# HG changeset patch
# User Peter Kovacs <kpeter@inf.elte.hu>
# Date 1258064254 -3600
# Node ID d3e32a777d0b7bb8338f1d581ff84528130035cf
# Parent  4db8d5ccd26bfffa41fe796e55216b3baf4e1d33
Port CapacityScaling from SVN -r3524 (#180)

diff -r 4db8d5ccd26b -r d3e32a777d0b lemon/Makefile.am
--- a/lemon/Makefile.am	Sun Dec 13 22:19:08 2009 +0100
+++ b/lemon/Makefile.am	Thu Nov 12 23:17:34 2009 +0100
@@ -62,6 +62,7 @@
 	lemon/bin_heap.h \
 	lemon/binom_heap.h \
 	lemon/bucket_heap.h \
+	lemon/capacity_scaling.h \
 	lemon/cbc.h \
 	lemon/circulation.h \
 	lemon/clp.h \
diff -r 4db8d5ccd26b -r d3e32a777d0b lemon/capacity_scaling.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/capacity_scaling.h	Thu Nov 12 23:17:34 2009 +0100
@@ -0,0 +1,717 @@
+/* -*- 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_CAPACITY_SCALING_H
+#define LEMON_CAPACITY_SCALING_H
+
+/// \ingroup min_cost_flow
+///
+/// \file
+/// \brief Capacity scaling algorithm for finding a minimum cost flow.
+
+#include <vector>
+#include <lemon/bin_heap.h>
+
+namespace lemon {
+
+  /// \addtogroup min_cost_flow
+  /// @{
+
+  /// \brief Implementation of the capacity scaling algorithm for
+  /// finding a minimum cost flow.
+  ///
+  /// \ref CapacityScaling implements the capacity scaling version
+  /// of the successive shortest path 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 CapacityScaling
+  {
+    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 typename Digraph::template NodeMap<Arc> PredMap;
+
+  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 Special implementation of the \ref Dijkstra algorithm
+    /// for finding shortest paths in the residual network.
+    ///
+    /// \ref ResidualDijkstra is a special implementation of the
+    /// \ref Dijkstra algorithm for finding shortest paths in the
+    /// residual network of the digraph with respect to the reduced arc
+    /// costs and modifying the node potentials according to the
+    /// distance of the nodes.
+    class ResidualDijkstra
+    {
+      typedef typename Digraph::template NodeMap<int> HeapCrossRef;
+      typedef BinHeap<Cost, HeapCrossRef> Heap;
+
+    private:
+
+      // The digraph the algorithm runs on
+      const Digraph &_graph;
+
+      // The main maps
+      const FlowMap &_flow;
+      const CapacityArcMap &_res_cap;
+      const CostMap &_cost;
+      const SupplyNodeMap &_excess;
+      PotentialMap &_potential;
+
+      // The distance map
+      PotentialMap _dist;
+      // The pred arc map
+      PredMap &_pred;
+      // The processed (i.e. permanently labeled) nodes
+      std::vector<Node> _proc_nodes;
+
+    public:
+
+      /// Constructor.
+      ResidualDijkstra( const Digraph &digraph,
+                        const FlowMap &flow,
+                        const CapacityArcMap &res_cap,
+                        const CostMap &cost,
+                        const SupplyMap &excess,
+                        PotentialMap &potential,
+                        PredMap &pred ) :
+        _graph(digraph), _flow(flow), _res_cap(res_cap), _cost(cost),
+        _excess(excess), _potential(potential), _dist(digraph),
+        _pred(pred)
+      {}
+
+      /// Run the algorithm from the given source node.
+      Node run(Node s, Capacity delta = 1) {
+        HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
+        Heap heap(heap_cross_ref);
+        heap.push(s, 0);
+        _pred[s] = INVALID;
+        _proc_nodes.clear();
+
+        // Processing nodes
+        while (!heap.empty() && _excess[heap.top()] > -delta) {
+          Node u = heap.top(), v;
+          Cost d = heap.prio() + _potential[u], nd;
+          _dist[u] = heap.prio();
+          heap.pop();
+          _proc_nodes.push_back(u);
+
+          // Traversing outgoing arcs
+          for (OutArcIt e(_graph, u); e != INVALID; ++e) {
+            if (_res_cap[e] >= delta) {
+              v = _graph.target(e);
+              switch(heap.state(v)) {
+              case Heap::PRE_HEAP:
+                heap.push(v, d + _cost[e] - _potential[v]);
+                _pred[v] = e;
+                break;
+              case Heap::IN_HEAP:
+                nd = d + _cost[e] - _potential[v];
+                if (nd < heap[v]) {
+                  heap.decrease(v, nd);
+                  _pred[v] = e;
+                }
+                break;
+              case Heap::POST_HEAP:
+                break;
+              }
+            }
+          }
+
+          // Traversing incoming arcs
+          for (InArcIt e(_graph, u); e != INVALID; ++e) {
+            if (_flow[e] >= delta) {
+              v = _graph.source(e);
+              switch(heap.state(v)) {
+              case Heap::PRE_HEAP:
+                heap.push(v, d - _cost[e] - _potential[v]);
+                _pred[v] = e;
+                break;
+              case Heap::IN_HEAP:
+                nd = d - _cost[e] - _potential[v];
+                if (nd < heap[v]) {
+                  heap.decrease(v, nd);
+                  _pred[v] = e;
+                }
+                break;
+              case Heap::POST_HEAP:
+                break;
+              }
+            }
+          }
+        }
+        if (heap.empty()) return INVALID;
+
+        // Updating potentials of processed nodes
+        Node t = heap.top();
+        Cost t_dist = heap.prio();
+        for (int i = 0; i < int(_proc_nodes.size()); ++i)
+          _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
+
+        return t;
+      }
+
+    }; //class ResidualDijkstra
+
+  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 capacity map
+    CapacityArcMap _res_cap;
+    // The excess map
+    SupplyNodeMap _excess;
+    // The excess nodes (i.e. nodes with positive excess)
+    std::vector<Node> _excess_nodes;
+    // The deficit nodes (i.e. nodes with negative excess)
+    std::vector<Node> _deficit_nodes;
+
+    // The delta parameter used for capacity scaling
+    Capacity _delta;
+    // The maximum number of phases
+    int _phase_num;
+
+    // The pred arc map
+    PredMap _pred;
+    // Implementation of the Dijkstra algorithm for finding augmenting
+    // shortest paths in the residual network
+    ResidualDijkstra *_dijkstra;
+
+  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).
+    CapacityScaling( 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_cap(digraph), _excess(digraph), _pred(digraph), _dijkstra(NULL)
+    {
+      Supply sum = 0;
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        _supply[n] = supply[n];
+        _excess[n] = supply[n];
+        sum += supply[n];
+      }
+      _valid_supply = sum == 0;
+      for (ArcIt a(_graph); a != INVALID; ++a) {
+        _capacity[a] = capacity[a];
+        _res_cap[a] = capacity[a];
+      }
+
+      // Remove non-zero lower bounds
+      typename LowerMap::Value lcap;
+      for (ArcIt e(_graph); e != INVALID; ++e) {
+        if ((lcap = lower[e]) != 0) {
+          _capacity[e] -= lcap;
+          _res_cap[e] -= lcap;
+          _supply[_graph.source(e)] -= lcap;
+          _supply[_graph.target(e)] += lcap;
+          _excess[_graph.source(e)] -= lcap;
+          _excess[_graph.target(e)] += lcap;
+        }
+      }
+    }
+/*
+    /// \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).
+    CapacityScaling( 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_cap(capacity), _excess(supply), _pred(digraph), _dijkstra(NULL)
+    {
+      // 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).
+    CapacityScaling( 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_cap(capacity), _excess(digraph, 0), _pred(digraph), _dijkstra(NULL)
+    {
+      // Remove non-zero lower bounds
+      _supply[s] = _excess[s] =  flow_value;
+      _supply[t] = _excess[t] = -flow_value;
+      typename LowerMap::Value lcap;
+      for (ArcIt e(_graph); e != INVALID; ++e) {
+        if ((lcap = lower[e]) != 0) {
+          _capacity[e] -= lcap;
+          _res_cap[e] -= lcap;
+          _supply[_graph.source(e)] -= lcap;
+          _supply[_graph.target(e)] += lcap;
+          _excess[_graph.source(e)] -= lcap;
+          _excess[_graph.target(e)] += lcap;
+        }
+      }
+      _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).
+    CapacityScaling( 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_cap(capacity), _excess(digraph, 0), _pred(digraph), _dijkstra(NULL)
+    {
+      _supply[s] = _excess[s] =  flow_value;
+      _supply[t] = _excess[t] = -flow_value;
+      _valid_supply = true;
+    }
+*/
+    /// Destructor.
+    ~CapacityScaling() {
+      if (_local_flow) delete _flow;
+      if (_local_potential) delete _potential;
+      delete _dijkstra;
+    }
+
+    /// \brief Set the flow map.
+    ///
+    /// Set the flow map.
+    ///
+    /// \return \c (*this)
+    CapacityScaling& 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)
+    CapacityScaling& potentialMap(PotentialMap &map) {
+      if (_local_potential) {
+        delete _potential;
+        _local_potential = false;
+      }
+      _potential = &map;
+      return *this;
+    }
+
+    /// \name Execution control
+
+    /// @{
+
+    /// \brief Run the algorithm.
+    ///
+    /// This function runs the algorithm.
+    ///
+    /// \param scaling Enable or disable capacity scaling.
+    /// If the maximum arc capacity and/or the amount of total supply
+    /// is rather small, the algorithm could be slightly faster without
+    /// scaling.
+    ///
+    /// \return \c true if a feasible flow can be found.
+    bool run(bool scaling = true) {
+      return init(scaling) && start();
+    }
+
+    /// @}
+
+    /// \name Query Functions
+    /// The results of the algorithm can be obtained using these
+    /// functions.\n
+    /// \ref lemon::CapacityScaling::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(bool scaling) {
+      if (!_valid_supply) return false;
+
+      // Initializing maps
+      if (!_flow) {
+        _flow = new FlowMap(_graph);
+        _local_flow = true;
+      }
+      if (!_potential) {
+        _potential = new PotentialMap(_graph);
+        _local_potential = true;
+      }
+      for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
+      for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
+
+      _dijkstra = new ResidualDijkstra( _graph, *_flow, _res_cap, _cost,
+                                        _excess, *_potential, _pred );
+
+      // Initializing delta value
+      if (scaling) {
+        // With scaling
+        Supply max_sup = 0, max_dem = 0;
+        for (NodeIt n(_graph); n != INVALID; ++n) {
+          if ( _supply[n] > max_sup) max_sup =  _supply[n];
+          if (-_supply[n] > max_dem) max_dem = -_supply[n];
+        }
+        Capacity max_cap = 0;
+        for (ArcIt e(_graph); e != INVALID; ++e) {
+          if (_capacity[e] > max_cap) max_cap = _capacity[e];
+        }
+        max_sup = std::min(std::min(max_sup, max_dem), max_cap);
+        _phase_num = 0;
+        for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2)
+          ++_phase_num;
+      } else {
+        // Without scaling
+        _delta = 1;
+      }
+
+      return true;
+    }
+
+    bool start() {
+      if (_delta > 1)
+        return startWithScaling();
+      else
+        return startWithoutScaling();
+    }
+
+    /// Execute the capacity scaling algorithm.
+    bool startWithScaling() {
+      // Processing capacity scaling phases
+      Node s, t;
+      int phase_cnt = 0;
+      int factor = 4;
+      while (true) {
+        // Saturating all arcs not satisfying the optimality condition
+        for (ArcIt e(_graph); e != INVALID; ++e) {
+          Node u = _graph.source(e), v = _graph.target(e);
+          Cost c = _cost[e] + (*_potential)[u] - (*_potential)[v];
+          if (c < 0 && _res_cap[e] >= _delta) {
+            _excess[u] -= _res_cap[e];
+            _excess[v] += _res_cap[e];
+            (*_flow)[e] = _capacity[e];
+            _res_cap[e] = 0;
+          }
+          else if (c > 0 && (*_flow)[e] >= _delta) {
+            _excess[u] += (*_flow)[e];
+            _excess[v] -= (*_flow)[e];
+            (*_flow)[e] = 0;
+            _res_cap[e] = _capacity[e];
+          }
+        }
+
+        // Finding excess nodes and deficit nodes
+        _excess_nodes.clear();
+        _deficit_nodes.clear();
+        for (NodeIt n(_graph); n != INVALID; ++n) {
+          if (_excess[n] >=  _delta) _excess_nodes.push_back(n);
+          if (_excess[n] <= -_delta) _deficit_nodes.push_back(n);
+        }
+        int next_node = 0, next_def_node = 0;
+
+        // Finding augmenting shortest paths
+        while (next_node < int(_excess_nodes.size())) {
+          // Checking deficit nodes
+          if (_delta > 1) {
+            bool delta_deficit = false;
+            for ( ; next_def_node < int(_deficit_nodes.size());
+                    ++next_def_node ) {
+              if (_excess[_deficit_nodes[next_def_node]] <= -_delta) {
+                delta_deficit = true;
+                break;
+              }
+            }
+            if (!delta_deficit) break;
+          }
+
+          // Running Dijkstra
+          s = _excess_nodes[next_node];
+          if ((t = _dijkstra->run(s, _delta)) == INVALID) {
+            if (_delta > 1) {
+              ++next_node;
+              continue;
+            }
+            return false;
+          }
+
+          // Augmenting along a shortest path from s to t.
+          Capacity d = std::min(_excess[s], -_excess[t]);
+          Node u = t;
+          Arc e;
+          if (d > _delta) {
+            while ((e = _pred[u]) != INVALID) {
+              Capacity rc;
+              if (u == _graph.target(e)) {
+                rc = _res_cap[e];
+                u = _graph.source(e);
+              } else {
+                rc = (*_flow)[e];
+                u = _graph.target(e);
+              }
+              if (rc < d) d = rc;
+            }
+          }
+          u = t;
+          while ((e = _pred[u]) != INVALID) {
+            if (u == _graph.target(e)) {
+              (*_flow)[e] += d;
+              _res_cap[e] -= d;
+              u = _graph.source(e);
+            } else {
+              (*_flow)[e] -= d;
+              _res_cap[e] += d;
+              u = _graph.target(e);
+            }
+          }
+          _excess[s] -= d;
+          _excess[t] += d;
+
+          if (_excess[s] < _delta) ++next_node;
+        }
+
+        if (_delta == 1) break;
+        if (++phase_cnt > _phase_num / 4) factor = 2;
+        _delta = _delta <= factor ? 1 : _delta / factor;
+      }
+
+      // Handling non-zero lower bounds
+      if (_lower) {
+        for (ArcIt e(_graph); e != INVALID; ++e)
+          (*_flow)[e] += (*_lower)[e];
+      }
+      return true;
+    }
+
+    /// Execute the successive shortest path algorithm.
+    bool startWithoutScaling() {
+      // Finding excess nodes
+      for (NodeIt n(_graph); n != INVALID; ++n)
+        if (_excess[n] > 0) _excess_nodes.push_back(n);
+      if (_excess_nodes.size() == 0) return true;
+      int next_node = 0;
+
+      // Finding shortest paths
+      Node s, t;
+      while ( _excess[_excess_nodes[next_node]] > 0 ||
+              ++next_node < int(_excess_nodes.size()) )
+      {
+        // Running Dijkstra
+        s = _excess_nodes[next_node];
+        if ((t = _dijkstra->run(s)) == INVALID) return false;
+
+        // Augmenting along a shortest path from s to t
+        Capacity d = std::min(_excess[s], -_excess[t]);
+        Node u = t;
+        Arc e;
+        if (d > 1) {
+          while ((e = _pred[u]) != INVALID) {
+            Capacity rc;
+            if (u == _graph.target(e)) {
+              rc = _res_cap[e];
+              u = _graph.source(e);
+            } else {
+              rc = (*_flow)[e];
+              u = _graph.target(e);
+            }
+            if (rc < d) d = rc;
+          }
+        }
+        u = t;
+        while ((e = _pred[u]) != INVALID) {
+          if (u == _graph.target(e)) {
+            (*_flow)[e] += d;
+            _res_cap[e] -= d;
+            u = _graph.source(e);
+          } else {
+            (*_flow)[e] -= d;
+            _res_cap[e] += d;
+            u = _graph.target(e);
+          }
+        }
+        _excess[s] -= d;
+        _excess[t] += d;
+      }
+
+      // Handling non-zero lower bounds
+      if (_lower) {
+        for (ArcIt e(_graph); e != INVALID; ++e)
+          (*_flow)[e] += (*_lower)[e];
+      }
+      return true;
+    }
+
+  }; //class CapacityScaling
+
+  ///@}
+
+} //namespace lemon
+
+#endif //LEMON_CAPACITY_SCALING_H