lemon/network_simplex.h
author Alpar Juttner <alpar@cs.elte.hu>
Sat, 25 May 2013 06:59:31 +0200
changeset 1064 fc3854d936f7
parent 984 fcb6ad1e67d0
parent 1003 16f55008c863
child 1049 7bf489cf624e
child 1070 ee9bac10f58e
permissions -rw-r--r--
Enable/disable options for LP/MIP backends (#465)
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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) 2003-2010
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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_algs
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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_algs
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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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  /// \ref amo93networkflows, \ref dantzig63linearprog,
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  /// \ref kellyoneill91netsimplex.
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  /// This algorithm is a highly efficient specialized version of the
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  /// linear programming simplex method directly for the minimum cost
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  /// flow problem.
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  ///
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  /// In general, \ref NetworkSimplex and \ref CostScaling are the fastest
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  /// implementations available in LEMON for solving this problem.
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  /// (For more information, see \ref min_cost_flow_algs "the module page".)
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  /// Furthermore, this class supports both directions of the supply/demand
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  /// inequality constraints. For more information, see \ref SupplyType.
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  ///
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  /// Most of the parameters of the problem (except for the digraph)
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  /// can be given using separate functions, and the algorithm can be
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  /// executed using the \ref run() function. If some parameters are not
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  /// specified, then default values will be used.
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  ///
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  /// \tparam GR The digraph type the algorithm runs on.
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  /// \tparam V The number type used for flow amounts, capacity bounds
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  /// and supply values in the algorithm. By default, it is \c int.
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  /// \tparam C The number type used for costs and potentials in the
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  /// algorithm. By default, it is the same as \c V.
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  ///
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  /// \warning Both \c V and \c C must be signed number types.
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  /// \warning All input data (capacities, supply values, and costs) must
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  /// be integer.
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  ///
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  /// \note %NetworkSimplex provides five different pivot rule
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  /// implementations, from which the most efficient one is used
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  /// by default. For more information, see \ref PivotRule.
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  template <typename GR, typename V = int, typename C = V>
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  class NetworkSimplex
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  {
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  public:
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    /// The type of the flow amounts, capacity bounds and supply values
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    typedef V Value;
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    /// The type of the arc costs
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    typedef C Cost;
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  public:
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    /// \brief Problem type constants for the \c run() function.
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    ///
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    /// Enum type containing the problem type constants that can be
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    /// returned by the \ref run() function of the algorithm.
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    enum ProblemType {
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      /// The problem has no feasible solution (flow).
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      INFEASIBLE,
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      /// The problem has optimal solution (i.e. it is feasible and
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      /// bounded), and the algorithm has found optimal flow and node
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      /// potentials (primal and dual solutions).
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      OPTIMAL,
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      /// The objective function of the problem is unbounded, i.e.
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      /// there is a directed cycle having negative total cost and
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      /// infinite upper bound.
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      UNBOUNDED
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    };
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    /// \brief Constants for selecting the type of the supply constraints.
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    ///
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    /// Enum type containing constants for selecting the supply type,
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    /// i.e. the direction of the inequalities in the supply/demand
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    /// constraints of the \ref min_cost_flow "minimum cost flow problem".
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    ///
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    /// The default supply type is \c GEQ, the \c LEQ type can be
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    /// selected using \ref supplyType().
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    /// The equality form is a special case of both supply types.
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    enum SupplyType {
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      /// This option means that there are <em>"greater or equal"</em>
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      /// supply/demand constraints in the definition of the problem.
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      GEQ,
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      /// This option means that there are <em>"less or equal"</em>
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      /// supply/demand constraints in the definition of the problem.
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      LEQ
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    };
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    /// \brief Constants for selecting the pivot rule.
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    ///
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    /// Enum type containing constants for selecting the pivot rule for
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    /// the \ref run() function.
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    ///
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    /// \ref NetworkSimplex provides five different implementations for
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    /// the pivot strategy that significantly affects the running time
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    /// of the algorithm.
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    /// According to experimental tests conducted on various problem
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    /// instances, \ref BLOCK_SEARCH "Block Search" and
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    /// \ref ALTERING_LIST "Altering Candidate List" rules turned out
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    /// to be the most efficient.
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    /// Since \ref BLOCK_SEARCH "Block Search" is a simpler strategy that
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    /// seemed to be slightly more robust, it is used by default.
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    /// However, another pivot rule can easily be selected using the
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    /// \ref run() function with the proper parameter.
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    enum PivotRule {
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      /// The \e First \e 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 \e Best \e 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 \e Block \e 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 \e Candidate \e 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 \e Altering \e Candidate \e List pivot rule.
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      /// It is a modified version of the Candidate List method.
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      /// It keeps only a few of the 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 std::vector<int> IntVector;
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    typedef std::vector<Value> ValueVector;
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    typedef std::vector<Cost> CostVector;
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    typedef std::vector<signed char> CharVector;
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    // Note: vector<signed char> is used instead of vector<ArcState> and
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    // vector<ArcDirection> for efficiency reasons
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    // State constants for arcs
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    enum ArcState {
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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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    // Direction constants for tree arcs
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    enum ArcDirection {
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      DIR_DOWN = -1,
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      DIR_UP   =  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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    int _all_arc_num;
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    int _search_arc_num;
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    // Parameters of the problem
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    bool _have_lower;
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    SupplyType _stype;
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    Value _sum_supply;
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    // Data structures for storing the digraph
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    IntNodeMap _node_id;
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    IntArcMap _arc_id;
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    IntVector _source;
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    IntVector _target;
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    bool _arc_mixing;
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    // Node and arc data
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    ValueVector _lower;
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    ValueVector _upper;
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    ValueVector _cap;
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    CostVector _cost;
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    ValueVector _supply;
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    ValueVector _flow;
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    CostVector _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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    CharVector _pred_dir;
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    CharVector _state;
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    IntVector _dirty_revs;
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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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    Value delta;
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    const Value MAX;
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  public:
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    /// \brief Constant for infinite upper bounds (capacities).
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    ///
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    /// Constant for infinite upper bounds (capacities).
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    /// It is \c std::numeric_limits<Value>::infinity() if available,
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    /// \c std::numeric_limits<Value>::max() otherwise.
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    const Value INF;
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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 CostVector &_cost;
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      const CharVector &_state;
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      const CostVector &_pi;
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      int &_in_arc;
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      int _search_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), _search_arc_num(ns._search_arc_num),
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        _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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        Cost c;
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        for (int e = _next_arc; e != _search_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 CostVector &_cost;
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      const CharVector &_state;
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      const CostVector &_pi;
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      int &_in_arc;
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      int _search_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), _search_arc_num(ns._search_arc_num)
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      {}
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      // Find next entering arc
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      bool findEnteringArc() {
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        Cost c, min = 0;
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        for (int e = 0; e != _search_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 CostVector &_cost;
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      const CharVector &_state;
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      const CostVector &_pi;
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      int &_in_arc;
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      int _search_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), _search_arc_num(ns._search_arc_num),
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        _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 = 1.0;
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        const int MIN_BLOCK_SIZE = 10;
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        _block_size = std::max( int(BLOCK_SIZE_FACTOR *
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                                    std::sqrt(double(_search_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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        Cost c, min = 0;
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        int cnt = _block_size;
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        int e;
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        for (e = _next_arc; e != _search_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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          if (--cnt == 0) {
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            if (min < 0) goto search_end;
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            cnt = _block_size;
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          }
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        }
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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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            _in_arc = e;
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          }
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          if (--cnt == 0) {
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            if (min < 0) goto search_end;
kpeter@727
   401
            cnt = _block_size;
kpeter@601
   402
          }
kpeter@601
   403
        }
kpeter@601
   404
        if (min >= 0) return false;
kpeter@727
   405
kpeter@727
   406
      search_end:
kpeter@601
   407
        _next_arc = e;
kpeter@601
   408
        return true;
kpeter@601
   409
      }
kpeter@601
   410
kpeter@601
   411
    }; //class BlockSearchPivotRule
kpeter@601
   412
kpeter@601
   413
kpeter@605
   414
    // Implementation of the Candidate List pivot rule
kpeter@601
   415
    class CandidateListPivotRule
kpeter@601
   416
    {
kpeter@601
   417
    private:
kpeter@601
   418
kpeter@601
   419
      // References to the NetworkSimplex class
kpeter@601
   420
      const IntVector  &_source;
kpeter@601
   421
      const IntVector  &_target;
kpeter@607
   422
      const CostVector &_cost;
kpeter@895
   423
      const CharVector &_state;
kpeter@607
   424
      const CostVector &_pi;
kpeter@601
   425
      int &_in_arc;
kpeter@663
   426
      int _search_arc_num;
kpeter@601
   427
kpeter@601
   428
      // Pivot rule data
kpeter@601
   429
      IntVector _candidates;
kpeter@601
   430
      int _list_length, _minor_limit;
kpeter@601
   431
      int _curr_length, _minor_count;
kpeter@601
   432
      int _next_arc;
kpeter@601
   433
kpeter@601
   434
    public:
kpeter@601
   435
kpeter@601
   436
      /// Constructor
kpeter@601
   437
      CandidateListPivotRule(NetworkSimplex &ns) :
kpeter@603
   438
        _source(ns._source), _target(ns._target),
kpeter@601
   439
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@663
   440
        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
kpeter@663
   441
        _next_arc(0)
kpeter@601
   442
      {
kpeter@601
   443
        // The main parameters of the pivot rule
kpeter@727
   444
        const double LIST_LENGTH_FACTOR = 0.25;
kpeter@601
   445
        const int MIN_LIST_LENGTH = 10;
kpeter@601
   446
        const double MINOR_LIMIT_FACTOR = 0.1;
kpeter@601
   447
        const int MIN_MINOR_LIMIT = 3;
kpeter@601
   448
alpar@612
   449
        _list_length = std::max( int(LIST_LENGTH_FACTOR *
kpeter@663
   450
                                     std::sqrt(double(_search_arc_num))),
kpeter@601
   451
                                 MIN_LIST_LENGTH );
kpeter@601
   452
        _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
kpeter@601
   453
                                 MIN_MINOR_LIMIT );
kpeter@601
   454
        _curr_length = _minor_count = 0;
kpeter@601
   455
        _candidates.resize(_list_length);
kpeter@601
   456
      }
kpeter@601
   457
kpeter@601
   458
      /// Find next entering arc
kpeter@601
   459
      bool findEnteringArc() {
kpeter@607
   460
        Cost min, c;
kpeter@727
   461
        int e;
kpeter@601
   462
        if (_curr_length > 0 && _minor_count < _minor_limit) {
kpeter@601
   463
          // Minor iteration: select the best eligible arc from the
kpeter@601
   464
          // current candidate list
kpeter@601
   465
          ++_minor_count;
kpeter@601
   466
          min = 0;
kpeter@601
   467
          for (int i = 0; i < _curr_length; ++i) {
kpeter@601
   468
            e = _candidates[i];
kpeter@601
   469
            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   470
            if (c < min) {
kpeter@601
   471
              min = c;
kpeter@727
   472
              _in_arc = e;
kpeter@601
   473
            }
kpeter@727
   474
            else if (c >= 0) {
kpeter@601
   475
              _candidates[i--] = _candidates[--_curr_length];
kpeter@601
   476
            }
kpeter@601
   477
          }
kpeter@727
   478
          if (min < 0) return true;
kpeter@601
   479
        }
kpeter@601
   480
kpeter@601
   481
        // Major iteration: build a new candidate list
kpeter@601
   482
        min = 0;
kpeter@601
   483
        _curr_length = 0;
kpeter@839
   484
        for (e = _next_arc; e != _search_arc_num; ++e) {
kpeter@601
   485
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   486
          if (c < 0) {
kpeter@601
   487
            _candidates[_curr_length++] = e;
kpeter@601
   488
            if (c < min) {
kpeter@601
   489
              min = c;
kpeter@727
   490
              _in_arc = e;
kpeter@601
   491
            }
kpeter@727
   492
            if (_curr_length == _list_length) goto search_end;
kpeter@601
   493
          }
kpeter@601
   494
        }
kpeter@839
   495
        for (e = 0; e != _next_arc; ++e) {
kpeter@727
   496
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@727
   497
          if (c < 0) {
kpeter@727
   498
            _candidates[_curr_length++] = e;
kpeter@727
   499
            if (c < min) {
kpeter@727
   500
              min = c;
kpeter@727
   501
              _in_arc = e;
kpeter@601
   502
            }
kpeter@727
   503
            if (_curr_length == _list_length) goto search_end;
kpeter@601
   504
          }
kpeter@601
   505
        }
kpeter@601
   506
        if (_curr_length == 0) return false;
alpar@877
   507
alpar@877
   508
      search_end:
kpeter@601
   509
        _minor_count = 1;
kpeter@601
   510
        _next_arc = e;
kpeter@601
   511
        return true;
kpeter@601
   512
      }
kpeter@601
   513
kpeter@601
   514
    }; //class CandidateListPivotRule
kpeter@601
   515
kpeter@601
   516
kpeter@605
   517
    // Implementation of the Altering Candidate List pivot rule
kpeter@601
   518
    class AlteringListPivotRule
kpeter@601
   519
    {
kpeter@601
   520
    private:
kpeter@601
   521
kpeter@601
   522
      // References to the NetworkSimplex class
kpeter@601
   523
      const IntVector  &_source;
kpeter@601
   524
      const IntVector  &_target;
kpeter@607
   525
      const CostVector &_cost;
kpeter@895
   526
      const CharVector &_state;
kpeter@607
   527
      const CostVector &_pi;
kpeter@601
   528
      int &_in_arc;
kpeter@663
   529
      int _search_arc_num;
kpeter@601
   530
kpeter@601
   531
      // Pivot rule data
kpeter@601
   532
      int _block_size, _head_length, _curr_length;
kpeter@601
   533
      int _next_arc;
kpeter@601
   534
      IntVector _candidates;
kpeter@607
   535
      CostVector _cand_cost;
kpeter@601
   536
kpeter@601
   537
      // Functor class to compare arcs during sort of the candidate list
kpeter@601
   538
      class SortFunc
kpeter@601
   539
      {
kpeter@601
   540
      private:
kpeter@607
   541
        const CostVector &_map;
kpeter@601
   542
      public:
kpeter@607
   543
        SortFunc(const CostVector &map) : _map(map) {}
kpeter@601
   544
        bool operator()(int left, int right) {
kpeter@984
   545
          return _map[left] < _map[right];
kpeter@601
   546
        }
kpeter@601
   547
      };
kpeter@601
   548
kpeter@601
   549
      SortFunc _sort_func;
kpeter@601
   550
kpeter@601
   551
    public:
kpeter@601
   552
kpeter@605
   553
      // Constructor
kpeter@601
   554
      AlteringListPivotRule(NetworkSimplex &ns) :
kpeter@603
   555
        _source(ns._source), _target(ns._target),
kpeter@601
   556
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@663
   557
        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
kpeter@663
   558
        _next_arc(0), _cand_cost(ns._search_arc_num), _sort_func(_cand_cost)
kpeter@601
   559
      {
kpeter@601
   560
        // The main parameters of the pivot rule
kpeter@727
   561
        const double BLOCK_SIZE_FACTOR = 1.0;
kpeter@601
   562
        const int MIN_BLOCK_SIZE = 10;
kpeter@984
   563
        const double HEAD_LENGTH_FACTOR = 0.01;
kpeter@601
   564
        const int MIN_HEAD_LENGTH = 3;
kpeter@601
   565
alpar@612
   566
        _block_size = std::max( int(BLOCK_SIZE_FACTOR *
kpeter@663
   567
                                    std::sqrt(double(_search_arc_num))),
kpeter@601
   568
                                MIN_BLOCK_SIZE );
kpeter@601
   569
        _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),
kpeter@601
   570
                                 MIN_HEAD_LENGTH );
kpeter@601
   571
        _candidates.resize(_head_length + _block_size);
kpeter@601
   572
        _curr_length = 0;
kpeter@601
   573
      }
kpeter@601
   574
kpeter@605
   575
      // Find next entering arc
kpeter@601
   576
      bool findEnteringArc() {
kpeter@601
   577
        // Check the current candidate list
kpeter@601
   578
        int e;
kpeter@895
   579
        Cost c;
kpeter@839
   580
        for (int i = 0; i != _curr_length; ++i) {
kpeter@601
   581
          e = _candidates[i];
kpeter@895
   582
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@895
   583
          if (c < 0) {
kpeter@895
   584
            _cand_cost[e] = c;
kpeter@895
   585
          } else {
kpeter@601
   586
            _candidates[i--] = _candidates[--_curr_length];
kpeter@601
   587
          }
kpeter@601
   588
        }
kpeter@601
   589
kpeter@601
   590
        // Extend the list
kpeter@601
   591
        int cnt = _block_size;
kpeter@601
   592
        int limit = _head_length;
kpeter@601
   593
kpeter@839
   594
        for (e = _next_arc; e != _search_arc_num; ++e) {
kpeter@895
   595
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@895
   596
          if (c < 0) {
kpeter@895
   597
            _cand_cost[e] = c;
kpeter@601
   598
            _candidates[_curr_length++] = e;
kpeter@601
   599
          }
kpeter@601
   600
          if (--cnt == 0) {
kpeter@727
   601
            if (_curr_length > limit) goto search_end;
kpeter@601
   602
            limit = 0;
kpeter@601
   603
            cnt = _block_size;
kpeter@601
   604
          }
kpeter@601
   605
        }
kpeter@839
   606
        for (e = 0; e != _next_arc; ++e) {
kpeter@984
   607
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@984
   608
          if (c < 0) {
kpeter@984
   609
            _cand_cost[e] = c;
kpeter@727
   610
            _candidates[_curr_length++] = e;
kpeter@727
   611
          }
kpeter@727
   612
          if (--cnt == 0) {
kpeter@727
   613
            if (_curr_length > limit) goto search_end;
kpeter@727
   614
            limit = 0;
kpeter@727
   615
            cnt = _block_size;
kpeter@601
   616
          }
kpeter@601
   617
        }
kpeter@601
   618
        if (_curr_length == 0) return false;
alpar@877
   619
kpeter@727
   620
      search_end:
kpeter@601
   621
kpeter@984
   622
        // Perform partial sort operation on the candidate list
kpeter@984
   623
        int new_length = std::min(_head_length + 1, _curr_length);
kpeter@984
   624
        std::partial_sort(_candidates.begin(), _candidates.begin() + new_length,
kpeter@984
   625
                          _candidates.begin() + _curr_length, _sort_func);
kpeter@601
   626
kpeter@984
   627
        // Select the entering arc and remove it from the list
kpeter@601
   628
        _in_arc = _candidates[0];
kpeter@727
   629
        _next_arc = e;
kpeter@984
   630
        _candidates[0] = _candidates[new_length - 1];
kpeter@984
   631
        _curr_length = new_length - 1;
kpeter@601
   632
        return true;
kpeter@601
   633
      }
kpeter@601
   634
kpeter@601
   635
    }; //class AlteringListPivotRule
kpeter@601
   636
kpeter@601
   637
  public:
kpeter@601
   638
kpeter@605
   639
    /// \brief Constructor.
kpeter@601
   640
    ///
kpeter@609
   641
    /// The constructor of the class.
kpeter@601
   642
    ///
kpeter@603
   643
    /// \param graph The digraph the algorithm runs on.
kpeter@896
   644
    /// \param arc_mixing Indicate if the arcs will be stored in a
alpar@877
   645
    /// mixed order in the internal data structure.
kpeter@896
   646
    /// In general, it leads to similar performance as using the original
kpeter@896
   647
    /// arc order, but it makes the algorithm more robust and in special
kpeter@896
   648
    /// cases, even significantly faster. Therefore, it is enabled by default.
kpeter@896
   649
    NetworkSimplex(const GR& graph, bool arc_mixing = true) :
kpeter@642
   650
      _graph(graph), _node_id(graph), _arc_id(graph),
kpeter@830
   651
      _arc_mixing(arc_mixing),
kpeter@811
   652
      MAX(std::numeric_limits<Value>::max()),
kpeter@641
   653
      INF(std::numeric_limits<Value>::has_infinity ?
kpeter@811
   654
          std::numeric_limits<Value>::infinity() : MAX)
kpeter@605
   655
    {
kpeter@812
   656
      // Check the number types
kpeter@641
   657
      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
kpeter@640
   658
        "The flow type of NetworkSimplex must be signed");
kpeter@640
   659
      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
kpeter@640
   660
        "The cost type of NetworkSimplex must be signed");
kpeter@601
   661
kpeter@830
   662
      // Reset data structures
kpeter@729
   663
      reset();
kpeter@601
   664
    }
kpeter@601
   665
kpeter@609
   666
    /// \name Parameters
kpeter@609
   667
    /// The parameters of the algorithm can be specified using these
kpeter@609
   668
    /// functions.
kpeter@609
   669
kpeter@609
   670
    /// @{
kpeter@609
   671
kpeter@605
   672
    /// \brief Set the lower bounds on the arcs.
kpeter@605
   673
    ///
kpeter@605
   674
    /// This function sets the lower bounds on the arcs.
kpeter@640
   675
    /// If it is not used before calling \ref run(), the lower bounds
kpeter@640
   676
    /// will be set to zero on all arcs.
kpeter@605
   677
    ///
kpeter@605
   678
    /// \param map An arc map storing the lower bounds.
kpeter@641
   679
    /// Its \c Value type must be convertible to the \c Value type
kpeter@605
   680
    /// of the algorithm.
kpeter@605
   681
    ///
kpeter@605
   682
    /// \return <tt>(*this)</tt>
kpeter@640
   683
    template <typename LowerMap>
kpeter@640
   684
    NetworkSimplex& lowerMap(const LowerMap& map) {
kpeter@642
   685
      _have_lower = true;
kpeter@605
   686
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   687
        _lower[_arc_id[a]] = map[a];
kpeter@605
   688
      }
kpeter@605
   689
      return *this;
kpeter@605
   690
    }
kpeter@605
   691
kpeter@605
   692
    /// \brief Set the upper bounds (capacities) on the arcs.
kpeter@605
   693
    ///
kpeter@605
   694
    /// This function sets the upper bounds (capacities) on the arcs.
kpeter@640
   695
    /// If it is not used before calling \ref run(), the upper bounds
kpeter@640
   696
    /// will be set to \ref INF on all arcs (i.e. the flow value will be
kpeter@812
   697
    /// unbounded from above).
kpeter@605
   698
    ///
kpeter@605
   699
    /// \param map An arc map storing the upper bounds.
kpeter@641
   700
    /// Its \c Value type must be convertible to the \c Value type
kpeter@605
   701
    /// of the algorithm.
kpeter@605
   702
    ///
kpeter@605
   703
    /// \return <tt>(*this)</tt>
kpeter@640
   704
    template<typename UpperMap>
kpeter@640
   705
    NetworkSimplex& upperMap(const UpperMap& map) {
kpeter@605
   706
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   707
        _upper[_arc_id[a]] = map[a];
kpeter@605
   708
      }
kpeter@605
   709
      return *this;
kpeter@605
   710
    }
kpeter@605
   711
kpeter@605
   712
    /// \brief Set the costs of the arcs.
kpeter@605
   713
    ///
kpeter@605
   714
    /// This function sets the costs of the arcs.
kpeter@605
   715
    /// If it is not used before calling \ref run(), the costs
kpeter@605
   716
    /// will be set to \c 1 on all arcs.
kpeter@605
   717
    ///
kpeter@605
   718
    /// \param map An arc map storing the costs.
kpeter@607
   719
    /// Its \c Value type must be convertible to the \c Cost type
kpeter@605
   720
    /// of the algorithm.
kpeter@605
   721
    ///
kpeter@605
   722
    /// \return <tt>(*this)</tt>
kpeter@640
   723
    template<typename CostMap>
kpeter@640
   724
    NetworkSimplex& costMap(const CostMap& map) {
kpeter@605
   725
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   726
        _cost[_arc_id[a]] = map[a];
kpeter@605
   727
      }
kpeter@605
   728
      return *this;
kpeter@605
   729
    }
kpeter@605
   730
kpeter@605
   731
    /// \brief Set the supply values of the nodes.
kpeter@605
   732
    ///
kpeter@605
   733
    /// This function sets the supply values of the nodes.
kpeter@605
   734
    /// If neither this function nor \ref stSupply() is used before
kpeter@605
   735
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@605
   736
    ///
kpeter@605
   737
    /// \param map A node map storing the supply values.
kpeter@641
   738
    /// Its \c Value type must be convertible to the \c Value type
kpeter@605
   739
    /// of the algorithm.
kpeter@605
   740
    ///
kpeter@605
   741
    /// \return <tt>(*this)</tt>
kpeter@919
   742
    ///
kpeter@919
   743
    /// \sa supplyType()
kpeter@640
   744
    template<typename SupplyMap>
kpeter@640
   745
    NetworkSimplex& supplyMap(const SupplyMap& map) {
kpeter@605
   746
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@642
   747
        _supply[_node_id[n]] = map[n];
kpeter@605
   748
      }
kpeter@605
   749
      return *this;
kpeter@605
   750
    }
kpeter@605
   751
kpeter@605
   752
    /// \brief Set single source and target nodes and a supply value.
kpeter@605
   753
    ///
kpeter@605
   754
    /// This function sets a single source node and a single target node
kpeter@605
   755
    /// and the required flow value.
kpeter@605
   756
    /// If neither this function nor \ref supplyMap() is used before
kpeter@605
   757
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@605
   758
    ///
kpeter@640
   759
    /// Using this function has the same effect as using \ref supplyMap()
kpeter@919
   760
    /// with a map in which \c k is assigned to \c s, \c -k is
kpeter@640
   761
    /// assigned to \c t and all other nodes have zero supply value.
kpeter@640
   762
    ///
kpeter@605
   763
    /// \param s The source node.
kpeter@605
   764
    /// \param t The target node.
kpeter@605
   765
    /// \param k The required amount of flow from node \c s to node \c t
kpeter@605
   766
    /// (i.e. the supply of \c s and the demand of \c t).
kpeter@605
   767
    ///
kpeter@605
   768
    /// \return <tt>(*this)</tt>
kpeter@641
   769
    NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) {
kpeter@642
   770
      for (int i = 0; i != _node_num; ++i) {
kpeter@642
   771
        _supply[i] = 0;
kpeter@642
   772
      }
kpeter@642
   773
      _supply[_node_id[s]] =  k;
kpeter@642
   774
      _supply[_node_id[t]] = -k;
kpeter@605
   775
      return *this;
kpeter@605
   776
    }
alpar@877
   777
kpeter@640
   778
    /// \brief Set the type of the supply constraints.
kpeter@609
   779
    ///
kpeter@640
   780
    /// This function sets the type of the supply/demand constraints.
kpeter@640
   781
    /// If it is not used before calling \ref run(), the \ref GEQ supply
kpeter@609
   782
    /// type will be used.
kpeter@609
   783
    ///
kpeter@786
   784
    /// For more information, see \ref SupplyType.
kpeter@609
   785
    ///
kpeter@609
   786
    /// \return <tt>(*this)</tt>
kpeter@640
   787
    NetworkSimplex& supplyType(SupplyType supply_type) {
kpeter@640
   788
      _stype = supply_type;
kpeter@609
   789
      return *this;
kpeter@609
   790
    }
kpeter@605
   791
kpeter@609
   792
    /// @}
kpeter@601
   793
kpeter@605
   794
    /// \name Execution Control
kpeter@605
   795
    /// The algorithm can be executed using \ref run().
kpeter@605
   796
kpeter@601
   797
    /// @{
kpeter@601
   798
kpeter@601
   799
    /// \brief Run the algorithm.
kpeter@601
   800
    ///
kpeter@601
   801
    /// This function runs the algorithm.
kpeter@609
   802
    /// The paramters can be specified using functions \ref lowerMap(),
alpar@877
   803
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(),
kpeter@642
   804
    /// \ref supplyType().
kpeter@609
   805
    /// For example,
kpeter@605
   806
    /// \code
kpeter@605
   807
    ///   NetworkSimplex<ListDigraph> ns(graph);
kpeter@640
   808
    ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@605
   809
    ///     .supplyMap(sup).run();
kpeter@605
   810
    /// \endcode
kpeter@601
   811
    ///
kpeter@830
   812
    /// This function can be called more than once. All the given parameters
kpeter@830
   813
    /// are kept for the next call, unless \ref resetParams() or \ref reset()
kpeter@830
   814
    /// is used, thus only the modified parameters have to be set again.
kpeter@830
   815
    /// If the underlying digraph was also modified after the construction
kpeter@830
   816
    /// of the class (or the last \ref reset() call), then the \ref reset()
kpeter@830
   817
    /// function must be called.
kpeter@606
   818
    ///
kpeter@605
   819
    /// \param pivot_rule The pivot rule that will be used during the
kpeter@786
   820
    /// algorithm. For more information, see \ref PivotRule.
kpeter@601
   821
    ///
kpeter@640
   822
    /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@640
   823
    /// \n \c OPTIMAL if the problem has optimal solution
kpeter@640
   824
    /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@640
   825
    /// optimal flow and node potentials (primal and dual solutions),
kpeter@640
   826
    /// \n \c UNBOUNDED if the objective function of the problem is
kpeter@640
   827
    /// unbounded, i.e. there is a directed cycle having negative total
kpeter@640
   828
    /// cost and infinite upper bound.
kpeter@640
   829
    ///
kpeter@640
   830
    /// \see ProblemType, PivotRule
kpeter@830
   831
    /// \see resetParams(), reset()
kpeter@640
   832
    ProblemType run(PivotRule pivot_rule = BLOCK_SEARCH) {
kpeter@640
   833
      if (!init()) return INFEASIBLE;
kpeter@640
   834
      return start(pivot_rule);
kpeter@601
   835
    }
kpeter@601
   836
kpeter@606
   837
    /// \brief Reset all the parameters that have been given before.
kpeter@606
   838
    ///
kpeter@606
   839
    /// This function resets all the paramaters that have been given
kpeter@609
   840
    /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@642
   841
    /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType().
kpeter@606
   842
    ///
kpeter@830
   843
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830
   844
    /// parameters are kept for the next \ref run() call, unless
kpeter@830
   845
    /// \ref resetParams() or \ref reset() is used.
kpeter@830
   846
    /// If the underlying digraph was also modified after the construction
kpeter@830
   847
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830
   848
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@606
   849
    ///
kpeter@606
   850
    /// For example,
kpeter@606
   851
    /// \code
kpeter@606
   852
    ///   NetworkSimplex<ListDigraph> ns(graph);
kpeter@606
   853
    ///
kpeter@606
   854
    ///   // First run
kpeter@640
   855
    ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@606
   856
    ///     .supplyMap(sup).run();
kpeter@606
   857
    ///
kpeter@830
   858
    ///   // Run again with modified cost map (resetParams() is not called,
kpeter@606
   859
    ///   // so only the cost map have to be set again)
kpeter@606
   860
    ///   cost[e] += 100;
kpeter@606
   861
    ///   ns.costMap(cost).run();
kpeter@606
   862
    ///
kpeter@830
   863
    ///   // Run again from scratch using resetParams()
kpeter@606
   864
    ///   // (the lower bounds will be set to zero on all arcs)
kpeter@830
   865
    ///   ns.resetParams();
kpeter@640
   866
    ///   ns.upperMap(capacity).costMap(cost)
kpeter@606
   867
    ///     .supplyMap(sup).run();
kpeter@606
   868
    /// \endcode
kpeter@606
   869
    ///
kpeter@606
   870
    /// \return <tt>(*this)</tt>
kpeter@830
   871
    ///
kpeter@830
   872
    /// \see reset(), run()
kpeter@830
   873
    NetworkSimplex& resetParams() {
kpeter@642
   874
      for (int i = 0; i != _node_num; ++i) {
kpeter@642
   875
        _supply[i] = 0;
kpeter@642
   876
      }
kpeter@642
   877
      for (int i = 0; i != _arc_num; ++i) {
kpeter@642
   878
        _lower[i] = 0;
kpeter@642
   879
        _upper[i] = INF;
kpeter@642
   880
        _cost[i] = 1;
kpeter@642
   881
      }
kpeter@642
   882
      _have_lower = false;
kpeter@640
   883
      _stype = GEQ;
kpeter@606
   884
      return *this;
kpeter@606
   885
    }
kpeter@606
   886
kpeter@830
   887
    /// \brief Reset the internal data structures and all the parameters
kpeter@830
   888
    /// that have been given before.
kpeter@830
   889
    ///
kpeter@830
   890
    /// This function resets the internal data structures and all the
kpeter@830
   891
    /// paramaters that have been given before using functions \ref lowerMap(),
kpeter@830
   892
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(),
kpeter@830
   893
    /// \ref supplyType().
kpeter@830
   894
    ///
kpeter@830
   895
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830
   896
    /// parameters are kept for the next \ref run() call, unless
kpeter@830
   897
    /// \ref resetParams() or \ref reset() is used.
kpeter@830
   898
    /// If the underlying digraph was also modified after the construction
kpeter@830
   899
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830
   900
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@830
   901
    ///
kpeter@830
   902
    /// See \ref resetParams() for examples.
kpeter@830
   903
    ///
kpeter@830
   904
    /// \return <tt>(*this)</tt>
kpeter@830
   905
    ///
kpeter@830
   906
    /// \see resetParams(), run()
kpeter@830
   907
    NetworkSimplex& reset() {
kpeter@830
   908
      // Resize vectors
kpeter@830
   909
      _node_num = countNodes(_graph);
kpeter@830
   910
      _arc_num = countArcs(_graph);
kpeter@830
   911
      int all_node_num = _node_num + 1;
kpeter@830
   912
      int max_arc_num = _arc_num + 2 * _node_num;
kpeter@830
   913
kpeter@830
   914
      _source.resize(max_arc_num);
kpeter@830
   915
      _target.resize(max_arc_num);
kpeter@830
   916
kpeter@830
   917
      _lower.resize(_arc_num);
kpeter@830
   918
      _upper.resize(_arc_num);
kpeter@830
   919
      _cap.resize(max_arc_num);
kpeter@830
   920
      _cost.resize(max_arc_num);
kpeter@830
   921
      _supply.resize(all_node_num);
kpeter@830
   922
      _flow.resize(max_arc_num);
kpeter@830
   923
      _pi.resize(all_node_num);
kpeter@830
   924
kpeter@830
   925
      _parent.resize(all_node_num);
kpeter@830
   926
      _pred.resize(all_node_num);
kpeter@895
   927
      _pred_dir.resize(all_node_num);
kpeter@830
   928
      _thread.resize(all_node_num);
kpeter@830
   929
      _rev_thread.resize(all_node_num);
kpeter@830
   930
      _succ_num.resize(all_node_num);
kpeter@830
   931
      _last_succ.resize(all_node_num);
kpeter@830
   932
      _state.resize(max_arc_num);
kpeter@830
   933
kpeter@830
   934
      // Copy the graph
kpeter@830
   935
      int i = 0;
kpeter@830
   936
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830
   937
        _node_id[n] = i;
kpeter@830
   938
      }
kpeter@830
   939
      if (_arc_mixing) {
kpeter@830
   940
        // Store the arcs in a mixed order
kpeter@896
   941
        const int skip = std::max(_arc_num / _node_num, 3);
kpeter@830
   942
        int i = 0, j = 0;
kpeter@830
   943
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@830
   944
          _arc_id[a] = i;
kpeter@830
   945
          _source[i] = _node_id[_graph.source(a)];
kpeter@830
   946
          _target[i] = _node_id[_graph.target(a)];
kpeter@896
   947
          if ((i += skip) >= _arc_num) i = ++j;
kpeter@830
   948
        }
kpeter@830
   949
      } else {
kpeter@830
   950
        // Store the arcs in the original order
kpeter@830
   951
        int i = 0;
kpeter@830
   952
        for (ArcIt a(_graph); a != INVALID; ++a, ++i) {
kpeter@830
   953
          _arc_id[a] = i;
kpeter@830
   954
          _source[i] = _node_id[_graph.source(a)];
kpeter@830
   955
          _target[i] = _node_id[_graph.target(a)];
kpeter@830
   956
        }
kpeter@830
   957
      }
alpar@877
   958
kpeter@830
   959
      // Reset parameters
kpeter@830
   960
      resetParams();
kpeter@830
   961
      return *this;
kpeter@830
   962
    }
alpar@877
   963
kpeter@601
   964
    /// @}
kpeter@601
   965
kpeter@601
   966
    /// \name Query Functions
kpeter@601
   967
    /// The results of the algorithm can be obtained using these
kpeter@601
   968
    /// functions.\n
kpeter@605
   969
    /// The \ref run() function must be called before using them.
kpeter@605
   970
kpeter@601
   971
    /// @{
kpeter@601
   972
kpeter@605
   973
    /// \brief Return the total cost of the found flow.
kpeter@605
   974
    ///
kpeter@605
   975
    /// This function returns the total cost of the found flow.
kpeter@640
   976
    /// Its complexity is O(e).
kpeter@605
   977
    ///
kpeter@605
   978
    /// \note The return type of the function can be specified as a
kpeter@605
   979
    /// template parameter. For example,
kpeter@605
   980
    /// \code
kpeter@605
   981
    ///   ns.totalCost<double>();
kpeter@605
   982
    /// \endcode
kpeter@607
   983
    /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@605
   984
    /// type of the algorithm, which is the default return type of the
kpeter@605
   985
    /// function.
kpeter@605
   986
    ///
kpeter@605
   987
    /// \pre \ref run() must be called before using this function.
kpeter@642
   988
    template <typename Number>
kpeter@642
   989
    Number totalCost() const {
kpeter@642
   990
      Number c = 0;
kpeter@642
   991
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   992
        int i = _arc_id[a];
kpeter@642
   993
        c += Number(_flow[i]) * Number(_cost[i]);
kpeter@605
   994
      }
kpeter@605
   995
      return c;
kpeter@605
   996
    }
kpeter@605
   997
kpeter@605
   998
#ifndef DOXYGEN
kpeter@607
   999
    Cost totalCost() const {
kpeter@607
  1000
      return totalCost<Cost>();
kpeter@605
  1001
    }
kpeter@605
  1002
#endif
kpeter@605
  1003
kpeter@605
  1004
    /// \brief Return the flow on the given arc.
kpeter@605
  1005
    ///
kpeter@605
  1006
    /// This function returns the flow on the given arc.
kpeter@605
  1007
    ///
kpeter@605
  1008
    /// \pre \ref run() must be called before using this function.
kpeter@641
  1009
    Value flow(const Arc& a) const {
kpeter@642
  1010
      return _flow[_arc_id[a]];
kpeter@605
  1011
    }
kpeter@605
  1012
kpeter@1003
  1013
    /// \brief Copy the flow values (the primal solution) into the
kpeter@1003
  1014
    /// given map.
kpeter@601
  1015
    ///
kpeter@642
  1016
    /// This function copies the flow value on each arc into the given
kpeter@642
  1017
    /// map. The \c Value type of the algorithm must be convertible to
kpeter@642
  1018
    /// the \c Value type of the map.
kpeter@601
  1019
    ///
kpeter@601
  1020
    /// \pre \ref run() must be called before using this function.
kpeter@642
  1021
    template <typename FlowMap>
kpeter@642
  1022
    void flowMap(FlowMap &map) const {
kpeter@642
  1023
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
  1024
        map.set(a, _flow[_arc_id[a]]);
kpeter@642
  1025
      }
kpeter@601
  1026
    }
kpeter@601
  1027
kpeter@605
  1028
    /// \brief Return the potential (dual value) of the given node.
kpeter@605
  1029
    ///
kpeter@605
  1030
    /// This function returns the potential (dual value) of the
kpeter@605
  1031
    /// given node.
kpeter@605
  1032
    ///
kpeter@605
  1033
    /// \pre \ref run() must be called before using this function.
kpeter@607
  1034
    Cost potential(const Node& n) const {
kpeter@642
  1035
      return _pi[_node_id[n]];
kpeter@605
  1036
    }
kpeter@605
  1037
kpeter@1003
  1038
    /// \brief Copy the potential values (the dual solution) into the
kpeter@1003
  1039
    /// given map.
kpeter@601
  1040
    ///
kpeter@642
  1041
    /// This function copies the potential (dual value) of each node
kpeter@642
  1042
    /// into the given map.
kpeter@642
  1043
    /// The \c Cost type of the algorithm must be convertible to the
kpeter@642
  1044
    /// \c Value type of the map.
kpeter@601
  1045
    ///
kpeter@601
  1046
    /// \pre \ref run() must be called before using this function.
kpeter@642
  1047
    template <typename PotentialMap>
kpeter@642
  1048
    void potentialMap(PotentialMap &map) const {
kpeter@642
  1049
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@642
  1050
        map.set(n, _pi[_node_id[n]]);
kpeter@642
  1051
      }
kpeter@601
  1052
    }
kpeter@601
  1053
kpeter@601
  1054
    /// @}
kpeter@601
  1055
kpeter@601
  1056
  private:
kpeter@601
  1057
kpeter@601
  1058
    // Initialize internal data structures
kpeter@601
  1059
    bool init() {
kpeter@605
  1060
      if (_node_num == 0) return false;
kpeter@601
  1061
kpeter@642
  1062
      // Check the sum of supply values
kpeter@642
  1063
      _sum_supply = 0;
kpeter@642
  1064
      for (int i = 0; i != _node_num; ++i) {
kpeter@642
  1065
        _sum_supply += _supply[i];
kpeter@642
  1066
      }
alpar@643
  1067
      if ( !((_stype == GEQ && _sum_supply <= 0) ||
alpar@643
  1068
             (_stype == LEQ && _sum_supply >= 0)) ) return false;
kpeter@601
  1069
kpeter@642
  1070
      // Remove non-zero lower bounds
kpeter@642
  1071
      if (_have_lower) {
kpeter@642
  1072
        for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1073
          Value c = _lower[i];
kpeter@642
  1074
          if (c >= 0) {
kpeter@811
  1075
            _cap[i] = _upper[i] < MAX ? _upper[i] - c : INF;
kpeter@642
  1076
          } else {
kpeter@811
  1077
            _cap[i] = _upper[i] < MAX + c ? _upper[i] - c : INF;
kpeter@642
  1078
          }
kpeter@642
  1079
          _supply[_source[i]] -= c;
kpeter@642
  1080
          _supply[_target[i]] += c;
kpeter@642
  1081
        }
kpeter@642
  1082
      } else {
kpeter@642
  1083
        for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1084
          _cap[i] = _upper[i];
kpeter@642
  1085
        }
kpeter@605
  1086
      }
kpeter@601
  1087
kpeter@609
  1088
      // Initialize artifical cost
kpeter@640
  1089
      Cost ART_COST;
kpeter@609
  1090
      if (std::numeric_limits<Cost>::is_exact) {
kpeter@663
  1091
        ART_COST = std::numeric_limits<Cost>::max() / 2 + 1;
kpeter@609
  1092
      } else {
kpeter@888
  1093
        ART_COST = 0;
kpeter@609
  1094
        for (int i = 0; i != _arc_num; ++i) {
kpeter@640
  1095
          if (_cost[i] > ART_COST) ART_COST = _cost[i];
kpeter@609
  1096
        }
kpeter@640
  1097
        ART_COST = (ART_COST + 1) * _node_num;
kpeter@609
  1098
      }
kpeter@609
  1099
kpeter@642
  1100
      // Initialize arc maps
kpeter@642
  1101
      for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1102
        _flow[i] = 0;
kpeter@642
  1103
        _state[i] = STATE_LOWER;
kpeter@642
  1104
      }
alpar@877
  1105
kpeter@601
  1106
      // Set data for the artificial root node
kpeter@601
  1107
      _root = _node_num;
kpeter@601
  1108
      _parent[_root] = -1;
kpeter@601
  1109
      _pred[_root] = -1;
kpeter@601
  1110
      _thread[_root] = 0;
kpeter@604
  1111
      _rev_thread[0] = _root;
kpeter@642
  1112
      _succ_num[_root] = _node_num + 1;
kpeter@604
  1113
      _last_succ[_root] = _root - 1;
kpeter@640
  1114
      _supply[_root] = -_sum_supply;
kpeter@663
  1115
      _pi[_root] = 0;
kpeter@601
  1116
kpeter@601
  1117
      // Add artificial arcs and initialize the spanning tree data structure
kpeter@663
  1118
      if (_sum_supply == 0) {
kpeter@663
  1119
        // EQ supply constraints
kpeter@663
  1120
        _search_arc_num = _arc_num;
kpeter@663
  1121
        _all_arc_num = _arc_num + _node_num;
kpeter@663
  1122
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@663
  1123
          _parent[u] = _root;
kpeter@663
  1124
          _pred[u] = e;
kpeter@663
  1125
          _thread[u] = u + 1;
kpeter@663
  1126
          _rev_thread[u + 1] = u;
kpeter@663
  1127
          _succ_num[u] = 1;
kpeter@663
  1128
          _last_succ[u] = u;
kpeter@663
  1129
          _cap[e] = INF;
kpeter@663
  1130
          _state[e] = STATE_TREE;
kpeter@663
  1131
          if (_supply[u] >= 0) {
kpeter@895
  1132
            _pred_dir[u] = DIR_UP;
kpeter@663
  1133
            _pi[u] = 0;
kpeter@663
  1134
            _source[e] = u;
kpeter@663
  1135
            _target[e] = _root;
kpeter@663
  1136
            _flow[e] = _supply[u];
kpeter@663
  1137
            _cost[e] = 0;
kpeter@663
  1138
          } else {
kpeter@895
  1139
            _pred_dir[u] = DIR_DOWN;
kpeter@663
  1140
            _pi[u] = ART_COST;
kpeter@663
  1141
            _source[e] = _root;
kpeter@663
  1142
            _target[e] = u;
kpeter@663
  1143
            _flow[e] = -_supply[u];
kpeter@663
  1144
            _cost[e] = ART_COST;
kpeter@663
  1145
          }
kpeter@601
  1146
        }
kpeter@601
  1147
      }
kpeter@663
  1148
      else if (_sum_supply > 0) {
kpeter@663
  1149
        // LEQ supply constraints
kpeter@663
  1150
        _search_arc_num = _arc_num + _node_num;
kpeter@663
  1151
        int f = _arc_num + _node_num;
kpeter@663
  1152
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@663
  1153
          _parent[u] = _root;
kpeter@663
  1154
          _thread[u] = u + 1;
kpeter@663
  1155
          _rev_thread[u + 1] = u;
kpeter@663
  1156
          _succ_num[u] = 1;
kpeter@663
  1157
          _last_succ[u] = u;
kpeter@663
  1158
          if (_supply[u] >= 0) {
kpeter@895
  1159
            _pred_dir[u] = DIR_UP;
kpeter@663
  1160
            _pi[u] = 0;
kpeter@663
  1161
            _pred[u] = e;
kpeter@663
  1162
            _source[e] = u;
kpeter@663
  1163
            _target[e] = _root;
kpeter@663
  1164
            _cap[e] = INF;
kpeter@663
  1165
            _flow[e] = _supply[u];
kpeter@663
  1166
            _cost[e] = 0;
kpeter@663
  1167
            _state[e] = STATE_TREE;
kpeter@663
  1168
          } else {
kpeter@895
  1169
            _pred_dir[u] = DIR_DOWN;
kpeter@663
  1170
            _pi[u] = ART_COST;
kpeter@663
  1171
            _pred[u] = f;
kpeter@663
  1172
            _source[f] = _root;
kpeter@663
  1173
            _target[f] = u;
kpeter@663
  1174
            _cap[f] = INF;
kpeter@663
  1175
            _flow[f] = -_supply[u];
kpeter@663
  1176
            _cost[f] = ART_COST;
kpeter@663
  1177
            _state[f] = STATE_TREE;
kpeter@663
  1178
            _source[e] = u;
kpeter@663
  1179
            _target[e] = _root;
kpeter@663
  1180
            _cap[e] = INF;
kpeter@663
  1181
            _flow[e] = 0;
kpeter@663
  1182
            _cost[e] = 0;
kpeter@663
  1183
            _state[e] = STATE_LOWER;
kpeter@663
  1184
            ++f;
kpeter@663
  1185
          }
kpeter@663
  1186
        }
kpeter@663
  1187
        _all_arc_num = f;
kpeter@663
  1188
      }
kpeter@663
  1189
      else {
kpeter@663
  1190
        // GEQ supply constraints
kpeter@663
  1191
        _search_arc_num = _arc_num + _node_num;
kpeter@663
  1192
        int f = _arc_num + _node_num;
kpeter@663
  1193
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@663
  1194
          _parent[u] = _root;
kpeter@663
  1195
          _thread[u] = u + 1;
kpeter@663
  1196
          _rev_thread[u + 1] = u;
kpeter@663
  1197
          _succ_num[u] = 1;
kpeter@663
  1198
          _last_succ[u] = u;
kpeter@663
  1199
          if (_supply[u] <= 0) {
kpeter@895
  1200
            _pred_dir[u] = DIR_DOWN;
kpeter@663
  1201
            _pi[u] = 0;
kpeter@663
  1202
            _pred[u] = e;
kpeter@663
  1203
            _source[e] = _root;
kpeter@663
  1204
            _target[e] = u;
kpeter@663
  1205
            _cap[e] = INF;
kpeter@663
  1206
            _flow[e] = -_supply[u];
kpeter@663
  1207
            _cost[e] = 0;
kpeter@663
  1208
            _state[e] = STATE_TREE;
kpeter@663
  1209
          } else {
kpeter@895
  1210
            _pred_dir[u] = DIR_UP;
kpeter@663
  1211
            _pi[u] = -ART_COST;
kpeter@663
  1212
            _pred[u] = f;
kpeter@663
  1213
            _source[f] = u;
kpeter@663
  1214
            _target[f] = _root;
kpeter@663
  1215
            _cap[f] = INF;
kpeter@663
  1216
            _flow[f] = _supply[u];
kpeter@663
  1217
            _state[f] = STATE_TREE;
kpeter@663
  1218
            _cost[f] = ART_COST;
kpeter@663
  1219
            _source[e] = _root;
kpeter@663
  1220
            _target[e] = u;
kpeter@663
  1221
            _cap[e] = INF;
kpeter@663
  1222
            _flow[e] = 0;
kpeter@663
  1223
            _cost[e] = 0;
kpeter@663
  1224
            _state[e] = STATE_LOWER;
kpeter@663
  1225
            ++f;
kpeter@663
  1226
          }
kpeter@663
  1227
        }
kpeter@663
  1228
        _all_arc_num = f;
kpeter@663
  1229
      }
kpeter@601
  1230
kpeter@601
  1231
      return true;
kpeter@601
  1232
    }
kpeter@601
  1233
kpeter@601
  1234
    // Find the join node
kpeter@601
  1235
    void findJoinNode() {
kpeter@603
  1236
      int u = _source[in_arc];
kpeter@603
  1237
      int v = _target[in_arc];
kpeter@601
  1238
      while (u != v) {
kpeter@604
  1239
        if (_succ_num[u] < _succ_num[v]) {
kpeter@604
  1240
          u = _parent[u];
kpeter@604
  1241
        } else {
kpeter@604
  1242
          v = _parent[v];
kpeter@604
  1243
        }
kpeter@601
  1244
      }
kpeter@601
  1245
      join = u;
kpeter@601
  1246
    }
kpeter@601
  1247
kpeter@601
  1248
    // Find the leaving arc of the cycle and returns true if the
kpeter@601
  1249
    // leaving arc is not the same as the entering arc
kpeter@601
  1250
    bool findLeavingArc() {
kpeter@601
  1251
      // Initialize first and second nodes according to the direction
kpeter@601
  1252
      // of the cycle
kpeter@895
  1253
      int first, second;
kpeter@603
  1254
      if (_state[in_arc] == STATE_LOWER) {
kpeter@603
  1255
        first  = _source[in_arc];
kpeter@603
  1256
        second = _target[in_arc];
kpeter@601
  1257
      } else {
kpeter@603
  1258
        first  = _target[in_arc];
kpeter@603
  1259
        second = _source[in_arc];
kpeter@601
  1260
      }
kpeter@603
  1261
      delta = _cap[in_arc];
kpeter@601
  1262
      int result = 0;
kpeter@895
  1263
      Value c, d;
kpeter@601
  1264
      int e;
kpeter@601
  1265
kpeter@895
  1266
      // Search the cycle form the first node to the join node
kpeter@601
  1267
      for (int u = first; u != join; u = _parent[u]) {
kpeter@601
  1268
        e = _pred[u];
kpeter@895
  1269
        d = _flow[e];
kpeter@895
  1270
        if (_pred_dir[u] == DIR_DOWN) {
kpeter@895
  1271
          c = _cap[e];
kpeter@895
  1272
          d = c >= MAX ? INF : c - d;
kpeter@895
  1273
        }
kpeter@601
  1274
        if (d < delta) {
kpeter@601
  1275
          delta = d;
kpeter@601
  1276
          u_out = u;
kpeter@601
  1277
          result = 1;
kpeter@601
  1278
        }
kpeter@601
  1279
      }
kpeter@895
  1280
kpeter@895
  1281
      // Search the cycle form the second node to the join node
kpeter@601
  1282
      for (int u = second; u != join; u = _parent[u]) {
kpeter@601
  1283
        e = _pred[u];
kpeter@895
  1284
        d = _flow[e];
kpeter@895
  1285
        if (_pred_dir[u] == DIR_UP) {
kpeter@895
  1286
          c = _cap[e];
kpeter@895
  1287
          d = c >= MAX ? INF : c - d;
kpeter@895
  1288
        }
kpeter@601
  1289
        if (d <= delta) {
kpeter@601
  1290
          delta = d;
kpeter@601
  1291
          u_out = u;
kpeter@601
  1292
          result = 2;
kpeter@601
  1293
        }
kpeter@601
  1294
      }
kpeter@601
  1295
kpeter@601
  1296
      if (result == 1) {
kpeter@601
  1297
        u_in = first;
kpeter@601
  1298
        v_in = second;
kpeter@601
  1299
      } else {
kpeter@601
  1300
        u_in = second;
kpeter@601
  1301
        v_in = first;
kpeter@601
  1302
      }
kpeter@601
  1303
      return result != 0;
kpeter@601
  1304
    }
kpeter@601
  1305
kpeter@601
  1306
    // Change _flow and _state vectors
kpeter@601
  1307
    void changeFlow(bool change) {
kpeter@601
  1308
      // Augment along the cycle
kpeter@601
  1309
      if (delta > 0) {
kpeter@641
  1310
        Value val = _state[in_arc] * delta;
kpeter@603
  1311
        _flow[in_arc] += val;
kpeter@603
  1312
        for (int u = _source[in_arc]; u != join; u = _parent[u]) {
kpeter@895
  1313
          _flow[_pred[u]] -= _pred_dir[u] * val;
kpeter@601
  1314
        }
kpeter@603
  1315
        for (int u = _target[in_arc]; u != join; u = _parent[u]) {
kpeter@895
  1316
          _flow[_pred[u]] += _pred_dir[u] * val;
kpeter@601
  1317
        }
kpeter@601
  1318
      }
kpeter@601
  1319
      // Update the state of the entering and leaving arcs
kpeter@601
  1320
      if (change) {
kpeter@603
  1321
        _state[in_arc] = STATE_TREE;
kpeter@601
  1322
        _state[_pred[u_out]] =
kpeter@601
  1323
          (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
kpeter@601
  1324
      } else {
kpeter@603
  1325
        _state[in_arc] = -_state[in_arc];
kpeter@601
  1326
      }
kpeter@601
  1327
    }
kpeter@601
  1328
kpeter@604
  1329
    // Update the tree structure
kpeter@604
  1330
    void updateTreeStructure() {
kpeter@604
  1331
      int old_rev_thread = _rev_thread[u_out];
kpeter@604
  1332
      int old_succ_num = _succ_num[u_out];
kpeter@604
  1333
      int old_last_succ = _last_succ[u_out];
kpeter@601
  1334
      v_out = _parent[u_out];
kpeter@601
  1335
kpeter@895
  1336
      // Check if u_in and u_out coincide
kpeter@895
  1337
      if (u_in == u_out) {
kpeter@895
  1338
        // Update _parent, _pred, _pred_dir
kpeter@895
  1339
        _parent[u_in] = v_in;
kpeter@895
  1340
        _pred[u_in] = in_arc;
kpeter@895
  1341
        _pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN;
kpeter@604
  1342
kpeter@895
  1343
        // Update _thread and _rev_thread
kpeter@895
  1344
        if (_thread[v_in] != u_out) {
kpeter@895
  1345
          int after = _thread[old_last_succ];
kpeter@895
  1346
          _thread[old_rev_thread] = after;
kpeter@895
  1347
          _rev_thread[after] = old_rev_thread;
kpeter@895
  1348
          after = _thread[v_in];
kpeter@895
  1349
          _thread[v_in] = u_out;
kpeter@895
  1350
          _rev_thread[u_out] = v_in;
kpeter@895
  1351
          _thread[old_last_succ] = after;
kpeter@895
  1352
          _rev_thread[after] = old_last_succ;
kpeter@895
  1353
        }
kpeter@604
  1354
      } else {
kpeter@895
  1355
        // Handle the case when old_rev_thread equals to v_in
kpeter@895
  1356
        // (it also means that join and v_out coincide)
kpeter@895
  1357
        int thread_continue = old_rev_thread == v_in ?
kpeter@895
  1358
          _thread[old_last_succ] : _thread[v_in];
kpeter@601
  1359
kpeter@895
  1360
        // Update _thread and _parent along the stem nodes (i.e. the nodes
kpeter@895
  1361
        // between u_in and u_out, whose parent have to be changed)
kpeter@895
  1362
        int stem = u_in;              // the current stem node
kpeter@895
  1363
        int par_stem = v_in;          // the new parent of stem
kpeter@895
  1364
        int next_stem;                // the next stem node
kpeter@895
  1365
        int last = _last_succ[u_in];  // the last successor of stem
kpeter@895
  1366
        int before, after = _thread[last];
kpeter@895
  1367
        _thread[v_in] = u_in;
kpeter@895
  1368
        _dirty_revs.clear();
kpeter@895
  1369
        _dirty_revs.push_back(v_in);
kpeter@895
  1370
        while (stem != u_out) {
kpeter@895
  1371
          // Insert the next stem node into the thread list
kpeter@895
  1372
          next_stem = _parent[stem];
kpeter@895
  1373
          _thread[last] = next_stem;
kpeter@895
  1374
          _dirty_revs.push_back(last);
kpeter@601
  1375
kpeter@895
  1376
          // Remove the subtree of stem from the thread list
kpeter@895
  1377
          before = _rev_thread[stem];
kpeter@895
  1378
          _thread[before] = after;
kpeter@895
  1379
          _rev_thread[after] = before;
kpeter@601
  1380
kpeter@895
  1381
          // Change the parent node and shift stem nodes
kpeter@895
  1382
          _parent[stem] = par_stem;
kpeter@895
  1383
          par_stem = stem;
kpeter@895
  1384
          stem = next_stem;
kpeter@601
  1385
kpeter@895
  1386
          // Update last and after
kpeter@895
  1387
          last = _last_succ[stem] == _last_succ[par_stem] ?
kpeter@895
  1388
            _rev_thread[par_stem] : _last_succ[stem];
kpeter@895
  1389
          after = _thread[last];
kpeter@895
  1390
        }
kpeter@895
  1391
        _parent[u_out] = par_stem;
kpeter@895
  1392
        _thread[last] = thread_continue;
kpeter@895
  1393
        _rev_thread[thread_continue] = last;
kpeter@895
  1394
        _last_succ[u_out] = last;
kpeter@601
  1395
kpeter@895
  1396
        // Remove the subtree of u_out from the thread list except for
kpeter@895
  1397
        // the case when old_rev_thread equals to v_in
kpeter@895
  1398
        if (old_rev_thread != v_in) {
kpeter@895
  1399
          _thread[old_rev_thread] = after;
kpeter@895
  1400
          _rev_thread[after] = old_rev_thread;
kpeter@895
  1401
        }
kpeter@604
  1402
kpeter@895
  1403
        // Update _rev_thread using the new _thread values
kpeter@895
  1404
        for (int i = 0; i != int(_dirty_revs.size()); ++i) {
kpeter@895
  1405
          int u = _dirty_revs[i];
kpeter@895
  1406
          _rev_thread[_thread[u]] = u;
kpeter@895
  1407
        }
kpeter@604
  1408
kpeter@895
  1409
        // Update _pred, _pred_dir, _last_succ and _succ_num for the
kpeter@895
  1410
        // stem nodes from u_out to u_in
kpeter@895
  1411
        int tmp_sc = 0, tmp_ls = _last_succ[u_out];
kpeter@895
  1412
        for (int u = u_out, p = _parent[u]; u != u_in; u = p, p = _parent[u]) {
kpeter@895
  1413
          _pred[u] = _pred[p];
kpeter@895
  1414
          _pred_dir[u] = -_pred_dir[p];
kpeter@895
  1415
          tmp_sc += _succ_num[u] - _succ_num[p];
kpeter@895
  1416
          _succ_num[u] = tmp_sc;
kpeter@895
  1417
          _last_succ[p] = tmp_ls;
kpeter@895
  1418
        }
kpeter@895
  1419
        _pred[u_in] = in_arc;
kpeter@895
  1420
        _pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN;
kpeter@895
  1421
        _succ_num[u_in] = old_succ_num;
kpeter@604
  1422
      }
kpeter@604
  1423
kpeter@604
  1424
      // Update _last_succ from v_in towards the root
kpeter@895
  1425
      int up_limit_out = _last_succ[join] == v_in ? join : -1;
kpeter@895
  1426
      int last_succ_out = _last_succ[u_out];
kpeter@895
  1427
      for (int u = v_in; u != -1 && _last_succ[u] == v_in; u = _parent[u]) {
kpeter@895
  1428
        _last_succ[u] = last_succ_out;
kpeter@604
  1429
      }
kpeter@895
  1430
kpeter@604
  1431
      // Update _last_succ from v_out towards the root
kpeter@604
  1432
      if (join != old_rev_thread && v_in != old_rev_thread) {
kpeter@895
  1433
        for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@604
  1434
             u = _parent[u]) {
kpeter@604
  1435
          _last_succ[u] = old_rev_thread;
kpeter@604
  1436
        }
kpeter@895
  1437
      }
kpeter@895
  1438
      else if (last_succ_out != old_last_succ) {
kpeter@895
  1439
        for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@604
  1440
             u = _parent[u]) {
kpeter@895
  1441
          _last_succ[u] = last_succ_out;
kpeter@604
  1442
        }
kpeter@604
  1443
      }
kpeter@604
  1444
kpeter@604
  1445
      // Update _succ_num from v_in to join
kpeter@895
  1446
      for (int u = v_in; u != join; u = _parent[u]) {
kpeter@604
  1447
        _succ_num[u] += old_succ_num;
kpeter@604
  1448
      }
kpeter@604
  1449
      // Update _succ_num from v_out to join
kpeter@895
  1450
      for (int u = v_out; u != join; u = _parent[u]) {
kpeter@604
  1451
        _succ_num[u] -= old_succ_num;
kpeter@601
  1452
      }
kpeter@601
  1453
    }
kpeter@601
  1454
kpeter@895
  1455
    // Update potentials in the subtree that has been moved
kpeter@604
  1456
    void updatePotential() {
kpeter@895
  1457
      Cost sigma = _pi[v_in] - _pi[u_in] -
kpeter@895
  1458
                   _pred_dir[u_in] * _cost[in_arc];
kpeter@608
  1459
      int end = _thread[_last_succ[u_in]];
kpeter@608
  1460
      for (int u = u_in; u != end; u = _thread[u]) {
kpeter@608
  1461
        _pi[u] += sigma;
kpeter@601
  1462
      }
kpeter@601
  1463
    }
kpeter@601
  1464
kpeter@839
  1465
    // Heuristic initial pivots
kpeter@839
  1466
    bool initialPivots() {
kpeter@839
  1467
      Value curr, total = 0;
kpeter@839
  1468
      std::vector<Node> supply_nodes, demand_nodes;
kpeter@839
  1469
      for (NodeIt u(_graph); u != INVALID; ++u) {
kpeter@839
  1470
        curr = _supply[_node_id[u]];
kpeter@839
  1471
        if (curr > 0) {
kpeter@839
  1472
          total += curr;
kpeter@839
  1473
          supply_nodes.push_back(u);
kpeter@839
  1474
        }
kpeter@839
  1475
        else if (curr < 0) {
kpeter@839
  1476
          demand_nodes.push_back(u);
kpeter@839
  1477
        }
kpeter@839
  1478
      }
kpeter@839
  1479
      if (_sum_supply > 0) total -= _sum_supply;
kpeter@839
  1480
      if (total <= 0) return true;
kpeter@839
  1481
kpeter@839
  1482
      IntVector arc_vector;
kpeter@839
  1483
      if (_sum_supply >= 0) {
kpeter@839
  1484
        if (supply_nodes.size() == 1 && demand_nodes.size() == 1) {
kpeter@839
  1485
          // Perform a reverse graph search from the sink to the source
kpeter@839
  1486
          typename GR::template NodeMap<bool> reached(_graph, false);
kpeter@839
  1487
          Node s = supply_nodes[0], t = demand_nodes[0];
kpeter@839
  1488
          std::vector<Node> stack;
kpeter@839
  1489
          reached[t] = true;
kpeter@839
  1490
          stack.push_back(t);
kpeter@839
  1491
          while (!stack.empty()) {
kpeter@839
  1492
            Node u, v = stack.back();
kpeter@839
  1493
            stack.pop_back();
kpeter@839
  1494
            if (v == s) break;
kpeter@839
  1495
            for (InArcIt a(_graph, v); a != INVALID; ++a) {
kpeter@839
  1496
              if (reached[u = _graph.source(a)]) continue;
kpeter@839
  1497
              int j = _arc_id[a];
kpeter@839
  1498
              if (_cap[j] >= total) {
kpeter@839
  1499
                arc_vector.push_back(j);
kpeter@839
  1500
                reached[u] = true;
kpeter@839
  1501
                stack.push_back(u);
kpeter@839
  1502
              }
kpeter@839
  1503
            }
kpeter@839
  1504
          }
kpeter@839
  1505
        } else {
kpeter@839
  1506
          // Find the min. cost incomming arc for each demand node
kpeter@839
  1507
          for (int i = 0; i != int(demand_nodes.size()); ++i) {
kpeter@839
  1508
            Node v = demand_nodes[i];
kpeter@839
  1509
            Cost c, min_cost = std::numeric_limits<Cost>::max();
kpeter@839
  1510
            Arc min_arc = INVALID;
kpeter@839
  1511
            for (InArcIt a(_graph, v); a != INVALID; ++a) {
kpeter@839
  1512
              c = _cost[_arc_id[a]];
kpeter@839
  1513
              if (c < min_cost) {
kpeter@839
  1514
                min_cost = c;
kpeter@839
  1515
                min_arc = a;
kpeter@839
  1516
              }
kpeter@839
  1517
            }
kpeter@839
  1518
            if (min_arc != INVALID) {
kpeter@839
  1519
              arc_vector.push_back(_arc_id[min_arc]);
kpeter@839
  1520
            }
kpeter@839
  1521
          }
kpeter@839
  1522
        }
kpeter@839
  1523
      } else {
kpeter@839
  1524
        // Find the min. cost outgoing arc for each supply node
kpeter@839
  1525
        for (int i = 0; i != int(supply_nodes.size()); ++i) {
kpeter@839
  1526
          Node u = supply_nodes[i];
kpeter@839
  1527
          Cost c, min_cost = std::numeric_limits<Cost>::max();
kpeter@839
  1528
          Arc min_arc = INVALID;
kpeter@839
  1529
          for (OutArcIt a(_graph, u); a != INVALID; ++a) {
kpeter@839
  1530
            c = _cost[_arc_id[a]];
kpeter@839
  1531
            if (c < min_cost) {
kpeter@839
  1532
              min_cost = c;
kpeter@839
  1533
              min_arc = a;
kpeter@839
  1534
            }
kpeter@839
  1535
          }
kpeter@839
  1536
          if (min_arc != INVALID) {
kpeter@839
  1537
            arc_vector.push_back(_arc_id[min_arc]);
kpeter@839
  1538
          }
kpeter@839
  1539
        }
kpeter@839
  1540
      }
kpeter@839
  1541
kpeter@839
  1542
      // Perform heuristic initial pivots
kpeter@839
  1543
      for (int i = 0; i != int(arc_vector.size()); ++i) {
kpeter@839
  1544
        in_arc = arc_vector[i];
kpeter@839
  1545
        if (_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] -
kpeter@839
  1546
            _pi[_target[in_arc]]) >= 0) continue;
kpeter@839
  1547
        findJoinNode();
kpeter@839
  1548
        bool change = findLeavingArc();
kpeter@839
  1549
        if (delta >= MAX) return false;
kpeter@839
  1550
        changeFlow(change);
kpeter@839
  1551
        if (change) {
kpeter@839
  1552
          updateTreeStructure();
kpeter@839
  1553
          updatePotential();
kpeter@839
  1554
        }
kpeter@839
  1555
      }
kpeter@839
  1556
      return true;
kpeter@839
  1557
    }
kpeter@839
  1558
kpeter@601
  1559
    // Execute the algorithm
kpeter@640
  1560
    ProblemType start(PivotRule pivot_rule) {
kpeter@601
  1561
      // Select the pivot rule implementation
kpeter@601
  1562
      switch (pivot_rule) {
kpeter@605
  1563
        case FIRST_ELIGIBLE:
kpeter@601
  1564
          return start<FirstEligiblePivotRule>();
kpeter@605
  1565
        case BEST_ELIGIBLE:
kpeter@601
  1566
          return start<BestEligiblePivotRule>();
kpeter@605
  1567
        case BLOCK_SEARCH:
kpeter@601
  1568
          return start<BlockSearchPivotRule>();
kpeter@605
  1569
        case CANDIDATE_LIST:
kpeter@601
  1570
          return start<CandidateListPivotRule>();
kpeter@605
  1571
        case ALTERING_LIST:
kpeter@601
  1572
          return start<AlteringListPivotRule>();
kpeter@601
  1573
      }
kpeter@640
  1574
      return INFEASIBLE; // avoid warning
kpeter@601
  1575
    }
kpeter@601
  1576
kpeter@605
  1577
    template <typename PivotRuleImpl>
kpeter@640
  1578
    ProblemType start() {
kpeter@605
  1579
      PivotRuleImpl pivot(*this);
kpeter@601
  1580
kpeter@839
  1581
      // Perform heuristic initial pivots
kpeter@839
  1582
      if (!initialPivots()) return UNBOUNDED;
kpeter@839
  1583
kpeter@605
  1584
      // Execute the Network Simplex algorithm
kpeter@601
  1585
      while (pivot.findEnteringArc()) {
kpeter@601
  1586
        findJoinNode();
kpeter@601
  1587
        bool change = findLeavingArc();
kpeter@811
  1588
        if (delta >= MAX) return UNBOUNDED;
kpeter@601
  1589
        changeFlow(change);
kpeter@601
  1590
        if (change) {
kpeter@604
  1591
          updateTreeStructure();
kpeter@604
  1592
          updatePotential();
kpeter@601
  1593
        }
kpeter@601
  1594
      }
alpar@877
  1595
kpeter@640
  1596
      // Check feasibility
kpeter@663
  1597
      for (int e = _search_arc_num; e != _all_arc_num; ++e) {
kpeter@663
  1598
        if (_flow[e] != 0) return INFEASIBLE;
kpeter@640
  1599
      }
kpeter@601
  1600
kpeter@642
  1601
      // Transform the solution and the supply map to the original form
kpeter@642
  1602
      if (_have_lower) {
kpeter@601
  1603
        for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1604
          Value c = _lower[i];
kpeter@642
  1605
          if (c != 0) {
kpeter@642
  1606
            _flow[i] += c;
kpeter@642
  1607
            _supply[_source[i]] += c;
kpeter@642
  1608
            _supply[_target[i]] -= c;
kpeter@642
  1609
          }
kpeter@601
  1610
        }
kpeter@601
  1611
      }
alpar@877
  1612
kpeter@663
  1613
      // Shift potentials to meet the requirements of the GEQ/LEQ type
kpeter@663
  1614
      // optimality conditions
kpeter@663
  1615
      if (_sum_supply == 0) {
kpeter@663
  1616
        if (_stype == GEQ) {
kpeter@888
  1617
          Cost max_pot = -std::numeric_limits<Cost>::max();
kpeter@663
  1618
          for (int i = 0; i != _node_num; ++i) {
kpeter@663
  1619
            if (_pi[i] > max_pot) max_pot = _pi[i];
kpeter@663
  1620
          }
kpeter@663
  1621
          if (max_pot > 0) {
kpeter@663
  1622
            for (int i = 0; i != _node_num; ++i)
kpeter@663
  1623
              _pi[i] -= max_pot;
kpeter@663
  1624
          }
kpeter@663
  1625
        } else {
kpeter@663
  1626
          Cost min_pot = std::numeric_limits<Cost>::max();
kpeter@663
  1627
          for (int i = 0; i != _node_num; ++i) {
kpeter@663
  1628
            if (_pi[i] < min_pot) min_pot = _pi[i];
kpeter@663
  1629
          }
kpeter@663
  1630
          if (min_pot < 0) {
kpeter@663
  1631
            for (int i = 0; i != _node_num; ++i)
kpeter@663
  1632
              _pi[i] -= min_pot;
kpeter@663
  1633
          }
kpeter@663
  1634
        }
kpeter@663
  1635
      }
kpeter@601
  1636
kpeter@640
  1637
      return OPTIMAL;
kpeter@601
  1638
    }
kpeter@601
  1639
kpeter@601
  1640
  }; //class NetworkSimplex
kpeter@601
  1641
kpeter@601
  1642
  ///@}
kpeter@601
  1643
kpeter@601
  1644
} //namespace lemon
kpeter@601
  1645
kpeter@601
  1646
#endif //LEMON_NETWORK_SIMPLEX_H