lemon/network_simplex.h
author Peter Kovacs <kpeter@inf.elte.hu>
Wed, 25 Mar 2009 21:37:50 +0100
changeset 653 c7d160f73d52
parent 652 5232721b3f14
child 654 9ad8d2122b50
permissions -rw-r--r--
Support multiple run() calls in NetworkSimplex (#234)
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2009
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#ifndef LEMON_NETWORK_SIMPLEX_H
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#define LEMON_NETWORK_SIMPLEX_H
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/// \ingroup min_cost_flow
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///
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/// \file
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/// \brief Network Simplex algorithm for finding a minimum cost flow.
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#include <vector>
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#include <limits>
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#include <algorithm>
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#include <lemon/core.h>
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#include <lemon/math.h>
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namespace lemon {
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  /// \addtogroup min_cost_flow
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  /// @{
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  /// \brief Implementation of the primal Network Simplex algorithm
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  /// for finding a \ref min_cost_flow "minimum cost flow".
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  ///
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  /// \ref NetworkSimplex implements the primal Network Simplex algorithm
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  /// for finding a \ref min_cost_flow "minimum cost flow".
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  /// This algorithm is a specialized version of the linear programming
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  /// simplex method directly for the minimum cost flow problem.
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  /// It is one of the most efficient solution methods.
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  ///
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  /// In general this class is the fastest implementation available
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  /// in LEMON for the minimum cost flow problem.
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  ///
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  /// \tparam GR The digraph type the algorithm runs on.
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  /// \tparam V The value type used in the algorithm.
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  /// By default it is \c int.
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  ///
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  /// \warning The value type must be a signed integer type.
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  ///
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  /// \note %NetworkSimplex provides five different pivot rule
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  /// implementations. For more information see \ref PivotRule.
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  template <typename GR, typename V = int>
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  class NetworkSimplex
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  {
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  public:
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    /// The value type of the algorithm
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    typedef V Value;
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    /// The type of the flow map
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    typedef typename GR::template ArcMap<Value> FlowMap;
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    /// The type of the potential map
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    typedef typename GR::template NodeMap<Value> PotentialMap;
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  public:
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    /// \brief Enum type for selecting the pivot rule.
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    ///
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    /// Enum type for selecting the pivot rule for the \ref run()
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    /// function.
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    ///
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    /// \ref NetworkSimplex provides five different pivot rule
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    /// implementations that significantly affect the running time
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    /// of the algorithm.
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    /// By default \ref BLOCK_SEARCH "Block Search" is used, which
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    /// proved to be the most efficient and the most robust on various
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    /// test inputs according to our benchmark tests.
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    /// However another pivot rule can be selected using the \ref run()
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    /// function with the proper parameter.
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    enum PivotRule {
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      /// The First Eligible pivot rule.
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      /// The next eligible arc is selected in a wraparound fashion
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      /// in every iteration.
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      FIRST_ELIGIBLE,
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      /// The Best Eligible pivot rule.
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      /// The best eligible arc is selected in every iteration.
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      BEST_ELIGIBLE,
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      /// The Block Search pivot rule.
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      /// A specified number of arcs are examined in every iteration
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      /// in a wraparound fashion and the best eligible arc is selected
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      /// from this block.
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      BLOCK_SEARCH,
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      /// The Candidate List pivot rule.
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      /// In a major iteration a candidate list is built from eligible arcs
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      /// in a wraparound fashion and in the following minor iterations
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      /// the best eligible arc is selected from this list.
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      CANDIDATE_LIST,
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      /// The Altering Candidate List pivot rule.
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      /// It is a modified version of the Candidate List method.
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      /// It keeps only the several best eligible arcs from the former
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      /// candidate list and extends this list in every iteration.
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      ALTERING_LIST
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    };
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  private:
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    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
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    typedef typename GR::template ArcMap<Value> ValueArcMap;
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    typedef typename GR::template NodeMap<Value> ValueNodeMap;
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    typedef std::vector<Arc> ArcVector;
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    typedef std::vector<Node> NodeVector;
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    typedef std::vector<int> IntVector;
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    typedef std::vector<bool> BoolVector;
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    typedef std::vector<Value> ValueVector;
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    // State constants for arcs
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    enum ArcStateEnum {
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      STATE_UPPER = -1,
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      STATE_TREE  =  0,
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      STATE_LOWER =  1
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    };
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  private:
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    // Data related to the underlying digraph
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    const GR &_graph;
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    int _node_num;
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    int _arc_num;
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    // Parameters of the problem
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    ValueArcMap *_plower;
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    ValueArcMap *_pupper;
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    ValueArcMap *_pcost;
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    ValueNodeMap *_psupply;
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    bool _pstsup;
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    Node _psource, _ptarget;
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    Value _pstflow;
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    // Result maps
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    FlowMap *_flow_map;
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    PotentialMap *_potential_map;
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    bool _local_flow;
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    bool _local_potential;
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    // Data structures for storing the digraph
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    IntNodeMap _node_id;
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    ArcVector _arc_ref;
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    IntVector _source;
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    IntVector _target;
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    // Node and arc data
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    ValueVector _cap;
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    ValueVector _cost;
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    ValueVector _supply;
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    ValueVector _flow;
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    ValueVector _pi;
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    // Data for storing the spanning tree structure
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    IntVector _parent;
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    IntVector _pred;
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    IntVector _thread;
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    IntVector _rev_thread;
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    IntVector _succ_num;
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    IntVector _last_succ;
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    IntVector _dirty_revs;
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    BoolVector _forward;
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    IntVector _state;
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    int _root;
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    // Temporary data used in the current pivot iteration
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    int in_arc, join, u_in, v_in, u_out, v_out;
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    int first, second, right, last;
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    int stem, par_stem, new_stem;
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    Value delta;
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  private:
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    // Implementation of the First Eligible pivot rule
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    class FirstEligiblePivotRule
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    {
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    private:
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      // References to the NetworkSimplex class
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      const IntVector  &_source;
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      const IntVector  &_target;
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      const ValueVector &_cost;
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      const IntVector  &_state;
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      const ValueVector &_pi;
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      int &_in_arc;
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      int _arc_num;
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      // Pivot rule data
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      int _next_arc;
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    public:
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      // Constructor
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      FirstEligiblePivotRule(NetworkSimplex &ns) :
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        _source(ns._source), _target(ns._target),
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        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
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        _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0)
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      {}
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      // Find next entering arc
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      bool findEnteringArc() {
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        Value c;
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        for (int e = _next_arc; e < _arc_num; ++e) {
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          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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          if (c < 0) {
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            _in_arc = e;
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            _next_arc = e + 1;
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            return true;
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          }
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        }
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        for (int e = 0; e < _next_arc; ++e) {
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          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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          if (c < 0) {
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            _in_arc = e;
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            _next_arc = e + 1;
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            return true;
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          }
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        }
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        return false;
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      }
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    }; //class FirstEligiblePivotRule
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    // Implementation of the Best Eligible pivot rule
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    class BestEligiblePivotRule
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    {
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    private:
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      // References to the NetworkSimplex class
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      const IntVector  &_source;
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      const IntVector  &_target;
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      const ValueVector &_cost;
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      const IntVector  &_state;
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      const ValueVector &_pi;
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      int &_in_arc;
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      int _arc_num;
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    public:
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      // Constructor
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      BestEligiblePivotRule(NetworkSimplex &ns) :
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        _source(ns._source), _target(ns._target),
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        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
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        _in_arc(ns.in_arc), _arc_num(ns._arc_num)
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      {}
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      // Find next entering arc
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      bool findEnteringArc() {
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        Value c, min = 0;
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        for (int e = 0; e < _arc_num; ++e) {
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          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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          if (c < min) {
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            min = c;
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            _in_arc = e;
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          }
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        }
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        return min < 0;
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      }
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    }; //class BestEligiblePivotRule
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    // Implementation of the Block Search pivot rule
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    class BlockSearchPivotRule
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    {
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    private:
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      // References to the NetworkSimplex class
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      const IntVector  &_source;
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      const IntVector  &_target;
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      const ValueVector &_cost;
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      const IntVector  &_state;
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      const ValueVector &_pi;
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      int &_in_arc;
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      int _arc_num;
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      // Pivot rule data
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      int _block_size;
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      int _next_arc;
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    public:
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      // Constructor
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      BlockSearchPivotRule(NetworkSimplex &ns) :
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        _source(ns._source), _target(ns._target),
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        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
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        _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0)
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      {
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        // The main parameters of the pivot rule
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        const double BLOCK_SIZE_FACTOR = 2.0;
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        const int MIN_BLOCK_SIZE = 10;
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        _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)),
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                                MIN_BLOCK_SIZE );
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      }
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      // Find next entering arc
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      bool findEnteringArc() {
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        Value c, min = 0;
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        int cnt = _block_size;
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        int e, min_arc = _next_arc;
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        for (e = _next_arc; e < _arc_num; ++e) {
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          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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          if (c < min) {
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            min = c;
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            min_arc = e;
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          }
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          if (--cnt == 0) {
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            if (min < 0) break;
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            cnt = _block_size;
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          }
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        }
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        if (min == 0 || cnt > 0) {
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          for (e = 0; e < _next_arc; ++e) {
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            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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            if (c < min) {
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              min = c;
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              min_arc = e;
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            }
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            if (--cnt == 0) {
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              if (min < 0) break;
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              cnt = _block_size;
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            }
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          }
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        }
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        if (min >= 0) return false;
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        _in_arc = min_arc;
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        _next_arc = e;
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        return true;
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      }
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    }; //class BlockSearchPivotRule
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    // Implementation of the Candidate List pivot rule
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    class CandidateListPivotRule
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    {
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    private:
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      // References to the NetworkSimplex class
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      const IntVector  &_source;
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      const IntVector  &_target;
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      const ValueVector &_cost;
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      const IntVector  &_state;
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      const ValueVector &_pi;
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      int &_in_arc;
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      int _arc_num;
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      // Pivot rule data
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      IntVector _candidates;
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      int _list_length, _minor_limit;
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      int _curr_length, _minor_count;
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      int _next_arc;
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    public:
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      /// Constructor
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      CandidateListPivotRule(NetworkSimplex &ns) :
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        _source(ns._source), _target(ns._target),
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        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
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        _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0)
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      {
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        // The main parameters of the pivot rule
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        const double LIST_LENGTH_FACTOR = 1.0;
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        const int MIN_LIST_LENGTH = 10;
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        const double MINOR_LIMIT_FACTOR = 0.1;
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        const int MIN_MINOR_LIMIT = 3;
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        _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_arc_num)),
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                                 MIN_LIST_LENGTH );
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        _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
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                                 MIN_MINOR_LIMIT );
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        _curr_length = _minor_count = 0;
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        _candidates.resize(_list_length);
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      }
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      /// Find next entering arc
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      bool findEnteringArc() {
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        Value min, c;
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        int e, min_arc = _next_arc;
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        if (_curr_length > 0 && _minor_count < _minor_limit) {
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          // Minor iteration: select the best eligible arc from the
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          // current candidate list
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          ++_minor_count;
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          min = 0;
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          for (int i = 0; i < _curr_length; ++i) {
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            e = _candidates[i];
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            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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            if (c < min) {
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              min = c;
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              min_arc = e;
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            }
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            if (c >= 0) {
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   412
              _candidates[i--] = _candidates[--_curr_length];
kpeter@648
   413
            }
kpeter@648
   414
          }
kpeter@648
   415
          if (min < 0) {
kpeter@648
   416
            _in_arc = min_arc;
kpeter@648
   417
            return true;
kpeter@648
   418
          }
kpeter@648
   419
        }
kpeter@648
   420
kpeter@648
   421
        // Major iteration: build a new candidate list
kpeter@648
   422
        min = 0;
kpeter@648
   423
        _curr_length = 0;
kpeter@648
   424
        for (e = _next_arc; e < _arc_num; ++e) {
kpeter@648
   425
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   426
          if (c < 0) {
kpeter@648
   427
            _candidates[_curr_length++] = e;
kpeter@648
   428
            if (c < min) {
kpeter@648
   429
              min = c;
kpeter@648
   430
              min_arc = e;
kpeter@648
   431
            }
kpeter@648
   432
            if (_curr_length == _list_length) break;
kpeter@648
   433
          }
kpeter@648
   434
        }
kpeter@648
   435
        if (_curr_length < _list_length) {
kpeter@648
   436
          for (e = 0; e < _next_arc; ++e) {
kpeter@648
   437
            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   438
            if (c < 0) {
kpeter@648
   439
              _candidates[_curr_length++] = e;
kpeter@648
   440
              if (c < min) {
kpeter@648
   441
                min = c;
kpeter@648
   442
                min_arc = e;
kpeter@648
   443
              }
kpeter@648
   444
              if (_curr_length == _list_length) break;
kpeter@648
   445
            }
kpeter@648
   446
          }
kpeter@648
   447
        }
kpeter@648
   448
        if (_curr_length == 0) return false;
kpeter@648
   449
        _minor_count = 1;
kpeter@648
   450
        _in_arc = min_arc;
kpeter@648
   451
        _next_arc = e;
kpeter@648
   452
        return true;
kpeter@648
   453
      }
kpeter@648
   454
kpeter@648
   455
    }; //class CandidateListPivotRule
kpeter@648
   456
kpeter@648
   457
kpeter@652
   458
    // Implementation of the Altering Candidate List pivot rule
kpeter@648
   459
    class AlteringListPivotRule
kpeter@648
   460
    {
kpeter@648
   461
    private:
kpeter@648
   462
kpeter@648
   463
      // References to the NetworkSimplex class
kpeter@648
   464
      const IntVector  &_source;
kpeter@648
   465
      const IntVector  &_target;
kpeter@652
   466
      const ValueVector &_cost;
kpeter@648
   467
      const IntVector  &_state;
kpeter@652
   468
      const ValueVector &_pi;
kpeter@648
   469
      int &_in_arc;
kpeter@648
   470
      int _arc_num;
kpeter@648
   471
kpeter@648
   472
      // Pivot rule data
kpeter@648
   473
      int _block_size, _head_length, _curr_length;
kpeter@648
   474
      int _next_arc;
kpeter@648
   475
      IntVector _candidates;
kpeter@652
   476
      ValueVector _cand_cost;
kpeter@648
   477
kpeter@648
   478
      // Functor class to compare arcs during sort of the candidate list
kpeter@648
   479
      class SortFunc
kpeter@648
   480
      {
kpeter@648
   481
      private:
kpeter@652
   482
        const ValueVector &_map;
kpeter@648
   483
      public:
kpeter@652
   484
        SortFunc(const ValueVector &map) : _map(map) {}
kpeter@648
   485
        bool operator()(int left, int right) {
kpeter@648
   486
          return _map[left] > _map[right];
kpeter@648
   487
        }
kpeter@648
   488
      };
kpeter@648
   489
kpeter@648
   490
      SortFunc _sort_func;
kpeter@648
   491
kpeter@648
   492
    public:
kpeter@648
   493
kpeter@652
   494
      // Constructor
kpeter@648
   495
      AlteringListPivotRule(NetworkSimplex &ns) :
kpeter@650
   496
        _source(ns._source), _target(ns._target),
kpeter@648
   497
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@650
   498
        _in_arc(ns.in_arc), _arc_num(ns._arc_num),
kpeter@648
   499
        _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost)
kpeter@648
   500
      {
kpeter@648
   501
        // The main parameters of the pivot rule
kpeter@648
   502
        const double BLOCK_SIZE_FACTOR = 1.5;
kpeter@648
   503
        const int MIN_BLOCK_SIZE = 10;
kpeter@648
   504
        const double HEAD_LENGTH_FACTOR = 0.1;
kpeter@648
   505
        const int MIN_HEAD_LENGTH = 3;
kpeter@648
   506
kpeter@648
   507
        _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)),
kpeter@648
   508
                                MIN_BLOCK_SIZE );
kpeter@648
   509
        _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),
kpeter@648
   510
                                 MIN_HEAD_LENGTH );
kpeter@648
   511
        _candidates.resize(_head_length + _block_size);
kpeter@648
   512
        _curr_length = 0;
kpeter@648
   513
      }
kpeter@648
   514
kpeter@652
   515
      // Find next entering arc
kpeter@648
   516
      bool findEnteringArc() {
kpeter@648
   517
        // Check the current candidate list
kpeter@648
   518
        int e;
kpeter@648
   519
        for (int i = 0; i < _curr_length; ++i) {
kpeter@648
   520
          e = _candidates[i];
kpeter@648
   521
          _cand_cost[e] = _state[e] *
kpeter@648
   522
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   523
          if (_cand_cost[e] >= 0) {
kpeter@648
   524
            _candidates[i--] = _candidates[--_curr_length];
kpeter@648
   525
          }
kpeter@648
   526
        }
kpeter@648
   527
kpeter@648
   528
        // Extend the list
kpeter@648
   529
        int cnt = _block_size;
kpeter@650
   530
        int last_arc = 0;
kpeter@648
   531
        int limit = _head_length;
kpeter@648
   532
kpeter@648
   533
        for (int e = _next_arc; e < _arc_num; ++e) {
kpeter@648
   534
          _cand_cost[e] = _state[e] *
kpeter@648
   535
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   536
          if (_cand_cost[e] < 0) {
kpeter@648
   537
            _candidates[_curr_length++] = e;
kpeter@650
   538
            last_arc = e;
kpeter@648
   539
          }
kpeter@648
   540
          if (--cnt == 0) {
kpeter@648
   541
            if (_curr_length > limit) break;
kpeter@648
   542
            limit = 0;
kpeter@648
   543
            cnt = _block_size;
kpeter@648
   544
          }
kpeter@648
   545
        }
kpeter@648
   546
        if (_curr_length <= limit) {
kpeter@648
   547
          for (int e = 0; e < _next_arc; ++e) {
kpeter@648
   548
            _cand_cost[e] = _state[e] *
kpeter@648
   549
              (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   550
            if (_cand_cost[e] < 0) {
kpeter@648
   551
              _candidates[_curr_length++] = e;
kpeter@650
   552
              last_arc = e;
kpeter@648
   553
            }
kpeter@648
   554
            if (--cnt == 0) {
kpeter@648
   555
              if (_curr_length > limit) break;
kpeter@648
   556
              limit = 0;
kpeter@648
   557
              cnt = _block_size;
kpeter@648
   558
            }
kpeter@648
   559
          }
kpeter@648
   560
        }
kpeter@648
   561
        if (_curr_length == 0) return false;
kpeter@650
   562
        _next_arc = last_arc + 1;
kpeter@648
   563
kpeter@648
   564
        // Make heap of the candidate list (approximating a partial sort)
kpeter@648
   565
        make_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@648
   566
                   _sort_func );
kpeter@648
   567
kpeter@648
   568
        // Pop the first element of the heap
kpeter@648
   569
        _in_arc = _candidates[0];
kpeter@648
   570
        pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@648
   571
                  _sort_func );
kpeter@648
   572
        _curr_length = std::min(_head_length, _curr_length - 1);
kpeter@648
   573
        return true;
kpeter@648
   574
      }
kpeter@648
   575
kpeter@648
   576
    }; //class AlteringListPivotRule
kpeter@648
   577
kpeter@648
   578
  public:
kpeter@648
   579
kpeter@652
   580
    /// \brief Constructor.
kpeter@648
   581
    ///
kpeter@652
   582
    /// Constructor.
kpeter@648
   583
    ///
kpeter@650
   584
    /// \param graph The digraph the algorithm runs on.
kpeter@652
   585
    NetworkSimplex(const GR& graph) :
kpeter@652
   586
      _graph(graph),
kpeter@652
   587
      _plower(NULL), _pupper(NULL), _pcost(NULL),
kpeter@652
   588
      _psupply(NULL), _pstsup(false),
kpeter@650
   589
      _flow_map(NULL), _potential_map(NULL),
kpeter@648
   590
      _local_flow(false), _local_potential(false),
kpeter@650
   591
      _node_id(graph)
kpeter@652
   592
    {
kpeter@652
   593
      LEMON_ASSERT(std::numeric_limits<Value>::is_integer &&
kpeter@652
   594
                   std::numeric_limits<Value>::is_signed,
kpeter@652
   595
        "The value type of NetworkSimplex must be a signed integer");
kpeter@652
   596
    }
kpeter@648
   597
kpeter@648
   598
    /// Destructor.
kpeter@648
   599
    ~NetworkSimplex() {
kpeter@650
   600
      if (_local_flow) delete _flow_map;
kpeter@650
   601
      if (_local_potential) delete _potential_map;
kpeter@648
   602
    }
kpeter@648
   603
kpeter@652
   604
    /// \brief Set the lower bounds on the arcs.
kpeter@652
   605
    ///
kpeter@652
   606
    /// This function sets the lower bounds on the arcs.
kpeter@652
   607
    /// If neither this function nor \ref boundMaps() is used before
kpeter@652
   608
    /// calling \ref run(), the lower bounds will be set to zero
kpeter@652
   609
    /// on all arcs.
kpeter@652
   610
    ///
kpeter@652
   611
    /// \param map An arc map storing the lower bounds.
kpeter@652
   612
    /// Its \c Value type must be convertible to the \c Value type
kpeter@652
   613
    /// of the algorithm.
kpeter@652
   614
    ///
kpeter@652
   615
    /// \return <tt>(*this)</tt>
kpeter@652
   616
    template <typename LOWER>
kpeter@652
   617
    NetworkSimplex& lowerMap(const LOWER& map) {
kpeter@652
   618
      delete _plower;
kpeter@652
   619
      _plower = new ValueArcMap(_graph);
kpeter@652
   620
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@652
   621
        (*_plower)[a] = map[a];
kpeter@652
   622
      }
kpeter@652
   623
      return *this;
kpeter@652
   624
    }
kpeter@652
   625
kpeter@652
   626
    /// \brief Set the upper bounds (capacities) on the arcs.
kpeter@652
   627
    ///
kpeter@652
   628
    /// This function sets the upper bounds (capacities) on the arcs.
kpeter@652
   629
    /// If none of the functions \ref upperMap(), \ref capacityMap()
kpeter@652
   630
    /// and \ref boundMaps() is used before calling \ref run(),
kpeter@652
   631
    /// the upper bounds (capacities) will be set to
kpeter@652
   632
    /// \c std::numeric_limits<Value>::max() on all arcs.
kpeter@652
   633
    ///
kpeter@652
   634
    /// \param map An arc map storing the upper bounds.
kpeter@652
   635
    /// Its \c Value type must be convertible to the \c Value type
kpeter@652
   636
    /// of the algorithm.
kpeter@652
   637
    ///
kpeter@652
   638
    /// \return <tt>(*this)</tt>
kpeter@652
   639
    template<typename UPPER>
kpeter@652
   640
    NetworkSimplex& upperMap(const UPPER& map) {
kpeter@652
   641
      delete _pupper;
kpeter@652
   642
      _pupper = new ValueArcMap(_graph);
kpeter@652
   643
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@652
   644
        (*_pupper)[a] = map[a];
kpeter@652
   645
      }
kpeter@652
   646
      return *this;
kpeter@652
   647
    }
kpeter@652
   648
kpeter@652
   649
    /// \brief Set the upper bounds (capacities) on the arcs.
kpeter@652
   650
    ///
kpeter@652
   651
    /// This function sets the upper bounds (capacities) on the arcs.
kpeter@652
   652
    /// It is just an alias for \ref upperMap().
kpeter@652
   653
    ///
kpeter@652
   654
    /// \return <tt>(*this)</tt>
kpeter@652
   655
    template<typename CAP>
kpeter@652
   656
    NetworkSimplex& capacityMap(const CAP& map) {
kpeter@652
   657
      return upperMap(map);
kpeter@652
   658
    }
kpeter@652
   659
kpeter@652
   660
    /// \brief Set the lower and upper bounds on the arcs.
kpeter@652
   661
    ///
kpeter@652
   662
    /// This function sets the lower and upper bounds on the arcs.
kpeter@652
   663
    /// If neither this function nor \ref lowerMap() is used before
kpeter@652
   664
    /// calling \ref run(), the lower bounds will be set to zero
kpeter@652
   665
    /// on all arcs.
kpeter@652
   666
    /// If none of the functions \ref upperMap(), \ref capacityMap()
kpeter@652
   667
    /// and \ref boundMaps() is used before calling \ref run(),
kpeter@652
   668
    /// the upper bounds (capacities) will be set to
kpeter@652
   669
    /// \c std::numeric_limits<Value>::max() on all arcs.
kpeter@652
   670
    ///
kpeter@652
   671
    /// \param lower An arc map storing the lower bounds.
kpeter@652
   672
    /// \param upper An arc map storing the upper bounds.
kpeter@652
   673
    ///
kpeter@652
   674
    /// The \c Value type of the maps must be convertible to the
kpeter@652
   675
    /// \c Value type of the algorithm.
kpeter@652
   676
    ///
kpeter@652
   677
    /// \note This function is just a shortcut of calling \ref lowerMap()
kpeter@652
   678
    /// and \ref upperMap() separately.
kpeter@652
   679
    ///
kpeter@652
   680
    /// \return <tt>(*this)</tt>
kpeter@652
   681
    template <typename LOWER, typename UPPER>
kpeter@652
   682
    NetworkSimplex& boundMaps(const LOWER& lower, const UPPER& upper) {
kpeter@652
   683
      return lowerMap(lower).upperMap(upper);
kpeter@652
   684
    }
kpeter@652
   685
kpeter@652
   686
    /// \brief Set the costs of the arcs.
kpeter@652
   687
    ///
kpeter@652
   688
    /// This function sets the costs of the arcs.
kpeter@652
   689
    /// If it is not used before calling \ref run(), the costs
kpeter@652
   690
    /// will be set to \c 1 on all arcs.
kpeter@652
   691
    ///
kpeter@652
   692
    /// \param map An arc map storing the costs.
kpeter@652
   693
    /// Its \c Value type must be convertible to the \c Value type
kpeter@652
   694
    /// of the algorithm.
kpeter@652
   695
    ///
kpeter@652
   696
    /// \return <tt>(*this)</tt>
kpeter@652
   697
    template<typename COST>
kpeter@652
   698
    NetworkSimplex& costMap(const COST& map) {
kpeter@652
   699
      delete _pcost;
kpeter@652
   700
      _pcost = new ValueArcMap(_graph);
kpeter@652
   701
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@652
   702
        (*_pcost)[a] = map[a];
kpeter@652
   703
      }
kpeter@652
   704
      return *this;
kpeter@652
   705
    }
kpeter@652
   706
kpeter@652
   707
    /// \brief Set the supply values of the nodes.
kpeter@652
   708
    ///
kpeter@652
   709
    /// This function sets the supply values of the nodes.
kpeter@652
   710
    /// If neither this function nor \ref stSupply() is used before
kpeter@652
   711
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@652
   712
    /// (It makes sense only if non-zero lower bounds are given.)
kpeter@652
   713
    ///
kpeter@652
   714
    /// \param map A node map storing the supply values.
kpeter@652
   715
    /// Its \c Value type must be convertible to the \c Value type
kpeter@652
   716
    /// of the algorithm.
kpeter@652
   717
    ///
kpeter@652
   718
    /// \return <tt>(*this)</tt>
kpeter@652
   719
    template<typename SUP>
kpeter@652
   720
    NetworkSimplex& supplyMap(const SUP& map) {
kpeter@652
   721
      delete _psupply;
kpeter@652
   722
      _pstsup = false;
kpeter@652
   723
      _psupply = new ValueNodeMap(_graph);
kpeter@652
   724
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@652
   725
        (*_psupply)[n] = map[n];
kpeter@652
   726
      }
kpeter@652
   727
      return *this;
kpeter@652
   728
    }
kpeter@652
   729
kpeter@652
   730
    /// \brief Set single source and target nodes and a supply value.
kpeter@652
   731
    ///
kpeter@652
   732
    /// This function sets a single source node and a single target node
kpeter@652
   733
    /// and the required flow value.
kpeter@652
   734
    /// If neither this function nor \ref supplyMap() is used before
kpeter@652
   735
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@652
   736
    /// (It makes sense only if non-zero lower bounds are given.)
kpeter@652
   737
    ///
kpeter@652
   738
    /// \param s The source node.
kpeter@652
   739
    /// \param t The target node.
kpeter@652
   740
    /// \param k The required amount of flow from node \c s to node \c t
kpeter@652
   741
    /// (i.e. the supply of \c s and the demand of \c t).
kpeter@652
   742
    ///
kpeter@652
   743
    /// \return <tt>(*this)</tt>
kpeter@652
   744
    NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) {
kpeter@652
   745
      delete _psupply;
kpeter@652
   746
      _psupply = NULL;
kpeter@652
   747
      _pstsup = true;
kpeter@652
   748
      _psource = s;
kpeter@652
   749
      _ptarget = t;
kpeter@652
   750
      _pstflow = k;
kpeter@652
   751
      return *this;
kpeter@652
   752
    }
kpeter@652
   753
kpeter@648
   754
    /// \brief Set the flow map.
kpeter@648
   755
    ///
kpeter@648
   756
    /// This function sets the flow map.
kpeter@652
   757
    /// If it is not used before calling \ref run(), an instance will
kpeter@652
   758
    /// be allocated automatically. The destructor deallocates this
kpeter@652
   759
    /// automatically allocated map, of course.
kpeter@648
   760
    ///
kpeter@648
   761
    /// \return <tt>(*this)</tt>
kpeter@652
   762
    NetworkSimplex& flowMap(FlowMap& map) {
kpeter@648
   763
      if (_local_flow) {
kpeter@650
   764
        delete _flow_map;
kpeter@648
   765
        _local_flow = false;
kpeter@648
   766
      }
kpeter@650
   767
      _flow_map = &map;
kpeter@648
   768
      return *this;
kpeter@648
   769
    }
kpeter@648
   770
kpeter@648
   771
    /// \brief Set the potential map.
kpeter@648
   772
    ///
kpeter@652
   773
    /// This function sets the potential map, which is used for storing
kpeter@652
   774
    /// the dual solution.
kpeter@652
   775
    /// If it is not used before calling \ref run(), an instance will
kpeter@652
   776
    /// be allocated automatically. The destructor deallocates this
kpeter@652
   777
    /// automatically allocated map, of course.
kpeter@648
   778
    ///
kpeter@648
   779
    /// \return <tt>(*this)</tt>
kpeter@652
   780
    NetworkSimplex& potentialMap(PotentialMap& map) {
kpeter@648
   781
      if (_local_potential) {
kpeter@650
   782
        delete _potential_map;
kpeter@648
   783
        _local_potential = false;
kpeter@648
   784
      }
kpeter@650
   785
      _potential_map = &map;
kpeter@648
   786
      return *this;
kpeter@648
   787
    }
kpeter@648
   788
kpeter@652
   789
    /// \name Execution Control
kpeter@652
   790
    /// The algorithm can be executed using \ref run().
kpeter@652
   791
kpeter@648
   792
    /// @{
kpeter@648
   793
kpeter@648
   794
    /// \brief Run the algorithm.
kpeter@648
   795
    ///
kpeter@648
   796
    /// This function runs the algorithm.
kpeter@652
   797
    /// The paramters can be specified using \ref lowerMap(),
kpeter@653
   798
    /// \ref upperMap(), \ref capacityMap(), \ref boundMaps(),
kpeter@652
   799
    /// \ref costMap(), \ref supplyMap() and \ref stSupply()
kpeter@652
   800
    /// functions. For example,
kpeter@652
   801
    /// \code
kpeter@652
   802
    ///   NetworkSimplex<ListDigraph> ns(graph);
kpeter@652
   803
    ///   ns.boundMaps(lower, upper).costMap(cost)
kpeter@652
   804
    ///     .supplyMap(sup).run();
kpeter@652
   805
    /// \endcode
kpeter@648
   806
    ///
kpeter@653
   807
    /// This function can be called more than once. All the parameters
kpeter@653
   808
    /// that have been given are kept for the next call, unless
kpeter@653
   809
    /// \ref reset() is called, thus only the modified parameters
kpeter@653
   810
    /// have to be set again. See \ref reset() for examples.
kpeter@653
   811
    ///
kpeter@652
   812
    /// \param pivot_rule The pivot rule that will be used during the
kpeter@652
   813
    /// algorithm. For more information see \ref PivotRule.
kpeter@648
   814
    ///
kpeter@648
   815
    /// \return \c true if a feasible flow can be found.
kpeter@652
   816
    bool run(PivotRule pivot_rule = BLOCK_SEARCH) {
kpeter@648
   817
      return init() && start(pivot_rule);
kpeter@648
   818
    }
kpeter@648
   819
kpeter@653
   820
    /// \brief Reset all the parameters that have been given before.
kpeter@653
   821
    ///
kpeter@653
   822
    /// This function resets all the paramaters that have been given
kpeter@653
   823
    /// using \ref lowerMap(), \ref upperMap(), \ref capacityMap(),
kpeter@653
   824
    /// \ref boundMaps(), \ref costMap(), \ref supplyMap() and
kpeter@653
   825
    /// \ref stSupply() functions before.
kpeter@653
   826
    ///
kpeter@653
   827
    /// It is useful for multiple run() calls. If this function is not
kpeter@653
   828
    /// used, all the parameters given before are kept for the next
kpeter@653
   829
    /// \ref run() call.
kpeter@653
   830
    ///
kpeter@653
   831
    /// For example,
kpeter@653
   832
    /// \code
kpeter@653
   833
    ///   NetworkSimplex<ListDigraph> ns(graph);
kpeter@653
   834
    ///
kpeter@653
   835
    ///   // First run
kpeter@653
   836
    ///   ns.lowerMap(lower).capacityMap(cap).costMap(cost)
kpeter@653
   837
    ///     .supplyMap(sup).run();
kpeter@653
   838
    ///
kpeter@653
   839
    ///   // Run again with modified cost map (reset() is not called,
kpeter@653
   840
    ///   // so only the cost map have to be set again)
kpeter@653
   841
    ///   cost[e] += 100;
kpeter@653
   842
    ///   ns.costMap(cost).run();
kpeter@653
   843
    ///
kpeter@653
   844
    ///   // Run again from scratch using reset()
kpeter@653
   845
    ///   // (the lower bounds will be set to zero on all arcs)
kpeter@653
   846
    ///   ns.reset();
kpeter@653
   847
    ///   ns.capacityMap(cap).costMap(cost)
kpeter@653
   848
    ///     .supplyMap(sup).run();
kpeter@653
   849
    /// \endcode
kpeter@653
   850
    ///
kpeter@653
   851
    /// \return <tt>(*this)</tt>
kpeter@653
   852
    NetworkSimplex& reset() {
kpeter@653
   853
      delete _plower;
kpeter@653
   854
      delete _pupper;
kpeter@653
   855
      delete _pcost;
kpeter@653
   856
      delete _psupply;
kpeter@653
   857
      _plower = NULL;
kpeter@653
   858
      _pupper = NULL;
kpeter@653
   859
      _pcost = NULL;
kpeter@653
   860
      _psupply = NULL;
kpeter@653
   861
      _pstsup = false;
kpeter@653
   862
      return *this;
kpeter@653
   863
    }
kpeter@653
   864
kpeter@648
   865
    /// @}
kpeter@648
   866
kpeter@648
   867
    /// \name Query Functions
kpeter@648
   868
    /// The results of the algorithm can be obtained using these
kpeter@648
   869
    /// functions.\n
kpeter@652
   870
    /// The \ref run() function must be called before using them.
kpeter@652
   871
kpeter@648
   872
    /// @{
kpeter@648
   873
kpeter@652
   874
    /// \brief Return the total cost of the found flow.
kpeter@652
   875
    ///
kpeter@652
   876
    /// This function returns the total cost of the found flow.
kpeter@652
   877
    /// The complexity of the function is \f$ O(e) \f$.
kpeter@652
   878
    ///
kpeter@652
   879
    /// \note The return type of the function can be specified as a
kpeter@652
   880
    /// template parameter. For example,
kpeter@652
   881
    /// \code
kpeter@652
   882
    ///   ns.totalCost<double>();
kpeter@652
   883
    /// \endcode
kpeter@652
   884
    /// It is useful if the total cost cannot be stored in the \c Value
kpeter@652
   885
    /// type of the algorithm, which is the default return type of the
kpeter@652
   886
    /// function.
kpeter@652
   887
    ///
kpeter@652
   888
    /// \pre \ref run() must be called before using this function.
kpeter@652
   889
    template <typename Num>
kpeter@652
   890
    Num totalCost() const {
kpeter@652
   891
      Num c = 0;
kpeter@652
   892
      if (_pcost) {
kpeter@652
   893
        for (ArcIt e(_graph); e != INVALID; ++e)
kpeter@652
   894
          c += (*_flow_map)[e] * (*_pcost)[e];
kpeter@652
   895
      } else {
kpeter@652
   896
        for (ArcIt e(_graph); e != INVALID; ++e)
kpeter@652
   897
          c += (*_flow_map)[e];
kpeter@652
   898
      }
kpeter@652
   899
      return c;
kpeter@652
   900
    }
kpeter@652
   901
kpeter@652
   902
#ifndef DOXYGEN
kpeter@652
   903
    Value totalCost() const {
kpeter@652
   904
      return totalCost<Value>();
kpeter@652
   905
    }
kpeter@652
   906
#endif
kpeter@652
   907
kpeter@652
   908
    /// \brief Return the flow on the given arc.
kpeter@652
   909
    ///
kpeter@652
   910
    /// This function returns the flow on the given arc.
kpeter@652
   911
    ///
kpeter@652
   912
    /// \pre \ref run() must be called before using this function.
kpeter@652
   913
    Value flow(const Arc& a) const {
kpeter@652
   914
      return (*_flow_map)[a];
kpeter@652
   915
    }
kpeter@652
   916
kpeter@648
   917
    /// \brief Return a const reference to the flow map.
kpeter@648
   918
    ///
kpeter@648
   919
    /// This function returns a const reference to an arc map storing
kpeter@648
   920
    /// the found flow.
kpeter@648
   921
    ///
kpeter@648
   922
    /// \pre \ref run() must be called before using this function.
kpeter@648
   923
    const FlowMap& flowMap() const {
kpeter@650
   924
      return *_flow_map;
kpeter@648
   925
    }
kpeter@648
   926
kpeter@652
   927
    /// \brief Return the potential (dual value) of the given node.
kpeter@652
   928
    ///
kpeter@652
   929
    /// This function returns the potential (dual value) of the
kpeter@652
   930
    /// given node.
kpeter@652
   931
    ///
kpeter@652
   932
    /// \pre \ref run() must be called before using this function.
kpeter@652
   933
    Value potential(const Node& n) const {
kpeter@652
   934
      return (*_potential_map)[n];
kpeter@652
   935
    }
kpeter@652
   936
kpeter@648
   937
    /// \brief Return a const reference to the potential map
kpeter@648
   938
    /// (the dual solution).
kpeter@648
   939
    ///
kpeter@648
   940
    /// This function returns a const reference to a node map storing
kpeter@652
   941
    /// the found potentials, which form the dual solution of the
kpeter@652
   942
    /// \ref min_cost_flow "minimum cost flow" problem.
kpeter@648
   943
    ///
kpeter@648
   944
    /// \pre \ref run() must be called before using this function.
kpeter@648
   945
    const PotentialMap& potentialMap() const {
kpeter@650
   946
      return *_potential_map;
kpeter@648
   947
    }
kpeter@648
   948
kpeter@648
   949
    /// @}
kpeter@648
   950
kpeter@648
   951
  private:
kpeter@648
   952
kpeter@648
   953
    // Initialize internal data structures
kpeter@648
   954
    bool init() {
kpeter@648
   955
      // Initialize result maps
kpeter@650
   956
      if (!_flow_map) {
kpeter@650
   957
        _flow_map = new FlowMap(_graph);
kpeter@648
   958
        _local_flow = true;
kpeter@648
   959
      }
kpeter@650
   960
      if (!_potential_map) {
kpeter@650
   961
        _potential_map = new PotentialMap(_graph);
kpeter@648
   962
        _local_potential = true;
kpeter@648
   963
      }
kpeter@648
   964
kpeter@648
   965
      // Initialize vectors
kpeter@650
   966
      _node_num = countNodes(_graph);
kpeter@650
   967
      _arc_num = countArcs(_graph);
kpeter@648
   968
      int all_node_num = _node_num + 1;
kpeter@650
   969
      int all_arc_num = _arc_num + _node_num;
kpeter@652
   970
      if (_node_num == 0) return false;
kpeter@648
   971
kpeter@650
   972
      _arc_ref.resize(_arc_num);
kpeter@650
   973
      _source.resize(all_arc_num);
kpeter@650
   974
      _target.resize(all_arc_num);
kpeter@648
   975
kpeter@650
   976
      _cap.resize(all_arc_num);
kpeter@650
   977
      _cost.resize(all_arc_num);
kpeter@648
   978
      _supply.resize(all_node_num);
kpeter@653
   979
      _flow.resize(all_arc_num);
kpeter@653
   980
      _pi.resize(all_node_num);
kpeter@648
   981
kpeter@648
   982
      _parent.resize(all_node_num);
kpeter@648
   983
      _pred.resize(all_node_num);
kpeter@650
   984
      _forward.resize(all_node_num);
kpeter@648
   985
      _thread.resize(all_node_num);
kpeter@651
   986
      _rev_thread.resize(all_node_num);
kpeter@651
   987
      _succ_num.resize(all_node_num);
kpeter@651
   988
      _last_succ.resize(all_node_num);
kpeter@653
   989
      _state.resize(all_arc_num);
kpeter@648
   990
kpeter@648
   991
      // Initialize node related data
kpeter@648
   992
      bool valid_supply = true;
kpeter@652
   993
      if (!_pstsup && !_psupply) {
kpeter@652
   994
        _pstsup = true;
kpeter@652
   995
        _psource = _ptarget = NodeIt(_graph);
kpeter@652
   996
        _pstflow = 0;
kpeter@652
   997
      }
kpeter@652
   998
      if (_psupply) {
kpeter@652
   999
        Value sum = 0;
kpeter@648
  1000
        int i = 0;
kpeter@650
  1001
        for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@648
  1002
          _node_id[n] = i;
kpeter@652
  1003
          _supply[i] = (*_psupply)[n];
kpeter@648
  1004
          sum += _supply[i];
kpeter@648
  1005
        }
kpeter@648
  1006
        valid_supply = (sum == 0);
kpeter@648
  1007
      } else {
kpeter@648
  1008
        int i = 0;
kpeter@650
  1009
        for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@648
  1010
          _node_id[n] = i;
kpeter@648
  1011
          _supply[i] = 0;
kpeter@648
  1012
        }
kpeter@652
  1013
        _supply[_node_id[_psource]] =  _pstflow;
kpeter@652
  1014
        _supply[_node_id[_ptarget]]   = -_pstflow;
kpeter@648
  1015
      }
kpeter@648
  1016
      if (!valid_supply) return false;
kpeter@648
  1017
kpeter@648
  1018
      // Set data for the artificial root node
kpeter@648
  1019
      _root = _node_num;
kpeter@648
  1020
      _parent[_root] = -1;
kpeter@648
  1021
      _pred[_root] = -1;
kpeter@648
  1022
      _thread[_root] = 0;
kpeter@651
  1023
      _rev_thread[0] = _root;
kpeter@651
  1024
      _succ_num[_root] = all_node_num;
kpeter@651
  1025
      _last_succ[_root] = _root - 1;
kpeter@648
  1026
      _supply[_root] = 0;
kpeter@648
  1027
      _pi[_root] = 0;
kpeter@648
  1028
kpeter@648
  1029
      // Store the arcs in a mixed order
kpeter@648
  1030
      int k = std::max(int(sqrt(_arc_num)), 10);
kpeter@648
  1031
      int i = 0;
kpeter@650
  1032
      for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@650
  1033
        _arc_ref[i] = e;
kpeter@648
  1034
        if ((i += k) >= _arc_num) i = (i % k) + 1;
kpeter@648
  1035
      }
kpeter@648
  1036
kpeter@648
  1037
      // Initialize arc maps
kpeter@652
  1038
      if (_pupper && _pcost) {
kpeter@652
  1039
        for (int i = 0; i != _arc_num; ++i) {
kpeter@652
  1040
          Arc e = _arc_ref[i];
kpeter@652
  1041
          _source[i] = _node_id[_graph.source(e)];
kpeter@652
  1042
          _target[i] = _node_id[_graph.target(e)];
kpeter@652
  1043
          _cap[i] = (*_pupper)[e];
kpeter@652
  1044
          _cost[i] = (*_pcost)[e];
kpeter@653
  1045
          _flow[i] = 0;
kpeter@653
  1046
          _state[i] = STATE_LOWER;
kpeter@652
  1047
        }
kpeter@652
  1048
      } else {
kpeter@652
  1049
        for (int i = 0; i != _arc_num; ++i) {
kpeter@652
  1050
          Arc e = _arc_ref[i];
kpeter@652
  1051
          _source[i] = _node_id[_graph.source(e)];
kpeter@652
  1052
          _target[i] = _node_id[_graph.target(e)];
kpeter@653
  1053
          _flow[i] = 0;
kpeter@653
  1054
          _state[i] = STATE_LOWER;
kpeter@652
  1055
        }
kpeter@652
  1056
        if (_pupper) {
kpeter@652
  1057
          for (int i = 0; i != _arc_num; ++i)
kpeter@652
  1058
            _cap[i] = (*_pupper)[_arc_ref[i]];
kpeter@652
  1059
        } else {
kpeter@652
  1060
          Value val = std::numeric_limits<Value>::max();
kpeter@652
  1061
          for (int i = 0; i != _arc_num; ++i)
kpeter@652
  1062
            _cap[i] = val;
kpeter@652
  1063
        }
kpeter@652
  1064
        if (_pcost) {
kpeter@652
  1065
          for (int i = 0; i != _arc_num; ++i)
kpeter@652
  1066
            _cost[i] = (*_pcost)[_arc_ref[i]];
kpeter@652
  1067
        } else {
kpeter@652
  1068
          for (int i = 0; i != _arc_num; ++i)
kpeter@652
  1069
            _cost[i] = 1;
kpeter@652
  1070
        }
kpeter@648
  1071
      }
kpeter@648
  1072
kpeter@648
  1073
      // Remove non-zero lower bounds
kpeter@652
  1074
      if (_plower) {
kpeter@648
  1075
        for (int i = 0; i != _arc_num; ++i) {
kpeter@652
  1076
          Value c = (*_plower)[_arc_ref[i]];
kpeter@648
  1077
          if (c != 0) {
kpeter@648
  1078
            _cap[i] -= c;
kpeter@648
  1079
            _supply[_source[i]] -= c;
kpeter@648
  1080
            _supply[_target[i]] += c;
kpeter@648
  1081
          }
kpeter@648
  1082
        }
kpeter@648
  1083
      }
kpeter@648
  1084
kpeter@648
  1085
      // Add artificial arcs and initialize the spanning tree data structure
kpeter@652
  1086
      Value max_cap = std::numeric_limits<Value>::max();
kpeter@652
  1087
      Value max_cost = std::numeric_limits<Value>::max() / 4;
kpeter@648
  1088
      for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@648
  1089
        _thread[u] = u + 1;
kpeter@651
  1090
        _rev_thread[u + 1] = u;
kpeter@651
  1091
        _succ_num[u] = 1;
kpeter@651
  1092
        _last_succ[u] = u;
kpeter@648
  1093
        _parent[u] = _root;
kpeter@648
  1094
        _pred[u] = e;
kpeter@653
  1095
        _cost[e] = max_cost;
kpeter@653
  1096
        _cap[e] = max_cap;
kpeter@653
  1097
        _state[e] = STATE_TREE;
kpeter@648
  1098
        if (_supply[u] >= 0) {
kpeter@648
  1099
          _flow[e] = _supply[u];
kpeter@648
  1100
          _forward[u] = true;
kpeter@648
  1101
          _pi[u] = -max_cost;
kpeter@648
  1102
        } else {
kpeter@648
  1103
          _flow[e] = -_supply[u];
kpeter@648
  1104
          _forward[u] = false;
kpeter@648
  1105
          _pi[u] = max_cost;
kpeter@648
  1106
        }
kpeter@648
  1107
      }
kpeter@648
  1108
kpeter@648
  1109
      return true;
kpeter@648
  1110
    }
kpeter@648
  1111
kpeter@648
  1112
    // Find the join node
kpeter@648
  1113
    void findJoinNode() {
kpeter@650
  1114
      int u = _source[in_arc];
kpeter@650
  1115
      int v = _target[in_arc];
kpeter@648
  1116
      while (u != v) {
kpeter@651
  1117
        if (_succ_num[u] < _succ_num[v]) {
kpeter@651
  1118
          u = _parent[u];
kpeter@651
  1119
        } else {
kpeter@651
  1120
          v = _parent[v];
kpeter@651
  1121
        }
kpeter@648
  1122
      }
kpeter@648
  1123
      join = u;
kpeter@648
  1124
    }
kpeter@648
  1125
kpeter@648
  1126
    // Find the leaving arc of the cycle and returns true if the
kpeter@648
  1127
    // leaving arc is not the same as the entering arc
kpeter@648
  1128
    bool findLeavingArc() {
kpeter@648
  1129
      // Initialize first and second nodes according to the direction
kpeter@648
  1130
      // of the cycle
kpeter@650
  1131
      if (_state[in_arc] == STATE_LOWER) {
kpeter@650
  1132
        first  = _source[in_arc];
kpeter@650
  1133
        second = _target[in_arc];
kpeter@648
  1134
      } else {
kpeter@650
  1135
        first  = _target[in_arc];
kpeter@650
  1136
        second = _source[in_arc];
kpeter@648
  1137
      }
kpeter@650
  1138
      delta = _cap[in_arc];
kpeter@648
  1139
      int result = 0;
kpeter@652
  1140
      Value d;
kpeter@648
  1141
      int e;
kpeter@648
  1142
kpeter@648
  1143
      // Search the cycle along the path form the first node to the root
kpeter@648
  1144
      for (int u = first; u != join; u = _parent[u]) {
kpeter@648
  1145
        e = _pred[u];
kpeter@648
  1146
        d = _forward[u] ? _flow[e] : _cap[e] - _flow[e];
kpeter@648
  1147
        if (d < delta) {
kpeter@648
  1148
          delta = d;
kpeter@648
  1149
          u_out = u;
kpeter@648
  1150
          result = 1;
kpeter@648
  1151
        }
kpeter@648
  1152
      }
kpeter@648
  1153
      // Search the cycle along the path form the second node to the root
kpeter@648
  1154
      for (int u = second; u != join; u = _parent[u]) {
kpeter@648
  1155
        e = _pred[u];
kpeter@648
  1156
        d = _forward[u] ? _cap[e] - _flow[e] : _flow[e];
kpeter@648
  1157
        if (d <= delta) {
kpeter@648
  1158
          delta = d;
kpeter@648
  1159
          u_out = u;
kpeter@648
  1160
          result = 2;
kpeter@648
  1161
        }
kpeter@648
  1162
      }
kpeter@648
  1163
kpeter@648
  1164
      if (result == 1) {
kpeter@648
  1165
        u_in = first;
kpeter@648
  1166
        v_in = second;
kpeter@648
  1167
      } else {
kpeter@648
  1168
        u_in = second;
kpeter@648
  1169
        v_in = first;
kpeter@648
  1170
      }
kpeter@648
  1171
      return result != 0;
kpeter@648
  1172
    }
kpeter@648
  1173
kpeter@648
  1174
    // Change _flow and _state vectors
kpeter@648
  1175
    void changeFlow(bool change) {
kpeter@648
  1176
      // Augment along the cycle
kpeter@648
  1177
      if (delta > 0) {
kpeter@652
  1178
        Value val = _state[in_arc] * delta;
kpeter@650
  1179
        _flow[in_arc] += val;
kpeter@650
  1180
        for (int u = _source[in_arc]; u != join; u = _parent[u]) {
kpeter@648
  1181
          _flow[_pred[u]] += _forward[u] ? -val : val;
kpeter@648
  1182
        }
kpeter@650
  1183
        for (int u = _target[in_arc]; u != join; u = _parent[u]) {
kpeter@648
  1184
          _flow[_pred[u]] += _forward[u] ? val : -val;
kpeter@648
  1185
        }
kpeter@648
  1186
      }
kpeter@648
  1187
      // Update the state of the entering and leaving arcs
kpeter@648
  1188
      if (change) {
kpeter@650
  1189
        _state[in_arc] = STATE_TREE;
kpeter@648
  1190
        _state[_pred[u_out]] =
kpeter@648
  1191
          (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
kpeter@648
  1192
      } else {
kpeter@650
  1193
        _state[in_arc] = -_state[in_arc];
kpeter@648
  1194
      }
kpeter@648
  1195
    }
kpeter@648
  1196
kpeter@651
  1197
    // Update the tree structure
kpeter@651
  1198
    void updateTreeStructure() {
kpeter@651
  1199
      int u, w;
kpeter@651
  1200
      int old_rev_thread = _rev_thread[u_out];
kpeter@651
  1201
      int old_succ_num = _succ_num[u_out];
kpeter@651
  1202
      int old_last_succ = _last_succ[u_out];
kpeter@648
  1203
      v_out = _parent[u_out];
kpeter@648
  1204
kpeter@651
  1205
      u = _last_succ[u_in];  // the last successor of u_in
kpeter@651
  1206
      right = _thread[u];    // the node after it
kpeter@651
  1207
kpeter@651
  1208
      // Handle the case when old_rev_thread equals to v_in
kpeter@651
  1209
      // (it also means that join and v_out coincide)
kpeter@651
  1210
      if (old_rev_thread == v_in) {
kpeter@651
  1211
        last = _thread[_last_succ[u_out]];
kpeter@651
  1212
      } else {
kpeter@651
  1213
        last = _thread[v_in];
kpeter@648
  1214
      }
kpeter@648
  1215
kpeter@651
  1216
      // Update _thread and _parent along the stem nodes (i.e. the nodes
kpeter@651
  1217
      // between u_in and u_out, whose parent have to be changed)
kpeter@648
  1218
      _thread[v_in] = stem = u_in;
kpeter@651
  1219
      _dirty_revs.clear();
kpeter@651
  1220
      _dirty_revs.push_back(v_in);
kpeter@648
  1221
      par_stem = v_in;
kpeter@648
  1222
      while (stem != u_out) {
kpeter@651
  1223
        // Insert the next stem node into the thread list
kpeter@651
  1224
        new_stem = _parent[stem];
kpeter@651
  1225
        _thread[u] = new_stem;
kpeter@651
  1226
        _dirty_revs.push_back(u);
kpeter@648
  1227
kpeter@651
  1228
        // Remove the subtree of stem from the thread list
kpeter@651
  1229
        w = _rev_thread[stem];
kpeter@651
  1230
        _thread[w] = right;
kpeter@651
  1231
        _rev_thread[right] = w;
kpeter@648
  1232
kpeter@651
  1233
        // Change the parent node and shift stem nodes
kpeter@648
  1234
        _parent[stem] = par_stem;
kpeter@648
  1235
        par_stem = stem;
kpeter@648
  1236
        stem = new_stem;
kpeter@648
  1237
kpeter@651
  1238
        // Update u and right
kpeter@651
  1239
        u = _last_succ[stem] == _last_succ[par_stem] ?
kpeter@651
  1240
          _rev_thread[par_stem] : _last_succ[stem];
kpeter@648
  1241
        right = _thread[u];
kpeter@648
  1242
      }
kpeter@648
  1243
      _parent[u_out] = par_stem;
kpeter@648
  1244
      _thread[u] = last;
kpeter@651
  1245
      _rev_thread[last] = u;
kpeter@651
  1246
      _last_succ[u_out] = u;
kpeter@648
  1247
kpeter@651
  1248
      // Remove the subtree of u_out from the thread list except for
kpeter@651
  1249
      // the case when old_rev_thread equals to v_in
kpeter@651
  1250
      // (it also means that join and v_out coincide)
kpeter@651
  1251
      if (old_rev_thread != v_in) {
kpeter@651
  1252
        _thread[old_rev_thread] = right;
kpeter@651
  1253
        _rev_thread[right] = old_rev_thread;
kpeter@651
  1254
      }
kpeter@651
  1255
kpeter@651
  1256
      // Update _rev_thread using the new _thread values
kpeter@651
  1257
      for (int i = 0; i < int(_dirty_revs.size()); ++i) {
kpeter@651
  1258
        u = _dirty_revs[i];
kpeter@651
  1259
        _rev_thread[_thread[u]] = u;
kpeter@651
  1260
      }
kpeter@651
  1261
kpeter@651
  1262
      // Update _pred, _forward, _last_succ and _succ_num for the
kpeter@651
  1263
      // stem nodes from u_out to u_in
kpeter@651
  1264
      int tmp_sc = 0, tmp_ls = _last_succ[u_out];
kpeter@651
  1265
      u = u_out;
kpeter@651
  1266
      while (u != u_in) {
kpeter@651
  1267
        w = _parent[u];
kpeter@651
  1268
        _pred[u] = _pred[w];
kpeter@651
  1269
        _forward[u] = !_forward[w];
kpeter@651
  1270
        tmp_sc += _succ_num[u] - _succ_num[w];
kpeter@651
  1271
        _succ_num[u] = tmp_sc;
kpeter@651
  1272
        _last_succ[w] = tmp_ls;
kpeter@651
  1273
        u = w;
kpeter@651
  1274
      }
kpeter@651
  1275
      _pred[u_in] = in_arc;
kpeter@651
  1276
      _forward[u_in] = (u_in == _source[in_arc]);
kpeter@651
  1277
      _succ_num[u_in] = old_succ_num;
kpeter@651
  1278
kpeter@651
  1279
      // Set limits for updating _last_succ form v_in and v_out
kpeter@651
  1280
      // towards the root
kpeter@651
  1281
      int up_limit_in = -1;
kpeter@651
  1282
      int up_limit_out = -1;
kpeter@651
  1283
      if (_last_succ[join] == v_in) {
kpeter@651
  1284
        up_limit_out = join;
kpeter@648
  1285
      } else {
kpeter@651
  1286
        up_limit_in = join;
kpeter@651
  1287
      }
kpeter@651
  1288
kpeter@651
  1289
      // Update _last_succ from v_in towards the root
kpeter@651
  1290
      for (u = v_in; u != up_limit_in && _last_succ[u] == v_in;
kpeter@651
  1291
           u = _parent[u]) {
kpeter@651
  1292
        _last_succ[u] = _last_succ[u_out];
kpeter@651
  1293
      }
kpeter@651
  1294
      // Update _last_succ from v_out towards the root
kpeter@651
  1295
      if (join != old_rev_thread && v_in != old_rev_thread) {
kpeter@651
  1296
        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@651
  1297
             u = _parent[u]) {
kpeter@651
  1298
          _last_succ[u] = old_rev_thread;
kpeter@651
  1299
        }
kpeter@651
  1300
      } else {
kpeter@651
  1301
        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@651
  1302
             u = _parent[u]) {
kpeter@651
  1303
          _last_succ[u] = _last_succ[u_out];
kpeter@651
  1304
        }
kpeter@651
  1305
      }
kpeter@651
  1306
kpeter@651
  1307
      // Update _succ_num from v_in to join
kpeter@651
  1308
      for (u = v_in; u != join; u = _parent[u]) {
kpeter@651
  1309
        _succ_num[u] += old_succ_num;
kpeter@651
  1310
      }
kpeter@651
  1311
      // Update _succ_num from v_out to join
kpeter@651
  1312
      for (u = v_out; u != join; u = _parent[u]) {
kpeter@651
  1313
        _succ_num[u] -= old_succ_num;
kpeter@648
  1314
      }
kpeter@648
  1315
    }
kpeter@648
  1316
kpeter@651
  1317
    // Update potentials
kpeter@651
  1318
    void updatePotential() {
kpeter@652
  1319
      Value sigma = _forward[u_in] ?
kpeter@648
  1320
        _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
kpeter@648
  1321
        _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
kpeter@651
  1322
      if (_succ_num[u_in] > _node_num / 2) {
kpeter@651
  1323
        // Update in the upper subtree (which contains the root)
kpeter@651
  1324
        int before = _rev_thread[u_in];
kpeter@651
  1325
        int after = _thread[_last_succ[u_in]];
kpeter@651
  1326
        _thread[before] = after;
kpeter@651
  1327
        _pi[_root] -= sigma;
kpeter@651
  1328
        for (int u = _thread[_root]; u != _root; u = _thread[u]) {
kpeter@651
  1329
          _pi[u] -= sigma;
kpeter@651
  1330
        }
kpeter@651
  1331
        _thread[before] = u_in;
kpeter@651
  1332
      } else {
kpeter@651
  1333
        // Update in the lower subtree (which has been moved)
kpeter@651
  1334
        int end = _thread[_last_succ[u_in]];
kpeter@651
  1335
        for (int u = u_in; u != end; u = _thread[u]) {
kpeter@651
  1336
          _pi[u] += sigma;
kpeter@651
  1337
        }
kpeter@648
  1338
      }
kpeter@648
  1339
    }
kpeter@648
  1340
kpeter@648
  1341
    // Execute the algorithm
kpeter@652
  1342
    bool start(PivotRule pivot_rule) {
kpeter@648
  1343
      // Select the pivot rule implementation
kpeter@648
  1344
      switch (pivot_rule) {
kpeter@652
  1345
        case FIRST_ELIGIBLE:
kpeter@648
  1346
          return start<FirstEligiblePivotRule>();
kpeter@652
  1347
        case BEST_ELIGIBLE:
kpeter@648
  1348
          return start<BestEligiblePivotRule>();
kpeter@652
  1349
        case BLOCK_SEARCH:
kpeter@648
  1350
          return start<BlockSearchPivotRule>();
kpeter@652
  1351
        case CANDIDATE_LIST:
kpeter@648
  1352
          return start<CandidateListPivotRule>();
kpeter@652
  1353
        case ALTERING_LIST:
kpeter@648
  1354
          return start<AlteringListPivotRule>();
kpeter@648
  1355
      }
kpeter@648
  1356
      return false;
kpeter@648
  1357
    }
kpeter@648
  1358
kpeter@652
  1359
    template <typename PivotRuleImpl>
kpeter@648
  1360
    bool start() {
kpeter@652
  1361
      PivotRuleImpl pivot(*this);
kpeter@648
  1362
kpeter@652
  1363
      // Execute the Network Simplex algorithm
kpeter@648
  1364
      while (pivot.findEnteringArc()) {
kpeter@648
  1365
        findJoinNode();
kpeter@648
  1366
        bool change = findLeavingArc();
kpeter@648
  1367
        changeFlow(change);
kpeter@648
  1368
        if (change) {
kpeter@651
  1369
          updateTreeStructure();
kpeter@651
  1370
          updatePotential();
kpeter@648
  1371
        }
kpeter@648
  1372
      }
kpeter@648
  1373
kpeter@648
  1374
      // Check if the flow amount equals zero on all the artificial arcs
kpeter@648
  1375
      for (int e = _arc_num; e != _arc_num + _node_num; ++e) {
kpeter@648
  1376
        if (_flow[e] > 0) return false;
kpeter@648
  1377
      }
kpeter@648
  1378
kpeter@650
  1379
      // Copy flow values to _flow_map
kpeter@652
  1380
      if (_plower) {
kpeter@648
  1381
        for (int i = 0; i != _arc_num; ++i) {
kpeter@650
  1382
          Arc e = _arc_ref[i];
kpeter@652
  1383
          _flow_map->set(e, (*_plower)[e] + _flow[i]);
kpeter@648
  1384
        }
kpeter@648
  1385
      } else {
kpeter@648
  1386
        for (int i = 0; i != _arc_num; ++i) {
kpeter@650
  1387
          _flow_map->set(_arc_ref[i], _flow[i]);
kpeter@648
  1388
        }
kpeter@648
  1389
      }
kpeter@650
  1390
      // Copy potential values to _potential_map
kpeter@650
  1391
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@650
  1392
        _potential_map->set(n, _pi[_node_id[n]]);
kpeter@648
  1393
      }
kpeter@648
  1394
kpeter@648
  1395
      return true;
kpeter@648
  1396
    }
kpeter@648
  1397
kpeter@648
  1398
  }; //class NetworkSimplex
kpeter@648
  1399
kpeter@648
  1400
  ///@}
kpeter@648
  1401
kpeter@648
  1402
} //namespace lemon
kpeter@648
  1403
kpeter@648
  1404
#endif //LEMON_NETWORK_SIMPLEX_H