diff -r 3f1c7a6c33cd -r c9218405595b lemon/network_simplex.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/network_simplex.h	Mon May 07 11:42:18 2007 +0000
@@ -0,0 +1,945 @@
+/* -*- 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_NETWORK_SIMPLEX_H
+#define LEMON_NETWORK_SIMPLEX_H
+
+/// \ingroup min_cost_flow
+///
+/// \file
+/// \brief The network simplex algorithm for finding a minimum cost
+/// flow.
+
+#include <limits>
+#include <lemon/smart_graph.h>
+#include <lemon/graph_utils.h>
+
+/// \brief The pivot rule used in the algorithm.
+#define EDGE_BLOCK_PIVOT
+//#define FIRST_ELIGIBLE_PIVOT
+//#define BEST_ELIGIBLE_PIVOT
+//#define CANDIDATE_LIST_PIVOT
+//#define SORTED_LIST_PIVOT
+
+/// \brief State constant for edges at their lower bounds.
+#define LOWER	1
+/// \brief State constant for edges in the spanning tree.
+#define TREE	0
+/// \brief State constant for edges at their upper bounds.
+#define UPPER	-1
+
+#ifdef EDGE_BLOCK_PIVOT
+  /// \brief Number of blocks for the "Edge Block" pivot rule.
+  #define BLOCK_NUM	  100
+  /// \brief Lower bound for the number of edges to use "Edge Block"
+  // pivot rule instead of "First Eligible" pivot rule.
+  #define MIN_BOUND	  1000
+#endif
+
+#ifdef CANDIDATE_LIST_PIVOT
+  #include <list>
+  /// \brief The maximum length of the edge list for the
+  /// "Candidate List" pivot rule.
+  #define LIST_LENGTH	  100
+  /// \brief The maximum number of minor iterations between two major
+  /// itarations.
+  #define MINOR_LIMIT	  50
+#endif
+
+#ifdef SORTED_LIST_PIVOT
+  #include <deque>
+  #include <algorithm>
+  /// \brief The maximum length of the edge list for the
+  /// "Sorted List" pivot rule.
+  #define LIST_LENGTH	  500
+  #define LOWER_DIV	  4
+#endif
+
+//#define _DEBUG_ITER_
+
+namespace lemon {
+
+  /// \addtogroup min_cost_flow
+  /// @{
+
+  /// \brief Implementation of the network simplex algorithm for
+  /// finding a minimum cost flow.
+  ///
+  /// \ref lemon::NetworkSimplex "NetworkSimplex" implements the
+  /// network simplex 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 NetworkSimplex
+  {
+    typedef typename LowerMap::Value Lower;
+    typedef typename CapacityMap::Value Capacity;
+    typedef typename CostMap::Value Cost;
+    typedef typename SupplyMap::Value Supply;
+
+    typedef SmartGraph SGraph;
+    typedef typename SGraph::Node Node;
+    typedef typename SGraph::NodeIt NodeIt;
+    typedef typename SGraph::Edge Edge;
+    typedef typename SGraph::EdgeIt EdgeIt;
+    typedef typename SGraph::InEdgeIt InEdgeIt;
+    typedef typename SGraph::OutEdgeIt OutEdgeIt;
+
+    typedef typename SGraph::template EdgeMap<Lower> SLowerMap;
+    typedef typename SGraph::template EdgeMap<Capacity> SCapacityMap;
+    typedef typename SGraph::template EdgeMap<Cost> SCostMap;
+    typedef typename SGraph::template NodeMap<Supply> SSupplyMap;
+    typedef typename SGraph::template NodeMap<Cost> SPotentialMap;
+
+    typedef typename SGraph::template NodeMap<int> IntNodeMap;
+    typedef typename SGraph::template NodeMap<bool> BoolNodeMap;
+    typedef typename SGraph::template NodeMap<Node> NodeNodeMap;
+    typedef typename SGraph::template NodeMap<Edge> EdgeNodeMap;
+    typedef typename SGraph::template EdgeMap<int> IntEdgeMap;
+
+    typedef typename Graph::template NodeMap<Node> NodeRefMap;
+    typedef typename Graph::template EdgeMap<Edge> EdgeRefMap;
+
+  public:
+
+    /// \brief The type of the flow map.
+    typedef typename Graph::template EdgeMap<Capacity> 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<Edge, Cost>
+    {
+    private:
+
+      const SGraph &gr;
+      const SCostMap &cost_map;
+      const SPotentialMap &pot_map;
+
+    public:
+
+      typedef typename MapBase<Edge, Cost>::Value Value;
+      typedef typename MapBase<Edge, Cost>::Key Key;
+
+      ReducedCostMap( const SGraph &_gr,
+		      const SCostMap &_cm,
+		      const SPotentialMap &_pm ) :
+	gr(_gr), cost_map(_cm), pot_map(_pm) {}
+
+      Value operator[](const Key &e) const {
+	return cost_map[e] - pot_map[gr.source(e)] + pot_map[gr.target(e)];
+      }
+
+    }; //class ReducedCostMap
+
+  protected:
+
+    /// \brief The directed graph the algorithm runs on.
+    SGraph graph;
+    /// \brief The original graph.
+    const Graph &graph_ref;
+    /// \brief The original lower bound map.
+    const LowerMap *lower;
+    /// \brief The capacity map.
+    SCapacityMap capacity;
+    /// \brief The cost map.
+    SCostMap cost;
+    /// \brief The supply map.
+    SSupplyMap supply;
+    /// \brief The reduced cost map.
+    ReducedCostMap red_cost;
+    /// \brief The sum of supply values equals zero.
+    bool valid_supply;
+
+    /// \brief The edge map of the current flow.
+    SCapacityMap flow;
+    /// \brief The edge map of the found flow on the original graph.
+    FlowMap flow_result;
+    /// \brief The potential node map.
+    SPotentialMap potential;
+    /// \brief The potential node map on the original graph.
+    PotentialMap potential_result;
+
+    /// \brief Node reference for the original graph.
+    NodeRefMap node_ref;
+    /// \brief Edge reference for the original graph.
+    EdgeRefMap edge_ref;
+
+    /// \brief The depth node map of the spanning tree structure.
+    IntNodeMap depth;
+    /// \brief The parent node map of the spanning tree structure.
+    NodeNodeMap parent;
+    /// \brief The pred_edge node map of the spanning tree structure.
+    EdgeNodeMap pred_edge;
+    /// \brief The thread node map of the spanning tree structure.
+    NodeNodeMap thread;
+    /// \brief The forward node map of the spanning tree structure.
+    BoolNodeMap forward;
+    /// \brief The state edge map.
+    IntEdgeMap state;
+
+
+#ifdef EDGE_BLOCK_PIVOT
+    /// \brief The size of blocks for the "Edge Block" pivot rule.
+    int block_size;
+#endif
+#ifdef CANDIDATE_LIST_PIVOT
+    /// \brief The list of candidate edges for the "Candidate List"
+    /// pivot rule.
+    std::list<Edge> candidates;
+    /// \brief The number of minor iterations.
+    int minor_count;
+#endif
+#ifdef SORTED_LIST_PIVOT
+    /// \brief The list of candidate edges for the "Sorted List"
+    /// pivot rule.
+    std::deque<Edge> candidates;
+#endif
+
+    // Root node of the starting spanning tree.
+    Node root;
+    // The entering edge of the current pivot iteration.
+    Edge in_edge;
+    // Temporary nodes used in the current pivot iteration.
+    Node join, u_in, v_in, u_out, v_out;
+    Node right, first, second, last;
+    Node stem, par_stem, new_stem;
+    // The maximum augment amount along the cycle in the current pivot
+    // iteration.
+    Capacity delta;
+
+  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).
+    NetworkSimplex( const Graph &_graph,
+		    const LowerMap &_lower,
+		    const CapacityMap &_capacity,
+		    const CostMap &_cost,
+		    const SupplyMap &_supply ) :
+      graph_ref(_graph), lower(&_lower), capacity(graph), cost(graph),
+      supply(graph), flow(graph), flow_result(_graph), potential(graph),
+      potential_result(_graph), depth(graph), parent(graph),
+      pred_edge(graph), thread(graph), forward(graph), state(graph),
+      node_ref(graph_ref), edge_ref(graph_ref),
+      red_cost(graph, cost, potential)
+    {
+      // Checking the sum of supply values
+      Supply sum = 0;
+      for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n)
+	sum += _supply[n];
+      if (!(valid_supply = sum == 0)) return;
+
+      // Copying graph_ref to graph
+      copyGraph(graph, graph_ref)
+	.edgeMap(cost, _cost)
+	.nodeRef(node_ref)
+	.edgeRef(edge_ref)
+	.run();
+
+      // Removing nonzero lower bounds
+      for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) {
+	capacity[edge_ref[e]] = _capacity[e] - _lower[e];
+      }
+      for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) {
+	Supply s = _supply[n];
+	for (typename Graph::InEdgeIt e(graph_ref, n); e != INVALID; ++e)
+	  s += _lower[e];
+	for (typename Graph::OutEdgeIt e(graph_ref, n); e != INVALID; ++e)
+	  s -= _lower[e];
+	supply[node_ref[n]] = s;
+      }
+    }
+
+    /// \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).
+    NetworkSimplex( const Graph &_graph,
+		    const CapacityMap &_capacity,
+		    const CostMap &_cost,
+		    const SupplyMap &_supply ) :
+      graph_ref(_graph), lower(NULL), capacity(graph), cost(graph),
+      supply(graph), flow(graph), flow_result(_graph), potential(graph),
+      potential_result(_graph), depth(graph), parent(graph),
+      pred_edge(graph), thread(graph), forward(graph), state(graph),
+      node_ref(graph_ref), edge_ref(graph_ref),
+      red_cost(graph, cost, potential)
+    {
+      // Checking the sum of supply values
+      Supply sum = 0;
+      for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n)
+	sum += _supply[n];
+      if (!(valid_supply = sum == 0)) return;
+
+      // Copying graph_ref to graph
+      copyGraph(graph, graph_ref)
+	.edgeMap(capacity, _capacity)
+	.edgeMap(cost, _cost)
+	.nodeMap(supply, _supply)
+	.nodeRef(node_ref)
+	.edgeRef(edge_ref)
+	.run();
+    }
+
+    /// \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).
+    NetworkSimplex( const Graph &_graph,
+		    const LowerMap &_lower,
+		    const CapacityMap &_capacity,
+		    const CostMap &_cost,
+		    typename Graph::Node _s,
+		    typename Graph::Node _t,
+		    typename SupplyMap::Value _flow_value ) :
+      graph_ref(_graph), lower(&_lower), capacity(graph), cost(graph),
+      supply(graph), flow(graph), flow_result(_graph), potential(graph),
+      potential_result(_graph), depth(graph), parent(graph),
+      pred_edge(graph), thread(graph), forward(graph), state(graph),
+      node_ref(graph_ref), edge_ref(graph_ref),
+      red_cost(graph, cost, potential)
+    {
+      // Copying graph_ref to graph
+      copyGraph(graph, graph_ref)
+	.edgeMap(cost, _cost)
+	.nodeRef(node_ref)
+	.edgeRef(edge_ref)
+	.run();
+
+      // Removing nonzero lower bounds
+      for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) {
+	capacity[edge_ref[e]] = _capacity[e] - _lower[e];
+      }
+      for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) {
+	Supply s = 0;
+	if (n == _s) s =  _flow_value;
+	if (n == _t) s = -_flow_value;
+	for (typename Graph::InEdgeIt e(graph_ref, n); e != INVALID; ++e)
+	  s += _lower[e];
+	for (typename Graph::OutEdgeIt e(graph_ref, n); e != INVALID; ++e)
+	  s -= _lower[e];
+	supply[node_ref[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).
+    NetworkSimplex( const Graph &_graph,
+		    const CapacityMap &_capacity,
+		    const CostMap &_cost,
+		    typename Graph::Node _s,
+		    typename Graph::Node _t,
+		    typename SupplyMap::Value _flow_value ) :
+      graph_ref(_graph), lower(NULL), capacity(graph), cost(graph),
+      supply(graph, 0), flow(graph), flow_result(_graph), potential(graph),
+      potential_result(_graph), depth(graph), parent(graph),
+      pred_edge(graph), thread(graph), forward(graph), state(graph),
+      node_ref(graph_ref), edge_ref(graph_ref),
+      red_cost(graph, cost, potential)
+    {
+      // Copying graph_ref to graph
+      copyGraph(graph, graph_ref)
+	.edgeMap(capacity, _capacity)
+	.edgeMap(cost, _cost)
+	.nodeRef(node_ref)
+	.edgeRef(edge_ref)
+	.run();
+      supply[node_ref[_s]] =  _flow_value;
+      supply[node_ref[_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_result;
+    }
+
+    /// \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_result;
+    }
+
+    /// \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 (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e)
+	c += flow_result[e] * cost[edge_ref[e]];
+      return c;
+    }
+
+    /// \brief Runs the algorithm.
+    ///
+    /// Runs the algorithm.
+    ///
+    /// \return \c true if a feasible flow can be found.
+    bool run() {
+      return init() && start();
+    }
+
+  protected:
+
+    /// \brief Extends the underlaying graph and initializes all the
+    /// node and edge maps.
+    bool init() {
+      if (!valid_supply) return false;
+
+      // Initializing state and flow maps
+      for (EdgeIt e(graph); e != INVALID; ++e) {
+	flow[e] = 0;
+	state[e] = LOWER;
+      }
+
+      // Adding an artificial root node to the graph
+      root = graph.addNode();
+      parent[root] = INVALID;
+      pred_edge[root] = INVALID;
+      depth[root] = supply[root] = potential[root] = 0;
+
+      // Adding artificial edges to the graph and initializing the node
+      // maps of the spanning tree data structure
+      Supply sum = 0;
+      Node last = root;
+      Edge e;
+      Cost max_cost = std::numeric_limits<Cost>::max() / 4;
+      for (NodeIt u(graph); u != INVALID; ++u) {
+	if (u == root) continue;
+	thread[last] = u;
+	last = u;
+	parent[u] = root;
+	depth[u] = 1;
+	sum += supply[u];
+	if (supply[u] >= 0) {
+	  e = graph.addEdge(u, root);
+	  flow[e] = supply[u];
+	  forward[u] = true;
+	  potential[u] = max_cost;
+	} else {
+	  e = graph.addEdge(root, u);
+	  flow[e] = -supply[u];
+	  forward[u] = false;
+	  potential[u] = -max_cost;
+	}
+	cost[e] = max_cost;
+	capacity[e] = std::numeric_limits<Capacity>::max();
+	state[e] = TREE;
+	pred_edge[u] = e;
+      }
+      thread[last] = root;
+
+#ifdef EDGE_BLOCK_PIVOT
+      // Initializing block_size for the edge block pivot rule
+      int edge_num = countEdges(graph);
+      block_size = edge_num > MIN_BOUND ? edge_num / BLOCK_NUM + 1 : 1;
+#endif
+#ifdef CANDIDATE_LIST_PIVOT
+      minor_count = 0;
+#endif
+
+      return sum == 0;
+    }
+
+#ifdef FIRST_ELIGIBLE_PIVOT
+    /// \brief Finds entering edge according to the "First Eligible"
+    /// pivot rule.
+    bool findEnteringEdge(EdgeIt &next_edge) {
+      for (EdgeIt e = next_edge; e != INVALID; ++e) {
+	if (state[e] * red_cost[e] < 0) {
+	  in_edge = e;
+	  next_edge = ++e;
+	  return true;
+	}
+      }
+      for (EdgeIt e(graph); e != next_edge; ++e) {
+	if (state[e] * red_cost[e] < 0) {
+	  in_edge = e;
+	  next_edge = ++e;
+	  return true;
+	}
+      }
+      return false;
+    }
+#endif
+
+#ifdef BEST_ELIGIBLE_PIVOT
+    /// \brief Finds entering edge according to the "Best Eligible"
+    /// pivot rule.
+    bool findEnteringEdge() {
+      Cost min = 0;
+      for (EdgeIt e(graph); e != INVALID; ++e) {
+	if (state[e] * red_cost[e] < min) {
+	  min = state[e] * red_cost[e];
+	  in_edge = e;
+	}
+      }
+      return min < 0;
+    }
+#endif
+
+#ifdef EDGE_BLOCK_PIVOT
+    /// \brief Finds entering edge according to the "Edge Block"
+    /// pivot rule.
+    bool findEnteringEdge(EdgeIt &next_edge) {
+      if (block_size == 1) {
+	// Performing first eligible selection
+	for (EdgeIt e = next_edge; e != INVALID; ++e) {
+	  if (state[e] * red_cost[e] < 0) {
+	    in_edge = e;
+	    next_edge = ++e;
+	    return true;
+	  }
+	}
+	for (EdgeIt e(graph); e != next_edge; ++e) {
+	  if (state[e] * red_cost[e] < 0) {
+	    in_edge = e;
+	    next_edge = ++e;
+	    return true;
+	  }
+	}
+	return false;
+      } else {
+	// Performing edge block selection
+	Cost curr, min = 0;
+	EdgeIt min_edge(graph);
+	int cnt = 0;
+	for (EdgeIt e = next_edge; e != INVALID; ++e) {
+	  if ((curr = state[e] * red_cost[e]) < min) {
+	    min = curr;
+	    min_edge = e;
+	  }
+	  if (++cnt == block_size) {
+	    if (min < 0) break;
+	    cnt = 0;
+	  }
+	}
+	if (!(min < 0)) {
+	  for (EdgeIt e(graph); e != next_edge; ++e) {
+	    if ((curr = state[e] * red_cost[e]) < min) {
+	      min = curr;
+	      min_edge = e;
+	    }
+	    if (++cnt == block_size) {
+	      if (min < 0) break;
+	      cnt = 0;
+	    }
+	  }
+	}
+	in_edge = min_edge;
+	if ((next_edge = ++min_edge) == INVALID)
+	  next_edge = EdgeIt(graph);
+	return min < 0;
+      }
+    }
+#endif
+
+#ifdef CANDIDATE_LIST_PIVOT
+    /// \brief Functor class for removing non-eligible edges from the
+    /// candidate list.
+    class RemoveFunc
+    {
+    private:
+      const IntEdgeMap &st;
+      const ReducedCostMap &rc;
+    public:
+      RemoveFunc(const IntEdgeMap &_st, const ReducedCostMap &_rc) :
+	st(_st), rc(_rc) {}
+      bool operator()(const Edge &e) {
+	return st[e] * rc[e] >= 0;
+      }
+    };
+
+    /// \brief Finds entering edge according to the "Candidate List"
+    /// pivot rule.
+    bool findEnteringEdge() {
+      static RemoveFunc remove_func(state, red_cost);
+      typedef typename std::list<Edge>::iterator ListIt;
+
+      candidates.remove_if(remove_func);
+      if (minor_count >= MINOR_LIMIT || candidates.size() == 0) {
+	// Major iteration
+	for (EdgeIt e(graph); e != INVALID; ++e) {
+	  if (state[e] * red_cost[e] < 0) {
+	    candidates.push_back(e);
+	    if (candidates.size() == LIST_LENGTH) break;
+	  }
+	}
+	if (candidates.size() == 0) return false;
+      }
+
+      // Minor iteration
+      ++minor_count;
+      Cost min = 0;
+      for (ListIt it = candidates.begin(); it != candidates.end(); ++it) {
+	if (state[*it] * red_cost[*it] < min) {
+	  min = state[*it] * red_cost[*it];
+	  in_edge = *it;
+	}
+      }
+      return true;
+    }
+#endif
+
+#ifdef SORTED_LIST_PIVOT
+    /// \brief Functor class to compare edges during sort of the
+    /// candidate list.
+    class SortFunc
+    {
+    private:
+      const IntEdgeMap &st;
+      const ReducedCostMap &rc;
+    public:
+      SortFunc(const IntEdgeMap &_st, const ReducedCostMap &_rc) :
+	st(_st), rc(_rc) {}
+      bool operator()(const Edge &e1, const Edge &e2) {
+	return st[e1] * rc[e1] < st[e2] * rc[e2];
+      }
+    };
+
+    /// \brief Finds entering edge according to the "Sorted List"
+    /// pivot rule.
+    bool findEnteringEdge() {
+      static SortFunc sort_func(state, red_cost);
+
+      // Minor iteration
+      while (candidates.size() > 0) {
+	in_edge = candidates.front();
+	candidates.pop_front();
+	if (state[in_edge] * red_cost[in_edge] < 0) return true;
+      }
+
+      // Major iteration
+      Cost curr, min = 0;
+      for (EdgeIt e(graph); e != INVALID; ++e) {
+	if ((curr = state[e] * red_cost[e]) < min / LOWER_DIV) {
+	  candidates.push_back(e);
+	  if (curr < min) min = curr;
+	  if (candidates.size() >= LIST_LENGTH) break;
+	}
+      }
+      if (candidates.size() == 0) return false;
+      sort(candidates.begin(), candidates.end(), sort_func);
+      return true;
+    }
+#endif
+
+    /// \brief Finds the join node.
+    Node findJoinNode() {
+      // Finding the join node
+      Node u = graph.source(in_edge);
+      Node v = graph.target(in_edge);
+      while (u != v) {
+	if (depth[u] == depth[v]) {
+	  u = parent[u];
+	  v = parent[v];
+	}
+	else if (depth[u] > depth[v]) u = parent[u];
+	else v = parent[v];
+      }
+      return u;
+    }
+
+    /// \brief Finds the leaving edge of the cycle. Returns \c true if
+    /// the leaving edge is not the same as the entering edge.
+    bool findLeavingEdge() {
+      // Initializing first and second nodes according to the direction
+      // of the cycle
+      if (state[in_edge] == LOWER) {
+	first = graph.source(in_edge);
+	second	= graph.target(in_edge);
+      } else {
+	first = graph.target(in_edge);
+	second	= graph.source(in_edge);
+      }
+      delta = capacity[in_edge];
+      bool result = false;
+      Capacity d;
+      Edge e;
+
+      // Searching the cycle along the path form the first node to the
+      // root node
+      for (Node u = first; u != join; u = parent[u]) {
+	e = pred_edge[u];
+	d = forward[u] ? flow[e] : capacity[e] - flow[e];
+	if (d < delta) {
+	  delta = d;
+	  u_out = u;
+	  u_in = first;
+	  v_in = second;
+	  result = true;
+	}
+      }
+      // Searching the cycle along the path form the second node to the
+      // root node
+      for (Node u = second; u != join; u = parent[u]) {
+	e = pred_edge[u];
+	d = forward[u] ? capacity[e] - flow[e] : flow[e];
+	if (d <= delta) {
+	  delta = d;
+	  u_out = u;
+	  u_in = second;
+	  v_in = first;
+	  result = true;
+	}
+      }
+      return result;
+    }
+
+    /// \brief Changes flow and state edge maps.
+    void changeFlows(bool change) {
+      // Augmenting along the cycle
+      if (delta > 0) {
+	Capacity val = state[in_edge] * delta;
+	flow[in_edge] += val;
+	for (Node u = graph.source(in_edge); u != join; u = parent[u]) {
+	  flow[pred_edge[u]] += forward[u] ? -val : val;
+	}
+	for (Node u = graph.target(in_edge); u != join; u = parent[u]) {
+	  flow[pred_edge[u]] += forward[u] ? val : -val;
+	}
+      }
+      // Updating the state of the entering and leaving edges
+      if (change) {
+	state[in_edge] = TREE;
+	state[pred_edge[u_out]] =
+	  (flow[pred_edge[u_out]] == 0) ? LOWER : UPPER;
+      } else {
+	state[in_edge] = -state[in_edge];
+      }
+    }
+
+    /// \brief Updates thread and parent node maps.
+    void updateThreadParent() {
+      Node u;
+      v_out = parent[u_out];
+
+      // Handling the case when join and v_out coincide
+      bool par_first = false;
+      if (join == v_out) {
+	for (u = join; u != u_in && u != v_in; u = thread[u]) ;
+	if (u == v_in) {
+	  par_first = true;
+	  while (thread[u] != u_out) u = thread[u];
+	  first = u;
+	}
+      }
+
+      // Finding the last successor of u_in (u) and the node after it
+      // (right) according to the thread index
+      for (u = u_in; depth[thread[u]] > depth[u_in]; u = thread[u]) ;
+      right = thread[u];
+      if (thread[v_in] == u_out) {
+	for (last = u; depth[last] > depth[u_out]; last = thread[last]) ;
+	if (last == u_out) last = thread[last];
+      }
+      else last = thread[v_in];
+
+      // Updating stem nodes
+      thread[v_in] = stem = u_in;
+      par_stem = v_in;
+      while (stem != u_out) {
+	thread[u] = new_stem = parent[stem];
+
+	// Finding the node just before the stem node (u) according to
+	// the original thread index
+	for (u = new_stem; thread[u] != stem; u = thread[u]) ;
+	thread[u] = right;
+
+	// Changing the parent node of stem and shifting stem and
+	// par_stem nodes
+	parent[stem] = par_stem;
+	par_stem = stem;
+	stem = new_stem;
+
+	// Finding the last successor of stem (u) and the node after it
+	// (right) according to the thread index
+	for (u = stem; depth[thread[u]] > depth[stem]; u = thread[u]) ;
+	right = thread[u];
+      }
+      parent[u_out] = par_stem;
+      thread[u] = last;
+
+      if (join == v_out && par_first) {
+	if (first != v_in) thread[first] = right;
+      } else {
+	for (u = v_out; thread[u] != u_out; u = thread[u]) ;
+	thread[u] = right;
+      }
+    }
+
+    /// \brief Updates pred_edge and forward node maps.
+    void updatePredEdge() {
+      Node u = u_out, v;
+      while (u != u_in) {
+	v = parent[u];
+	pred_edge[u] = pred_edge[v];
+	forward[u] = !forward[v];
+	u = v;
+      }
+      pred_edge[u_in] = in_edge;
+      forward[u_in] = (u_in == graph.source(in_edge));
+    }
+
+    /// \brief Updates depth and potential node maps.
+    void updateDepthPotential() {
+      depth[u_in] = depth[v_in] + 1;
+      potential[u_in] = forward[u_in] ?
+	potential[v_in] + cost[pred_edge[u_in]] :
+	potential[v_in] - cost[pred_edge[u_in]];
+
+      Node u = thread[u_in], v;
+      while (true) {
+	v = parent[u];
+	if (v == INVALID) break;
+	depth[u] = depth[v] + 1;
+	potential[u] = forward[u] ?
+	  potential[v] + cost[pred_edge[u]] :
+	  potential[v] - cost[pred_edge[u]];
+	if (depth[u] <= depth[v_in]) break;
+	u = thread[u];
+      }
+    }
+
+    /// \brief Executes the algorithm.
+    bool start() {
+      // Processing pivots
+#ifdef _DEBUG_ITER_
+      int iter_num = 0;
+#endif
+#if defined(FIRST_ELIGIBLE_PIVOT) || defined(EDGE_BLOCK_PIVOT)
+      EdgeIt next_edge(graph);
+      while (findEnteringEdge(next_edge))
+#else
+      while (findEnteringEdge())
+#endif
+      {
+	join = findJoinNode();
+	bool change = findLeavingEdge();
+	changeFlows(change);
+	if (change) {
+	  updateThreadParent();
+	  updatePredEdge();
+	  updateDepthPotential();
+	}
+#ifdef _DEBUG_ITER_
+	++iter_num;
+#endif
+      }
+
+#ifdef _DEBUG_ITER_
+      t_iter.stop();
+      std::cout << "Network Simplex algorithm finished. " << iter_num
+		<< " pivot iterations performed.";
+#endif
+
+      // Checking if the flow amount equals zero on all the
+      // artificial edges
+      for (InEdgeIt e(graph, root); e != INVALID; ++e)
+	if (flow[e] > 0) return false;
+      for (OutEdgeIt e(graph, root); e != INVALID; ++e)
+	if (flow[e] > 0) return false;
+
+      // Copying flow values to flow_result
+      if (lower) {
+	for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e)
+	  flow_result[e] = (*lower)[e] + flow[edge_ref[e]];
+      } else {
+	for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e)
+	  flow_result[e] = flow[edge_ref[e]];
+      }
+      // Copying potential values to potential_result
+      for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n)
+	potential_result[n] = potential[node_ref[n]];
+
+      return true;
+    }
+
+  }; //class NetworkSimplex
+
+  ///@}
+
+} //namespace lemon
+
+#endif //LEMON_NETWORK_SIMPLEX_H