ -0,0 +1,680 @@
+/* -*- 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_CAPACITY_SCALING_H
+#define LEMON_CAPACITY_SCALING_H
+
+/// \ingroup min_cost_flow
+///
+/// \file
+/// \brief The capacity scaling algorithm for finding a minimum cost
+/// flow.
+
+#include <vector>
+#include <lemon/dijkstra.h>
+#include <lemon/graph_adaptor.h>
+
+#define WITH_SCALING
+
+namespace lemon {
+
+  /// \addtogroup min_cost_flow
+  /// @{
+
+  /// \brief Implementation of the capacity scaling version of the
+  /// succesive shortest path algorithm for finding a minimum cost flow.
+  ///
+  /// \ref lemon::CapacityScaling "CapacityScaling" implements a
+  /// capacity scaling algorithm for finding a minimum cost flow.
+  ///
+  /// \param Graph The directed graph type the algorithm runs on.
+  /// \param LowerMap The type of the lower bound map.
+  /// \param CapacityMap The type of the capacity (upper bound) map.
+  /// \param CostMap The type of the cost (length) map.
+  /// \param SupplyMap The type of the supply map.
+  ///
+  /// \warning
+  /// - Edge capacities and costs should be nonnegative integers.
+  ///	However \c CostMap::Value should be signed type.
+  /// - Supply values should be integers.
+  /// - \c LowerMap::Value must be convertible to
+  ///	\c CapacityMap::Value and \c CapacityMap::Value must be
+  ///	convertible to \c SupplyMap::Value.
+  ///
+  /// \author Peter Kovacs
+
+template < typename Graph,
+	   typename LowerMap = typename Graph::template EdgeMap<int>,
+	   typename CapacityMap = LowerMap,
+	   typename CostMap = typename Graph::template EdgeMap<int>,
+	   typename SupplyMap = typename Graph::template NodeMap
+				<typename CapacityMap::Value> >
+  class CapacityScaling
+  {
+    typedef typename Graph::Node Node;
+    typedef typename Graph::NodeIt NodeIt;
+    typedef typename Graph::Edge Edge;
+    typedef typename Graph::EdgeIt EdgeIt;
+    typedef typename Graph::InEdgeIt InEdgeIt;
+    typedef typename Graph::OutEdgeIt OutEdgeIt;
+
+    typedef typename LowerMap::Value Lower;
+    typedef typename CapacityMap::Value Capacity;
+    typedef typename CostMap::Value Cost;
+    typedef typename SupplyMap::Value Supply;
+    typedef typename Graph::template EdgeMap<Capacity> CapacityRefMap;
+    typedef typename Graph::template NodeMap<Supply> SupplyRefMap;
+
+    typedef ResGraphAdaptor< const Graph, Capacity,
+			     CapacityRefMap, CapacityRefMap > ResGraph;
+    typedef typename ResGraph::Node ResNode;
+    typedef typename ResGraph::NodeIt ResNodeIt;
+    typedef typename ResGraph::Edge ResEdge;
+    typedef typename ResGraph::EdgeIt ResEdgeIt;
+
+  public:
+
+    /// \brief The type of the flow map.
+    typedef CapacityRefMap FlowMap;
+    /// \brief The type of the potential map.
+    typedef typename Graph::template NodeMap<Cost> PotentialMap;
+
+  protected:
+
+    /// \brief Map adaptor class for handling reduced edge costs.
+    class ReducedCostMap : public MapBase<ResEdge, Cost>
+    {
+    private:
+
+      const ResGraph &gr;
+      const CostMap &cost_map;
+      const PotentialMap &pot_map;
+
+    public:
+
+      typedef typename MapBase<ResEdge, Cost>::Value Value;
+      typedef typename MapBase<ResEdge, Cost>::Key Key;
+
+      ReducedCostMap( const ResGraph &_gr,
+		      const CostMap &_cost,
+		      const PotentialMap &_pot ) :
+	gr(_gr), cost_map(_cost), pot_map(_pot) {}
+
+      Value operator[](const Key &e) const {
+	return ResGraph::forward(e) ?
+	   cost_map[e] - pot_map[gr.source(e)] + pot_map[gr.target(e)] :
+	  -cost_map[e] - pot_map[gr.source(e)] + pot_map[gr.target(e)];
+      }
+
+    }; //class ReducedCostMap
+
+    /// \brief Map adaptor for \ref lemon::Dijkstra "Dijkstra" class to
+    /// update node potentials.
+    class PotentialUpdateMap : public MapBase<ResNode, Cost>
+    {
+    private:
+
+      PotentialMap *pot;
+      typedef std::pair<ResNode, Cost> Pair;
+      std::vector<Pair> data;
+
+    public:
+
+      typedef typename MapBase<ResNode, Cost>::Value Value;
+      typedef typename MapBase<ResNode, Cost>::Key Key;
+
+      void potentialMap(PotentialMap &_pot) {
+	pot = &_pot;
+      }
+
+      void init() {
+	data.clear();
+      }
+
+      void set(const Key &n, const Value &v) {
+	data.push_back(Pair(n, v));
+      }
+
+      void update() {
+	Cost val = data[data.size()-1].second;
+	for (int i = 0; i < data.size()-1; ++i)
+	  (*pot)[data[i].first] += val - data[i].second;
+      }
+
+    }; //class PotentialUpdateMap
+
+#ifdef WITH_SCALING
+    /// \brief Map adaptor class for identifing deficit nodes.
+    class DeficitBoolMap : public MapBase<ResNode, bool>
+    {
+    private:
+
+      const SupplyRefMap &imb;
+      const Capacity &delta;
+
+    public:
+
+      DeficitBoolMap(const SupplyRefMap &_imb, const Capacity &_delta) :
+	imb(_imb), delta(_delta) {}
+
+      bool operator[](const ResNode &n) const {
+	return imb[n] <= -delta;
+      }
+
+    }; //class DeficitBoolMap
+
+    /// \brief Map adaptor class for filtering edges with at least
+    /// \c delta residual capacity
+    class DeltaFilterMap : public MapBase<ResEdge, bool>
+    {
+    private:
+
+      const ResGraph &gr;
+      const Capacity &delta;
+
+    public:
+
+      typedef typename MapBase<ResEdge, Cost>::Value Value;
+      typedef typename MapBase<ResEdge, Cost>::Key Key;
+
+      DeltaFilterMap(const ResGraph &_gr, const Capacity &_delta) :
+	gr(_gr), delta(_delta) {}
+
+      Value operator[](const Key &e) const {
+	return gr.rescap(e) >= delta;
+      }
+
+    }; //class DeltaFilterMap
+
+    typedef EdgeSubGraphAdaptor<const ResGraph, const DeltaFilterMap>
+      DeltaResGraph;
+
+    /// \brief Traits class for \ref lemon::Dijkstra "Dijkstra" class.
+    class ResDijkstraTraits :
+      public DijkstraDefaultTraits<DeltaResGraph, ReducedCostMap>
+    {
+    public:
+
+      typedef PotentialUpdateMap DistMap;
+
+      static DistMap *createDistMap(const DeltaResGraph&) {
+	return new DistMap();
+      }
+
+    }; //class ResDijkstraTraits
+
+#else //WITHOUT_CAPACITY_SCALING
+    /// \brief Map adaptor class for identifing deficit nodes.
+    class DeficitBoolMap : public MapBase<ResNode, bool>
+    {
+    private:
+
+      const SupplyRefMap &imb;
+
+    public:
+
+      DeficitBoolMap(const SupplyRefMap &_imb) : imb(_imb) {}
+
+      bool operator[](const ResNode &n) const {
+	return imb[n] < 0;
+      }
+
+    }; //class DeficitBoolMap
+
+    /// \brief Traits class for \ref lemon::Dijkstra "Dijkstra" class.
+    class ResDijkstraTraits :
+      public DijkstraDefaultTraits<ResGraph, ReducedCostMap>
+    {
+    public:
+
+      typedef PotentialUpdateMap DistMap;
+
+      static DistMap *createDistMap(const ResGraph&) {
+	return new DistMap();
+      }
+
+    }; //class ResDijkstraTraits
+#endif
+
+  protected:
+
+    /// \brief The directed graph the algorithm runs on.
+    const Graph &graph;
+    /// \brief The original lower bound map.
+    const LowerMap *lower;
+    /// \brief The modified capacity map.
+    CapacityRefMap capacity;
+    /// \brief The cost map.
+    const CostMap &cost;
+    /// \brief The modified supply map.
+    SupplyRefMap supply;
+    /// \brief The sum of supply values equals zero.
+    bool valid_supply;
+
+    /// \brief The edge map of the current flow.
+    FlowMap flow;
+    /// \brief The potential node map.
+    PotentialMap potential;
+    /// \brief The residual graph.
+    ResGraph res_graph;
+    /// \brief The reduced cost map.
+    ReducedCostMap red_cost;
+
+    /// \brief The imbalance map.
+    SupplyRefMap imbalance;
+    /// \brief The excess nodes.
+    std::vector<ResNode> excess_nodes;
+    /// \brief The index of the next excess node.
+    int next_node;
+
+#ifdef WITH_SCALING
+    typedef Dijkstra<DeltaResGraph, ReducedCostMap, ResDijkstraTraits>
+      ResDijkstra;
+    /// \brief \ref lemon::Dijkstra "Dijkstra" class for finding
+    /// shortest paths in the residual graph with respect to the
+    /// reduced edge costs.
+    ResDijkstra dijkstra;
+
+    /// \brief The delta parameter used for capacity scaling.
+    Capacity delta;
+    /// \brief Edge filter map.
+    DeltaFilterMap delta_filter;
+    /// \brief The delta residual graph.
+    DeltaResGraph dres_graph;
+    /// \brief Map for identifing deficit nodes.
+    DeficitBoolMap delta_deficit;
+
+#else //WITHOUT_CAPACITY_SCALING
+    typedef Dijkstra<ResGraph, ReducedCostMap, ResDijkstraTraits>
+      ResDijkstra;
+    /// \brief \ref lemon::Dijkstra "Dijkstra" class for finding
+    /// shortest paths in the residual graph with respect to the
+    /// reduced edge costs.
+    ResDijkstra dijkstra;
+    /// \brief Map for identifing deficit nodes.
+    DeficitBoolMap has_deficit;
+#endif
+
+    /// \brief Pred map for the \ref lemon::Dijkstra "Dijkstra" class.
+    typename ResDijkstra::PredMap pred;
+    /// \brief Dist map for the \ref lemon::Dijkstra "Dijkstra" class to
+    /// update node potentials.
+    PotentialUpdateMap updater;
+
+  public :
+
+    /// \brief General constructor of the class (with lower bounds).
+    ///
+    /// General constructor of the class (with lower bounds).
+    ///
+    /// \param _graph The directed graph the algorithm runs on.
+    /// \param _lower The lower bounds of the edges.
+    /// \param _capacity The capacities (upper bounds) of the edges.
+    /// \param _cost The cost (length) values of the edges.
+    /// \param _supply The supply values of the nodes (signed).
+    CapacityScaling( const Graph &_graph,
+		     const LowerMap &_lower,
+		     const CapacityMap &_capacity,
+		     const CostMap &_cost,
+		     const SupplyMap &_supply ) :
+      graph(_graph), lower(&_lower), capacity(_graph), cost(_cost),
+      supply(_graph), flow(_graph, 0), potential(_graph, 0),
+      res_graph(_graph, capacity, flow),
+      red_cost(res_graph, cost, potential), imbalance(_graph),
+#ifdef WITH_SCALING
+      delta(0), delta_filter(res_graph, delta),
+      dres_graph(res_graph, delta_filter),
+      dijkstra(dres_graph, red_cost), pred(dres_graph),
+      delta_deficit(imbalance, delta)
+#else //WITHOUT_CAPACITY_SCALING
+      dijkstra(res_graph, red_cost), pred(res_graph),
+      has_deficit(imbalance)
+#endif
+    {
+      // Removing nonzero lower bounds
+      capacity = subMap(_capacity, _lower);
+      Supply sum = 0;
+      for (NodeIt n(graph); n != INVALID; ++n) {
+	Supply s = _supply[n];
+	for (InEdgeIt e(graph, n); e != INVALID; ++e)
+	  s += _lower[e];
+	for (OutEdgeIt e(graph, n); e != INVALID; ++e)
+	  s -= _lower[e];
+	supply[n] = imbalance[n] = s;
+	sum += s;
+      }
+      valid_supply = sum == 0;
+    }
+
+    /// \brief General constructor of the class (without lower bounds).
+    ///
+    /// General constructor of the class (without lower bounds).
+    ///
+    /// \param _graph The directed graph the algorithm runs on.
+    /// \param _capacity The capacities (upper bounds) of the edges.
+    /// \param _cost The cost (length) values of the edges.
+    /// \param _supply The supply values of the nodes (signed).
+    CapacityScaling( const Graph &_graph,
+		     const CapacityMap &_capacity,
+		     const CostMap &_cost,
+		     const SupplyMap &_supply ) :
+      graph(_graph), lower(NULL), capacity(_capacity), cost(_cost),
+      supply(_supply), flow(_graph, 0), potential(_graph, 0),
+      res_graph(_graph, capacity, flow),
+      red_cost(res_graph, cost, potential), imbalance(_graph),
+#ifdef WITH_SCALING
+      delta(0), delta_filter(res_graph, delta),
+      dres_graph(res_graph, delta_filter),
+      dijkstra(dres_graph, red_cost), pred(dres_graph),
+      delta_deficit(imbalance, delta)
+#else //WITHOUT_CAPACITY_SCALING
+      dijkstra(res_graph, red_cost), pred(res_graph),
+      has_deficit(imbalance)
+#endif
+    {
+      // Checking 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 of the class (with lower bounds).
+    ///
+    /// Simple constructor of the class (with lower bounds).
+    ///
+    /// \param _graph The directed graph the algorithm runs on.
+    /// \param _lower The lower bounds of the edges.
+    /// \param _capacity The capacities (upper bounds) of the edges.
+    /// \param _cost The cost (length) values of the edges.
+    /// \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).
+    CapacityScaling( const Graph &_graph,
+		     const LowerMap &_lower,
+		     const CapacityMap &_capacity,
+		     const CostMap &_cost,
+		     Node _s, Node _t,
+		     Supply _flow_value ) :
+      graph(_graph), lower(&_lower), capacity(_graph), cost(_cost),
+      supply(_graph), flow(_graph, 0), potential(_graph, 0),
+      res_graph(_graph, capacity, flow),
+      red_cost(res_graph, cost, potential), imbalance(_graph),
+#ifdef WITH_SCALING
+      delta(0), delta_filter(res_graph, delta),
+      dres_graph(res_graph, delta_filter),
+      dijkstra(dres_graph, red_cost), pred(dres_graph),
+      delta_deficit(imbalance, delta)
+#else //WITHOUT_CAPACITY_SCALING
+      dijkstra(res_graph, red_cost), pred(res_graph),
+      has_deficit(imbalance)
+#endif
+    {
+      // Removing nonzero lower bounds
+      capacity = subMap(_capacity, _lower);
+      for (NodeIt n(graph); n != INVALID; ++n) {
+	Supply s = 0;
+	if (n == _s) s =  _flow_value;
+	if (n == _t) s = -_flow_value;
+	for (InEdgeIt e(graph, n); e != INVALID; ++e)
+	  s += _lower[e];
+	for (OutEdgeIt e(graph, n); e != INVALID; ++e)
+	  s -= _lower[e];
+	supply[n] = imbalance[n] = s;
+      }
+      valid_supply = true;
+    }
+
+    /// \brief Simple constructor of the class (without lower bounds).
+    ///
+    /// Simple constructor of the class (without lower bounds).
+    ///
+    /// \param _graph The directed graph the algorithm runs on.
+    /// \param _capacity The capacities (upper bounds) of the edges.
+    /// \param _cost The cost (length) values of the edges.
+    /// \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).
+    CapacityScaling( const Graph &_graph,
+		     const CapacityMap &_capacity,
+		     const CostMap &_cost,
+		     Node _s, Node _t,
+		     Supply _flow_value ) :
+      graph(_graph), lower(NULL), capacity(_capacity), cost(_cost),
+      supply(_graph, 0), flow(_graph, 0), potential(_graph, 0),
+      res_graph(_graph, capacity, flow),
+      red_cost(res_graph, cost, potential), imbalance(_graph),
+#ifdef WITH_SCALING
+      delta(0), delta_filter(res_graph, delta),
+      dres_graph(res_graph, delta_filter),
+      dijkstra(dres_graph, red_cost), pred(dres_graph),
+      delta_deficit(imbalance, delta)
+#else //WITHOUT_CAPACITY_SCALING
+      dijkstra(res_graph, red_cost), pred(res_graph),
+      has_deficit(imbalance)
+#endif
+    {
+      supply[_s] =  _flow_value;
+      supply[_t] = -_flow_value;
+      valid_supply = true;
+    }
+
+    /// \brief Returns a const reference to the flow map.
+    ///
+    /// Returns a const reference to the flow map.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    const FlowMap& flowMap() const {
+      return flow;
+    }
+
+    /// \brief Returns a const reference to the potential map (the dual
+    /// solution).
+    ///
+    /// Returns a const reference to the potential map (the dual
+    /// solution).
+    ///
+    /// \pre \ref run() must be called before using this function.
+    const PotentialMap& potentialMap() const {
+      return potential;
+    }
+
+    /// \brief Returns the total cost of the found flow.
+    ///
+    /// Returns 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 (EdgeIt e(graph); e != INVALID; ++e)
+	c += flow[e] * cost[e];
+      return c;
+    }
+
+    /// \brief Runs the successive shortest path algorithm.
+    ///
+    /// Runs the successive shortest path algorithm.
+    ///
+    /// \return \c true if a feasible flow can be found.
+    bool run() {
+      return init() && start();
+    }
+
+  protected:
+
+    /// \brief Initializes the algorithm.
+    bool init() {
+      if (!valid_supply) return false;
+
+      // Initalizing Dijkstra class
+      updater.potentialMap(potential);
+      dijkstra.distMap(updater).predMap(pred);
+
+#ifdef WITH_SCALING
+      // Initilaizing delta value
+      Capacity max_cap = 0;
+      for (EdgeIt e(graph); e != INVALID; ++e) {
+	if (capacity[e] > max_cap) max_cap = capacity[e];
+      }
+      for (delta = 1; 2 * delta < max_cap; delta *= 2) ;
+#endif
+      return true;
+    }
+
+#ifdef WITH_SCALING
+    /// \brief Executes the capacity scaling version of the successive
+    /// shortest path algorithm.
+    bool start() {
+      typedef typename DeltaResGraph::EdgeIt DeltaResEdgeIt;
+      typedef typename DeltaResGraph::Edge DeltaResEdge;
+
+      // Processing capacity scaling phases
+      ResNode s, t;
+      for ( ; delta >= 1; delta = delta < 4 && delta > 1 ?
+				  1 : delta / 4 )
+      {
+	// Saturating edges not satisfying the optimality condition
+	Capacity r;
+	for (DeltaResEdgeIt e(dres_graph); e != INVALID; ++e) {
+	  if (red_cost[e] < 0) {
+	    res_graph.augment(e, r = res_graph.rescap(e));
+	    imbalance[dres_graph.target(e)] += r;
+	    imbalance[dres_graph.source(e)] -= r;
+	  }
+	}
+
+	// Finding excess nodes
+	excess_nodes.clear();
+	for (ResNodeIt n(res_graph); n != INVALID; ++n) {
+	  if (imbalance[n] >= delta) excess_nodes.push_back(n);
+	}
+	next_node = 0;
+
+	// Finding successive shortest paths
+	while (next_node < excess_nodes.size()) {
+	  // Running Dijkstra
+	  s = excess_nodes[next_node];
+	  updater.init();
+	  dijkstra.init();
+	  dijkstra.addSource(s);
+	  if ((t = dijkstra.start(delta_deficit)) == INVALID) {
+	    if (delta > 1) {
+	      ++next_node;
+	      continue;
+	    }
+	    return false;
+	  }
+
+	  // Updating node potentials
+	  updater.update();
+
+	  // Augment along a shortest path from s to t
+	  Capacity d = imbalance[s] < -imbalance[t] ?
+	    imbalance[s] : -imbalance[t];
+	  ResNode u = t;
+	  ResEdge e;
+	  if (d > delta) {
+	    while ((e = pred[u]) != INVALID) {
+	      if (res_graph.rescap(e) < d) d = res_graph.rescap(e);
+	      u = dres_graph.source(e);
+	    }
+	  }
+	  u = t;
+	  while ((e = pred[u]) != INVALID) {
+	    res_graph.augment(e, d);
+	    u = dres_graph.source(e);
+	  }
+	  imbalance[s] -= d;
+	  imbalance[t] += d;
+	  if (imbalance[s] < delta) ++next_node;
+	}
+      }
+
+      // Handling nonzero lower bounds
+      if (lower) {
+	for (EdgeIt e(graph); e != INVALID; ++e)
+	  flow[e] += (*lower)[e];
+      }
+      return true;
+    }
+
+#else //WITHOUT_CAPACITY_SCALING
+    /// \brief Executes the successive shortest path algorithm without
+    /// capacity scaling.
+    bool start() {
+      // Finding excess nodes
+      for (ResNodeIt n(res_graph); n != INVALID; ++n) {
+	if (imbalance[n] > 0) excess_nodes.push_back(n);
+      }
+      if (excess_nodes.size() == 0) return true;
+      next_node = 0;
+
+      // Finding successive shortest paths
+      ResNode s, t;
+      while ( imbalance[excess_nodes[next_node]] > 0 ||
+	      ++next_node < excess_nodes.size() )
+      {
+	// Running Dijkstra
+	s = excess_nodes[next_node];
+	updater.init();
+	dijkstra.init();
+	dijkstra.addSource(s);
+	if ((t = dijkstra.start(has_deficit)) == INVALID)
+	  return false;
+
+	// Updating node potentials
+	updater.update();
+
+	// Augmenting along a shortest path from s to t
+	Capacity delta = imbalance[s] < -imbalance[t] ?
+	  imbalance[s] : -imbalance[t];
+	ResNode u = t;
+	ResEdge e;
+	while ((e = pred[u]) != INVALID) {
+	  if (res_graph.rescap(e) < delta) delta = res_graph.rescap(e);
+	  u = res_graph.source(e);
+	}
+	u = t;
+	while ((e = pred[u]) != INVALID) {
+	  res_graph.augment(e, delta);
+	  u = res_graph.source(e);
+	}
+	imbalance[s] -= delta;
+	imbalance[t] += delta;
+      }
+
+      // Handling nonzero lower bounds
+      if (lower) {
+	for (EdgeIt e(graph); e != INVALID; ++e)
+	  flow[e] += (*lower)[e];
+      }
+      return true;
+    }
+#endif
+
+  }; //class CapacityScaling
+
+  ///@}
+
+} //namespace lemon
+
+#endif //LEMON_CAPACITY_SCALING_H