lemon/network_simplex.h
author Alpar Juttner <alpar@cs.elte.hu>
Tue, 20 Dec 2011 19:35:47 +0100
changeset 969 cfdbf1574403
parent 877 141f9c0db4a3
parent 888 5205145fabf6
child 895 dca9eed2c375
permissions -rw-r--r--
Merge
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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, %NetworkSimplex is the fastest implementation available
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  /// in LEMON for this problem.
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  /// Moreover, it supports both directions of the supply/demand inequality
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  /// 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 number types must be signed and all input data 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 pivot rule
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    /// implementations that significantly affect the running time
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    /// of the algorithm.
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    /// By default, \ref BLOCK_SEARCH "Block Search" is used, which
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    /// proved to be the most efficient and the most robust on various
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    /// test inputs.
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    /// However, another pivot rule can be selected using the \ref run()
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    /// function with the proper parameter.
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    enum PivotRule {
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      /// The \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 the several best eligible arcs from the former
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      /// candidate list and extends this list in every iteration.
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      ALTERING_LIST
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    };
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  private:
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    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
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    typedef 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<char> BoolVector;
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    // Note: vector<char> is used instead of vector<bool> 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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    typedef std::vector<signed char> StateVector;
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    // Note: vector<signed char> is used instead of vector<ArcState> for
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    // efficiency reasons
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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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    IntVector _dirty_revs;
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    BoolVector _forward;
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    StateVector _state;
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    int _root;
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    // Temporary data used in the current pivot iteration
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    int in_arc, join, u_in, v_in, u_out, v_out;
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    int first, second, right, last;
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    int stem, par_stem, new_stem;
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    Value delta;
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    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 StateVector &_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 StateVector &_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 StateVector &_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;
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            cnt = _block_size;
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          }
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        }
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        if (min >= 0) return false;
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      search_end:
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        _next_arc = e;
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        return true;
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      }
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    }; //class BlockSearchPivotRule
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    // Implementation of the Candidate List pivot rule
kpeter@601
   409
    class CandidateListPivotRule
kpeter@601
   410
    {
kpeter@601
   411
    private:
kpeter@601
   412
kpeter@601
   413
      // References to the NetworkSimplex class
kpeter@601
   414
      const IntVector  &_source;
kpeter@601
   415
      const IntVector  &_target;
kpeter@607
   416
      const CostVector &_cost;
kpeter@862
   417
      const StateVector &_state;
kpeter@607
   418
      const CostVector &_pi;
kpeter@601
   419
      int &_in_arc;
kpeter@663
   420
      int _search_arc_num;
kpeter@601
   421
kpeter@601
   422
      // Pivot rule data
kpeter@601
   423
      IntVector _candidates;
kpeter@601
   424
      int _list_length, _minor_limit;
kpeter@601
   425
      int _curr_length, _minor_count;
kpeter@601
   426
      int _next_arc;
kpeter@601
   427
kpeter@601
   428
    public:
kpeter@601
   429
kpeter@601
   430
      /// Constructor
kpeter@601
   431
      CandidateListPivotRule(NetworkSimplex &ns) :
kpeter@603
   432
        _source(ns._source), _target(ns._target),
kpeter@601
   433
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@663
   434
        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
kpeter@663
   435
        _next_arc(0)
kpeter@601
   436
      {
kpeter@601
   437
        // The main parameters of the pivot rule
kpeter@727
   438
        const double LIST_LENGTH_FACTOR = 0.25;
kpeter@601
   439
        const int MIN_LIST_LENGTH = 10;
kpeter@601
   440
        const double MINOR_LIMIT_FACTOR = 0.1;
kpeter@601
   441
        const int MIN_MINOR_LIMIT = 3;
kpeter@601
   442
alpar@612
   443
        _list_length = std::max( int(LIST_LENGTH_FACTOR *
kpeter@663
   444
                                     std::sqrt(double(_search_arc_num))),
kpeter@601
   445
                                 MIN_LIST_LENGTH );
kpeter@601
   446
        _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
kpeter@601
   447
                                 MIN_MINOR_LIMIT );
kpeter@601
   448
        _curr_length = _minor_count = 0;
kpeter@601
   449
        _candidates.resize(_list_length);
kpeter@601
   450
      }
kpeter@601
   451
kpeter@601
   452
      /// Find next entering arc
kpeter@601
   453
      bool findEnteringArc() {
kpeter@607
   454
        Cost min, c;
kpeter@727
   455
        int e;
kpeter@601
   456
        if (_curr_length > 0 && _minor_count < _minor_limit) {
kpeter@601
   457
          // Minor iteration: select the best eligible arc from the
kpeter@601
   458
          // current candidate list
kpeter@601
   459
          ++_minor_count;
kpeter@601
   460
          min = 0;
kpeter@601
   461
          for (int i = 0; i < _curr_length; ++i) {
kpeter@601
   462
            e = _candidates[i];
kpeter@601
   463
            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   464
            if (c < min) {
kpeter@601
   465
              min = c;
kpeter@727
   466
              _in_arc = e;
kpeter@601
   467
            }
kpeter@727
   468
            else if (c >= 0) {
kpeter@601
   469
              _candidates[i--] = _candidates[--_curr_length];
kpeter@601
   470
            }
kpeter@601
   471
          }
kpeter@727
   472
          if (min < 0) return true;
kpeter@601
   473
        }
kpeter@601
   474
kpeter@601
   475
        // Major iteration: build a new candidate list
kpeter@601
   476
        min = 0;
kpeter@601
   477
        _curr_length = 0;
kpeter@839
   478
        for (e = _next_arc; e != _search_arc_num; ++e) {
kpeter@601
   479
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   480
          if (c < 0) {
kpeter@601
   481
            _candidates[_curr_length++] = e;
kpeter@601
   482
            if (c < min) {
kpeter@601
   483
              min = c;
kpeter@727
   484
              _in_arc = e;
kpeter@601
   485
            }
kpeter@727
   486
            if (_curr_length == _list_length) goto search_end;
kpeter@601
   487
          }
kpeter@601
   488
        }
kpeter@839
   489
        for (e = 0; e != _next_arc; ++e) {
kpeter@727
   490
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@727
   491
          if (c < 0) {
kpeter@727
   492
            _candidates[_curr_length++] = e;
kpeter@727
   493
            if (c < min) {
kpeter@727
   494
              min = c;
kpeter@727
   495
              _in_arc = e;
kpeter@601
   496
            }
kpeter@727
   497
            if (_curr_length == _list_length) goto search_end;
kpeter@601
   498
          }
kpeter@601
   499
        }
kpeter@601
   500
        if (_curr_length == 0) return false;
alpar@877
   501
alpar@877
   502
      search_end:
kpeter@601
   503
        _minor_count = 1;
kpeter@601
   504
        _next_arc = e;
kpeter@601
   505
        return true;
kpeter@601
   506
      }
kpeter@601
   507
kpeter@601
   508
    }; //class CandidateListPivotRule
kpeter@601
   509
kpeter@601
   510
kpeter@605
   511
    // Implementation of the Altering Candidate List pivot rule
kpeter@601
   512
    class AlteringListPivotRule
kpeter@601
   513
    {
kpeter@601
   514
    private:
kpeter@601
   515
kpeter@601
   516
      // References to the NetworkSimplex class
kpeter@601
   517
      const IntVector  &_source;
kpeter@601
   518
      const IntVector  &_target;
kpeter@607
   519
      const CostVector &_cost;
kpeter@862
   520
      const StateVector &_state;
kpeter@607
   521
      const CostVector &_pi;
kpeter@601
   522
      int &_in_arc;
kpeter@663
   523
      int _search_arc_num;
kpeter@601
   524
kpeter@601
   525
      // Pivot rule data
kpeter@601
   526
      int _block_size, _head_length, _curr_length;
kpeter@601
   527
      int _next_arc;
kpeter@601
   528
      IntVector _candidates;
kpeter@607
   529
      CostVector _cand_cost;
kpeter@601
   530
kpeter@601
   531
      // Functor class to compare arcs during sort of the candidate list
kpeter@601
   532
      class SortFunc
kpeter@601
   533
      {
kpeter@601
   534
      private:
kpeter@607
   535
        const CostVector &_map;
kpeter@601
   536
      public:
kpeter@607
   537
        SortFunc(const CostVector &map) : _map(map) {}
kpeter@601
   538
        bool operator()(int left, int right) {
kpeter@601
   539
          return _map[left] > _map[right];
kpeter@601
   540
        }
kpeter@601
   541
      };
kpeter@601
   542
kpeter@601
   543
      SortFunc _sort_func;
kpeter@601
   544
kpeter@601
   545
    public:
kpeter@601
   546
kpeter@605
   547
      // Constructor
kpeter@601
   548
      AlteringListPivotRule(NetworkSimplex &ns) :
kpeter@603
   549
        _source(ns._source), _target(ns._target),
kpeter@601
   550
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@663
   551
        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
kpeter@663
   552
        _next_arc(0), _cand_cost(ns._search_arc_num), _sort_func(_cand_cost)
kpeter@601
   553
      {
kpeter@601
   554
        // The main parameters of the pivot rule
kpeter@727
   555
        const double BLOCK_SIZE_FACTOR = 1.0;
kpeter@601
   556
        const int MIN_BLOCK_SIZE = 10;
kpeter@601
   557
        const double HEAD_LENGTH_FACTOR = 0.1;
kpeter@601
   558
        const int MIN_HEAD_LENGTH = 3;
kpeter@601
   559
alpar@612
   560
        _block_size = std::max( int(BLOCK_SIZE_FACTOR *
kpeter@663
   561
                                    std::sqrt(double(_search_arc_num))),
kpeter@601
   562
                                MIN_BLOCK_SIZE );
kpeter@601
   563
        _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),
kpeter@601
   564
                                 MIN_HEAD_LENGTH );
kpeter@601
   565
        _candidates.resize(_head_length + _block_size);
kpeter@601
   566
        _curr_length = 0;
kpeter@601
   567
      }
kpeter@601
   568
kpeter@605
   569
      // Find next entering arc
kpeter@601
   570
      bool findEnteringArc() {
kpeter@601
   571
        // Check the current candidate list
kpeter@601
   572
        int e;
kpeter@839
   573
        for (int i = 0; i != _curr_length; ++i) {
kpeter@601
   574
          e = _candidates[i];
kpeter@601
   575
          _cand_cost[e] = _state[e] *
kpeter@601
   576
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   577
          if (_cand_cost[e] >= 0) {
kpeter@601
   578
            _candidates[i--] = _candidates[--_curr_length];
kpeter@601
   579
          }
kpeter@601
   580
        }
kpeter@601
   581
kpeter@601
   582
        // Extend the list
kpeter@601
   583
        int cnt = _block_size;
kpeter@601
   584
        int limit = _head_length;
kpeter@601
   585
kpeter@839
   586
        for (e = _next_arc; e != _search_arc_num; ++e) {
kpeter@601
   587
          _cand_cost[e] = _state[e] *
kpeter@601
   588
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   589
          if (_cand_cost[e] < 0) {
kpeter@601
   590
            _candidates[_curr_length++] = e;
kpeter@601
   591
          }
kpeter@601
   592
          if (--cnt == 0) {
kpeter@727
   593
            if (_curr_length > limit) goto search_end;
kpeter@601
   594
            limit = 0;
kpeter@601
   595
            cnt = _block_size;
kpeter@601
   596
          }
kpeter@601
   597
        }
kpeter@839
   598
        for (e = 0; e != _next_arc; ++e) {
kpeter@727
   599
          _cand_cost[e] = _state[e] *
kpeter@727
   600
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@727
   601
          if (_cand_cost[e] < 0) {
kpeter@727
   602
            _candidates[_curr_length++] = e;
kpeter@727
   603
          }
kpeter@727
   604
          if (--cnt == 0) {
kpeter@727
   605
            if (_curr_length > limit) goto search_end;
kpeter@727
   606
            limit = 0;
kpeter@727
   607
            cnt = _block_size;
kpeter@601
   608
          }
kpeter@601
   609
        }
kpeter@601
   610
        if (_curr_length == 0) return false;
alpar@877
   611
kpeter@727
   612
      search_end:
kpeter@601
   613
kpeter@601
   614
        // Make heap of the candidate list (approximating a partial sort)
kpeter@601
   615
        make_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@601
   616
                   _sort_func );
kpeter@601
   617
kpeter@601
   618
        // Pop the first element of the heap
kpeter@601
   619
        _in_arc = _candidates[0];
kpeter@727
   620
        _next_arc = e;
kpeter@601
   621
        pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@601
   622
                  _sort_func );
kpeter@601
   623
        _curr_length = std::min(_head_length, _curr_length - 1);
kpeter@601
   624
        return true;
kpeter@601
   625
      }
kpeter@601
   626
kpeter@601
   627
    }; //class AlteringListPivotRule
kpeter@601
   628
kpeter@601
   629
  public:
kpeter@601
   630
kpeter@605
   631
    /// \brief Constructor.
kpeter@601
   632
    ///
kpeter@609
   633
    /// The constructor of the class.
kpeter@601
   634
    ///
kpeter@603
   635
    /// \param graph The digraph the algorithm runs on.
kpeter@728
   636
    /// \param arc_mixing Indicate if the arcs have to be stored in a
alpar@877
   637
    /// mixed order in the internal data structure.
kpeter@728
   638
    /// In special cases, it could lead to better overall performance,
kpeter@728
   639
    /// but it is usually slower. Therefore it is disabled by default.
kpeter@728
   640
    NetworkSimplex(const GR& graph, bool arc_mixing = false) :
kpeter@642
   641
      _graph(graph), _node_id(graph), _arc_id(graph),
kpeter@830
   642
      _arc_mixing(arc_mixing),
kpeter@811
   643
      MAX(std::numeric_limits<Value>::max()),
kpeter@641
   644
      INF(std::numeric_limits<Value>::has_infinity ?
kpeter@811
   645
          std::numeric_limits<Value>::infinity() : MAX)
kpeter@605
   646
    {
kpeter@812
   647
      // Check the number types
kpeter@641
   648
      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
kpeter@640
   649
        "The flow type of NetworkSimplex must be signed");
kpeter@640
   650
      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
kpeter@640
   651
        "The cost type of NetworkSimplex must be signed");
kpeter@601
   652
kpeter@830
   653
      // Reset data structures
kpeter@729
   654
      reset();
kpeter@601
   655
    }
kpeter@601
   656
kpeter@609
   657
    /// \name Parameters
kpeter@609
   658
    /// The parameters of the algorithm can be specified using these
kpeter@609
   659
    /// functions.
kpeter@609
   660
kpeter@609
   661
    /// @{
kpeter@609
   662
kpeter@605
   663
    /// \brief Set the lower bounds on the arcs.
kpeter@605
   664
    ///
kpeter@605
   665
    /// This function sets the lower bounds on the arcs.
kpeter@640
   666
    /// If it is not used before calling \ref run(), the lower bounds
kpeter@640
   667
    /// will be set to zero on all arcs.
kpeter@605
   668
    ///
kpeter@605
   669
    /// \param map An arc map storing the lower bounds.
kpeter@641
   670
    /// Its \c Value type must be convertible to the \c Value type
kpeter@605
   671
    /// of the algorithm.
kpeter@605
   672
    ///
kpeter@605
   673
    /// \return <tt>(*this)</tt>
kpeter@640
   674
    template <typename LowerMap>
kpeter@640
   675
    NetworkSimplex& lowerMap(const LowerMap& map) {
kpeter@642
   676
      _have_lower = true;
kpeter@605
   677
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   678
        _lower[_arc_id[a]] = map[a];
kpeter@605
   679
      }
kpeter@605
   680
      return *this;
kpeter@605
   681
    }
kpeter@605
   682
kpeter@605
   683
    /// \brief Set the upper bounds (capacities) on the arcs.
kpeter@605
   684
    ///
kpeter@605
   685
    /// This function sets the upper bounds (capacities) on the arcs.
kpeter@640
   686
    /// If it is not used before calling \ref run(), the upper bounds
kpeter@640
   687
    /// will be set to \ref INF on all arcs (i.e. the flow value will be
kpeter@812
   688
    /// unbounded from above).
kpeter@605
   689
    ///
kpeter@605
   690
    /// \param map An arc map storing the upper bounds.
kpeter@641
   691
    /// Its \c Value type must be convertible to the \c Value type
kpeter@605
   692
    /// of the algorithm.
kpeter@605
   693
    ///
kpeter@605
   694
    /// \return <tt>(*this)</tt>
kpeter@640
   695
    template<typename UpperMap>
kpeter@640
   696
    NetworkSimplex& upperMap(const UpperMap& map) {
kpeter@605
   697
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   698
        _upper[_arc_id[a]] = map[a];
kpeter@605
   699
      }
kpeter@605
   700
      return *this;
kpeter@605
   701
    }
kpeter@605
   702
kpeter@605
   703
    /// \brief Set the costs of the arcs.
kpeter@605
   704
    ///
kpeter@605
   705
    /// This function sets the costs of the arcs.
kpeter@605
   706
    /// If it is not used before calling \ref run(), the costs
kpeter@605
   707
    /// will be set to \c 1 on all arcs.
kpeter@605
   708
    ///
kpeter@605
   709
    /// \param map An arc map storing the costs.
kpeter@607
   710
    /// Its \c Value type must be convertible to the \c Cost type
kpeter@605
   711
    /// of the algorithm.
kpeter@605
   712
    ///
kpeter@605
   713
    /// \return <tt>(*this)</tt>
kpeter@640
   714
    template<typename CostMap>
kpeter@640
   715
    NetworkSimplex& costMap(const CostMap& map) {
kpeter@605
   716
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   717
        _cost[_arc_id[a]] = map[a];
kpeter@605
   718
      }
kpeter@605
   719
      return *this;
kpeter@605
   720
    }
kpeter@605
   721
kpeter@605
   722
    /// \brief Set the supply values of the nodes.
kpeter@605
   723
    ///
kpeter@605
   724
    /// This function sets the supply values of the nodes.
kpeter@605
   725
    /// If neither this function nor \ref stSupply() is used before
kpeter@605
   726
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@605
   727
    ///
kpeter@605
   728
    /// \param map A node map storing the supply values.
kpeter@641
   729
    /// Its \c Value type must be convertible to the \c Value type
kpeter@605
   730
    /// of the algorithm.
kpeter@605
   731
    ///
kpeter@605
   732
    /// \return <tt>(*this)</tt>
kpeter@640
   733
    template<typename SupplyMap>
kpeter@640
   734
    NetworkSimplex& supplyMap(const SupplyMap& map) {
kpeter@605
   735
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@642
   736
        _supply[_node_id[n]] = map[n];
kpeter@605
   737
      }
kpeter@605
   738
      return *this;
kpeter@605
   739
    }
kpeter@605
   740
kpeter@605
   741
    /// \brief Set single source and target nodes and a supply value.
kpeter@605
   742
    ///
kpeter@605
   743
    /// This function sets a single source node and a single target node
kpeter@605
   744
    /// and the required flow value.
kpeter@605
   745
    /// If neither this function nor \ref supplyMap() is used before
kpeter@605
   746
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@605
   747
    ///
kpeter@640
   748
    /// Using this function has the same effect as using \ref supplyMap()
kpeter@640
   749
    /// with such a map in which \c k is assigned to \c s, \c -k is
kpeter@640
   750
    /// assigned to \c t and all other nodes have zero supply value.
kpeter@640
   751
    ///
kpeter@605
   752
    /// \param s The source node.
kpeter@605
   753
    /// \param t The target node.
kpeter@605
   754
    /// \param k The required amount of flow from node \c s to node \c t
kpeter@605
   755
    /// (i.e. the supply of \c s and the demand of \c t).
kpeter@605
   756
    ///
kpeter@605
   757
    /// \return <tt>(*this)</tt>
kpeter@641
   758
    NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) {
kpeter@642
   759
      for (int i = 0; i != _node_num; ++i) {
kpeter@642
   760
        _supply[i] = 0;
kpeter@642
   761
      }
kpeter@642
   762
      _supply[_node_id[s]] =  k;
kpeter@642
   763
      _supply[_node_id[t]] = -k;
kpeter@605
   764
      return *this;
kpeter@605
   765
    }
alpar@877
   766
kpeter@640
   767
    /// \brief Set the type of the supply constraints.
kpeter@609
   768
    ///
kpeter@640
   769
    /// This function sets the type of the supply/demand constraints.
kpeter@640
   770
    /// If it is not used before calling \ref run(), the \ref GEQ supply
kpeter@609
   771
    /// type will be used.
kpeter@609
   772
    ///
kpeter@786
   773
    /// For more information, see \ref SupplyType.
kpeter@609
   774
    ///
kpeter@609
   775
    /// \return <tt>(*this)</tt>
kpeter@640
   776
    NetworkSimplex& supplyType(SupplyType supply_type) {
kpeter@640
   777
      _stype = supply_type;
kpeter@609
   778
      return *this;
kpeter@609
   779
    }
kpeter@605
   780
kpeter@609
   781
    /// @}
kpeter@601
   782
kpeter@605
   783
    /// \name Execution Control
kpeter@605
   784
    /// The algorithm can be executed using \ref run().
kpeter@605
   785
kpeter@601
   786
    /// @{
kpeter@601
   787
kpeter@601
   788
    /// \brief Run the algorithm.
kpeter@601
   789
    ///
kpeter@601
   790
    /// This function runs the algorithm.
kpeter@609
   791
    /// The paramters can be specified using functions \ref lowerMap(),
alpar@877
   792
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(),
kpeter@642
   793
    /// \ref supplyType().
kpeter@609
   794
    /// For example,
kpeter@605
   795
    /// \code
kpeter@605
   796
    ///   NetworkSimplex<ListDigraph> ns(graph);
kpeter@640
   797
    ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@605
   798
    ///     .supplyMap(sup).run();
kpeter@605
   799
    /// \endcode
kpeter@601
   800
    ///
kpeter@830
   801
    /// This function can be called more than once. All the given parameters
kpeter@830
   802
    /// are kept for the next call, unless \ref resetParams() or \ref reset()
kpeter@830
   803
    /// is used, thus only the modified parameters have to be set again.
kpeter@830
   804
    /// If the underlying digraph was also modified after the construction
kpeter@830
   805
    /// of the class (or the last \ref reset() call), then the \ref reset()
kpeter@830
   806
    /// function must be called.
kpeter@606
   807
    ///
kpeter@605
   808
    /// \param pivot_rule The pivot rule that will be used during the
kpeter@786
   809
    /// algorithm. For more information, see \ref PivotRule.
kpeter@601
   810
    ///
kpeter@640
   811
    /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@640
   812
    /// \n \c OPTIMAL if the problem has optimal solution
kpeter@640
   813
    /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@640
   814
    /// optimal flow and node potentials (primal and dual solutions),
kpeter@640
   815
    /// \n \c UNBOUNDED if the objective function of the problem is
kpeter@640
   816
    /// unbounded, i.e. there is a directed cycle having negative total
kpeter@640
   817
    /// cost and infinite upper bound.
kpeter@640
   818
    ///
kpeter@640
   819
    /// \see ProblemType, PivotRule
kpeter@830
   820
    /// \see resetParams(), reset()
kpeter@640
   821
    ProblemType run(PivotRule pivot_rule = BLOCK_SEARCH) {
kpeter@640
   822
      if (!init()) return INFEASIBLE;
kpeter@640
   823
      return start(pivot_rule);
kpeter@601
   824
    }
kpeter@601
   825
kpeter@606
   826
    /// \brief Reset all the parameters that have been given before.
kpeter@606
   827
    ///
kpeter@606
   828
    /// This function resets all the paramaters that have been given
kpeter@609
   829
    /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@642
   830
    /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType().
kpeter@606
   831
    ///
kpeter@830
   832
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830
   833
    /// parameters are kept for the next \ref run() call, unless
kpeter@830
   834
    /// \ref resetParams() or \ref reset() is used.
kpeter@830
   835
    /// If the underlying digraph was also modified after the construction
kpeter@830
   836
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830
   837
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@606
   838
    ///
kpeter@606
   839
    /// For example,
kpeter@606
   840
    /// \code
kpeter@606
   841
    ///   NetworkSimplex<ListDigraph> ns(graph);
kpeter@606
   842
    ///
kpeter@606
   843
    ///   // First run
kpeter@640
   844
    ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@606
   845
    ///     .supplyMap(sup).run();
kpeter@606
   846
    ///
kpeter@830
   847
    ///   // Run again with modified cost map (resetParams() is not called,
kpeter@606
   848
    ///   // so only the cost map have to be set again)
kpeter@606
   849
    ///   cost[e] += 100;
kpeter@606
   850
    ///   ns.costMap(cost).run();
kpeter@606
   851
    ///
kpeter@830
   852
    ///   // Run again from scratch using resetParams()
kpeter@606
   853
    ///   // (the lower bounds will be set to zero on all arcs)
kpeter@830
   854
    ///   ns.resetParams();
kpeter@640
   855
    ///   ns.upperMap(capacity).costMap(cost)
kpeter@606
   856
    ///     .supplyMap(sup).run();
kpeter@606
   857
    /// \endcode
kpeter@606
   858
    ///
kpeter@606
   859
    /// \return <tt>(*this)</tt>
kpeter@830
   860
    ///
kpeter@830
   861
    /// \see reset(), run()
kpeter@830
   862
    NetworkSimplex& resetParams() {
kpeter@642
   863
      for (int i = 0; i != _node_num; ++i) {
kpeter@642
   864
        _supply[i] = 0;
kpeter@642
   865
      }
kpeter@642
   866
      for (int i = 0; i != _arc_num; ++i) {
kpeter@642
   867
        _lower[i] = 0;
kpeter@642
   868
        _upper[i] = INF;
kpeter@642
   869
        _cost[i] = 1;
kpeter@642
   870
      }
kpeter@642
   871
      _have_lower = false;
kpeter@640
   872
      _stype = GEQ;
kpeter@606
   873
      return *this;
kpeter@606
   874
    }
kpeter@606
   875
kpeter@830
   876
    /// \brief Reset the internal data structures and all the parameters
kpeter@830
   877
    /// that have been given before.
kpeter@830
   878
    ///
kpeter@830
   879
    /// This function resets the internal data structures and all the
kpeter@830
   880
    /// paramaters that have been given before using functions \ref lowerMap(),
kpeter@830
   881
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(),
kpeter@830
   882
    /// \ref supplyType().
kpeter@830
   883
    ///
kpeter@830
   884
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830
   885
    /// parameters are kept for the next \ref run() call, unless
kpeter@830
   886
    /// \ref resetParams() or \ref reset() is used.
kpeter@830
   887
    /// If the underlying digraph was also modified after the construction
kpeter@830
   888
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830
   889
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@830
   890
    ///
kpeter@830
   891
    /// See \ref resetParams() for examples.
kpeter@830
   892
    ///
kpeter@830
   893
    /// \return <tt>(*this)</tt>
kpeter@830
   894
    ///
kpeter@830
   895
    /// \see resetParams(), run()
kpeter@830
   896
    NetworkSimplex& reset() {
kpeter@830
   897
      // Resize vectors
kpeter@830
   898
      _node_num = countNodes(_graph);
kpeter@830
   899
      _arc_num = countArcs(_graph);
kpeter@830
   900
      int all_node_num = _node_num + 1;
kpeter@830
   901
      int max_arc_num = _arc_num + 2 * _node_num;
kpeter@830
   902
kpeter@830
   903
      _source.resize(max_arc_num);
kpeter@830
   904
      _target.resize(max_arc_num);
kpeter@830
   905
kpeter@830
   906
      _lower.resize(_arc_num);
kpeter@830
   907
      _upper.resize(_arc_num);
kpeter@830
   908
      _cap.resize(max_arc_num);
kpeter@830
   909
      _cost.resize(max_arc_num);
kpeter@830
   910
      _supply.resize(all_node_num);
kpeter@830
   911
      _flow.resize(max_arc_num);
kpeter@830
   912
      _pi.resize(all_node_num);
kpeter@830
   913
kpeter@830
   914
      _parent.resize(all_node_num);
kpeter@830
   915
      _pred.resize(all_node_num);
kpeter@830
   916
      _forward.resize(all_node_num);
kpeter@830
   917
      _thread.resize(all_node_num);
kpeter@830
   918
      _rev_thread.resize(all_node_num);
kpeter@830
   919
      _succ_num.resize(all_node_num);
kpeter@830
   920
      _last_succ.resize(all_node_num);
kpeter@830
   921
      _state.resize(max_arc_num);
kpeter@830
   922
kpeter@830
   923
      // Copy the graph
kpeter@830
   924
      int i = 0;
kpeter@830
   925
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830
   926
        _node_id[n] = i;
kpeter@830
   927
      }
kpeter@830
   928
      if (_arc_mixing) {
kpeter@830
   929
        // Store the arcs in a mixed order
kpeter@830
   930
        int k = std::max(int(std::sqrt(double(_arc_num))), 10);
kpeter@830
   931
        int i = 0, j = 0;
kpeter@830
   932
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@830
   933
          _arc_id[a] = i;
kpeter@830
   934
          _source[i] = _node_id[_graph.source(a)];
kpeter@830
   935
          _target[i] = _node_id[_graph.target(a)];
kpeter@830
   936
          if ((i += k) >= _arc_num) i = ++j;
kpeter@830
   937
        }
kpeter@830
   938
      } else {
kpeter@830
   939
        // Store the arcs in the original order
kpeter@830
   940
        int i = 0;
kpeter@830
   941
        for (ArcIt a(_graph); a != INVALID; ++a, ++i) {
kpeter@830
   942
          _arc_id[a] = i;
kpeter@830
   943
          _source[i] = _node_id[_graph.source(a)];
kpeter@830
   944
          _target[i] = _node_id[_graph.target(a)];
kpeter@830
   945
        }
kpeter@830
   946
      }
alpar@877
   947
kpeter@830
   948
      // Reset parameters
kpeter@830
   949
      resetParams();
kpeter@830
   950
      return *this;
kpeter@830
   951
    }
alpar@877
   952
kpeter@601
   953
    /// @}
kpeter@601
   954
kpeter@601
   955
    /// \name Query Functions
kpeter@601
   956
    /// The results of the algorithm can be obtained using these
kpeter@601
   957
    /// functions.\n
kpeter@605
   958
    /// The \ref run() function must be called before using them.
kpeter@605
   959
kpeter@601
   960
    /// @{
kpeter@601
   961
kpeter@605
   962
    /// \brief Return the total cost of the found flow.
kpeter@605
   963
    ///
kpeter@605
   964
    /// This function returns the total cost of the found flow.
kpeter@640
   965
    /// Its complexity is O(e).
kpeter@605
   966
    ///
kpeter@605
   967
    /// \note The return type of the function can be specified as a
kpeter@605
   968
    /// template parameter. For example,
kpeter@605
   969
    /// \code
kpeter@605
   970
    ///   ns.totalCost<double>();
kpeter@605
   971
    /// \endcode
kpeter@607
   972
    /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@605
   973
    /// type of the algorithm, which is the default return type of the
kpeter@605
   974
    /// function.
kpeter@605
   975
    ///
kpeter@605
   976
    /// \pre \ref run() must be called before using this function.
kpeter@642
   977
    template <typename Number>
kpeter@642
   978
    Number totalCost() const {
kpeter@642
   979
      Number c = 0;
kpeter@642
   980
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   981
        int i = _arc_id[a];
kpeter@642
   982
        c += Number(_flow[i]) * Number(_cost[i]);
kpeter@605
   983
      }
kpeter@605
   984
      return c;
kpeter@605
   985
    }
kpeter@605
   986
kpeter@605
   987
#ifndef DOXYGEN
kpeter@607
   988
    Cost totalCost() const {
kpeter@607
   989
      return totalCost<Cost>();
kpeter@605
   990
    }
kpeter@605
   991
#endif
kpeter@605
   992
kpeter@605
   993
    /// \brief Return the flow on the given arc.
kpeter@605
   994
    ///
kpeter@605
   995
    /// This function returns the flow on the given arc.
kpeter@605
   996
    ///
kpeter@605
   997
    /// \pre \ref run() must be called before using this function.
kpeter@641
   998
    Value flow(const Arc& a) const {
kpeter@642
   999
      return _flow[_arc_id[a]];
kpeter@605
  1000
    }
kpeter@605
  1001
kpeter@642
  1002
    /// \brief Return the flow map (the primal solution).
kpeter@601
  1003
    ///
kpeter@642
  1004
    /// This function copies the flow value on each arc into the given
kpeter@642
  1005
    /// map. The \c Value type of the algorithm must be convertible to
kpeter@642
  1006
    /// the \c Value type of the map.
kpeter@601
  1007
    ///
kpeter@601
  1008
    /// \pre \ref run() must be called before using this function.
kpeter@642
  1009
    template <typename FlowMap>
kpeter@642
  1010
    void flowMap(FlowMap &map) const {
kpeter@642
  1011
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
  1012
        map.set(a, _flow[_arc_id[a]]);
kpeter@642
  1013
      }
kpeter@601
  1014
    }
kpeter@601
  1015
kpeter@605
  1016
    /// \brief Return the potential (dual value) of the given node.
kpeter@605
  1017
    ///
kpeter@605
  1018
    /// This function returns the potential (dual value) of the
kpeter@605
  1019
    /// given node.
kpeter@605
  1020
    ///
kpeter@605
  1021
    /// \pre \ref run() must be called before using this function.
kpeter@607
  1022
    Cost potential(const Node& n) const {
kpeter@642
  1023
      return _pi[_node_id[n]];
kpeter@605
  1024
    }
kpeter@605
  1025
kpeter@642
  1026
    /// \brief Return the potential map (the dual solution).
kpeter@601
  1027
    ///
kpeter@642
  1028
    /// This function copies the potential (dual value) of each node
kpeter@642
  1029
    /// into the given map.
kpeter@642
  1030
    /// The \c Cost type of the algorithm must be convertible to the
kpeter@642
  1031
    /// \c Value type of the map.
kpeter@601
  1032
    ///
kpeter@601
  1033
    /// \pre \ref run() must be called before using this function.
kpeter@642
  1034
    template <typename PotentialMap>
kpeter@642
  1035
    void potentialMap(PotentialMap &map) const {
kpeter@642
  1036
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@642
  1037
        map.set(n, _pi[_node_id[n]]);
kpeter@642
  1038
      }
kpeter@601
  1039
    }
kpeter@601
  1040
kpeter@601
  1041
    /// @}
kpeter@601
  1042
kpeter@601
  1043
  private:
kpeter@601
  1044
kpeter@601
  1045
    // Initialize internal data structures
kpeter@601
  1046
    bool init() {
kpeter@605
  1047
      if (_node_num == 0) return false;
kpeter@601
  1048
kpeter@642
  1049
      // Check the sum of supply values
kpeter@642
  1050
      _sum_supply = 0;
kpeter@642
  1051
      for (int i = 0; i != _node_num; ++i) {
kpeter@642
  1052
        _sum_supply += _supply[i];
kpeter@642
  1053
      }
alpar@643
  1054
      if ( !((_stype == GEQ && _sum_supply <= 0) ||
alpar@643
  1055
             (_stype == LEQ && _sum_supply >= 0)) ) return false;
kpeter@601
  1056
kpeter@642
  1057
      // Remove non-zero lower bounds
kpeter@642
  1058
      if (_have_lower) {
kpeter@642
  1059
        for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1060
          Value c = _lower[i];
kpeter@642
  1061
          if (c >= 0) {
kpeter@811
  1062
            _cap[i] = _upper[i] < MAX ? _upper[i] - c : INF;
kpeter@642
  1063
          } else {
kpeter@811
  1064
            _cap[i] = _upper[i] < MAX + c ? _upper[i] - c : INF;
kpeter@642
  1065
          }
kpeter@642
  1066
          _supply[_source[i]] -= c;
kpeter@642
  1067
          _supply[_target[i]] += c;
kpeter@642
  1068
        }
kpeter@642
  1069
      } else {
kpeter@642
  1070
        for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1071
          _cap[i] = _upper[i];
kpeter@642
  1072
        }
kpeter@605
  1073
      }
kpeter@601
  1074
kpeter@609
  1075
      // Initialize artifical cost
kpeter@640
  1076
      Cost ART_COST;
kpeter@609
  1077
      if (std::numeric_limits<Cost>::is_exact) {
kpeter@663
  1078
        ART_COST = std::numeric_limits<Cost>::max() / 2 + 1;
kpeter@609
  1079
      } else {
kpeter@888
  1080
        ART_COST = 0;
kpeter@609
  1081
        for (int i = 0; i != _arc_num; ++i) {
kpeter@640
  1082
          if (_cost[i] > ART_COST) ART_COST = _cost[i];
kpeter@609
  1083
        }
kpeter@640
  1084
        ART_COST = (ART_COST + 1) * _node_num;
kpeter@609
  1085
      }
kpeter@609
  1086
kpeter@642
  1087
      // Initialize arc maps
kpeter@642
  1088
      for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1089
        _flow[i] = 0;
kpeter@642
  1090
        _state[i] = STATE_LOWER;
kpeter@642
  1091
      }
alpar@877
  1092
kpeter@601
  1093
      // Set data for the artificial root node
kpeter@601
  1094
      _root = _node_num;
kpeter@601
  1095
      _parent[_root] = -1;
kpeter@601
  1096
      _pred[_root] = -1;
kpeter@601
  1097
      _thread[_root] = 0;
kpeter@604
  1098
      _rev_thread[0] = _root;
kpeter@642
  1099
      _succ_num[_root] = _node_num + 1;
kpeter@604
  1100
      _last_succ[_root] = _root - 1;
kpeter@640
  1101
      _supply[_root] = -_sum_supply;
kpeter@663
  1102
      _pi[_root] = 0;
kpeter@601
  1103
kpeter@601
  1104
      // Add artificial arcs and initialize the spanning tree data structure
kpeter@663
  1105
      if (_sum_supply == 0) {
kpeter@663
  1106
        // EQ supply constraints
kpeter@663
  1107
        _search_arc_num = _arc_num;
kpeter@663
  1108
        _all_arc_num = _arc_num + _node_num;
kpeter@663
  1109
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@663
  1110
          _parent[u] = _root;
kpeter@663
  1111
          _pred[u] = e;
kpeter@663
  1112
          _thread[u] = u + 1;
kpeter@663
  1113
          _rev_thread[u + 1] = u;
kpeter@663
  1114
          _succ_num[u] = 1;
kpeter@663
  1115
          _last_succ[u] = u;
kpeter@663
  1116
          _cap[e] = INF;
kpeter@663
  1117
          _state[e] = STATE_TREE;
kpeter@663
  1118
          if (_supply[u] >= 0) {
kpeter@663
  1119
            _forward[u] = true;
kpeter@663
  1120
            _pi[u] = 0;
kpeter@663
  1121
            _source[e] = u;
kpeter@663
  1122
            _target[e] = _root;
kpeter@663
  1123
            _flow[e] = _supply[u];
kpeter@663
  1124
            _cost[e] = 0;
kpeter@663
  1125
          } else {
kpeter@663
  1126
            _forward[u] = false;
kpeter@663
  1127
            _pi[u] = ART_COST;
kpeter@663
  1128
            _source[e] = _root;
kpeter@663
  1129
            _target[e] = u;
kpeter@663
  1130
            _flow[e] = -_supply[u];
kpeter@663
  1131
            _cost[e] = ART_COST;
kpeter@663
  1132
          }
kpeter@601
  1133
        }
kpeter@601
  1134
      }
kpeter@663
  1135
      else if (_sum_supply > 0) {
kpeter@663
  1136
        // LEQ supply constraints
kpeter@663
  1137
        _search_arc_num = _arc_num + _node_num;
kpeter@663
  1138
        int f = _arc_num + _node_num;
kpeter@663
  1139
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@663
  1140
          _parent[u] = _root;
kpeter@663
  1141
          _thread[u] = u + 1;
kpeter@663
  1142
          _rev_thread[u + 1] = u;
kpeter@663
  1143
          _succ_num[u] = 1;
kpeter@663
  1144
          _last_succ[u] = u;
kpeter@663
  1145
          if (_supply[u] >= 0) {
kpeter@663
  1146
            _forward[u] = true;
kpeter@663
  1147
            _pi[u] = 0;
kpeter@663
  1148
            _pred[u] = e;
kpeter@663
  1149
            _source[e] = u;
kpeter@663
  1150
            _target[e] = _root;
kpeter@663
  1151
            _cap[e] = INF;
kpeter@663
  1152
            _flow[e] = _supply[u];
kpeter@663
  1153
            _cost[e] = 0;
kpeter@663
  1154
            _state[e] = STATE_TREE;
kpeter@663
  1155
          } else {
kpeter@663
  1156
            _forward[u] = false;
kpeter@663
  1157
            _pi[u] = ART_COST;
kpeter@663
  1158
            _pred[u] = f;
kpeter@663
  1159
            _source[f] = _root;
kpeter@663
  1160
            _target[f] = u;
kpeter@663
  1161
            _cap[f] = INF;
kpeter@663
  1162
            _flow[f] = -_supply[u];
kpeter@663
  1163
            _cost[f] = ART_COST;
kpeter@663
  1164
            _state[f] = STATE_TREE;
kpeter@663
  1165
            _source[e] = u;
kpeter@663
  1166
            _target[e] = _root;
kpeter@663
  1167
            _cap[e] = INF;
kpeter@663
  1168
            _flow[e] = 0;
kpeter@663
  1169
            _cost[e] = 0;
kpeter@663
  1170
            _state[e] = STATE_LOWER;
kpeter@663
  1171
            ++f;
kpeter@663
  1172
          }
kpeter@663
  1173
        }
kpeter@663
  1174
        _all_arc_num = f;
kpeter@663
  1175
      }
kpeter@663
  1176
      else {
kpeter@663
  1177
        // GEQ supply constraints
kpeter@663
  1178
        _search_arc_num = _arc_num + _node_num;
kpeter@663
  1179
        int f = _arc_num + _node_num;
kpeter@663
  1180
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@663
  1181
          _parent[u] = _root;
kpeter@663
  1182
          _thread[u] = u + 1;
kpeter@663
  1183
          _rev_thread[u + 1] = u;
kpeter@663
  1184
          _succ_num[u] = 1;
kpeter@663
  1185
          _last_succ[u] = u;
kpeter@663
  1186
          if (_supply[u] <= 0) {
kpeter@663
  1187
            _forward[u] = false;
kpeter@663
  1188
            _pi[u] = 0;
kpeter@663
  1189
            _pred[u] = e;
kpeter@663
  1190
            _source[e] = _root;
kpeter@663
  1191
            _target[e] = u;
kpeter@663
  1192
            _cap[e] = INF;
kpeter@663
  1193
            _flow[e] = -_supply[u];
kpeter@663
  1194
            _cost[e] = 0;
kpeter@663
  1195
            _state[e] = STATE_TREE;
kpeter@663
  1196
          } else {
kpeter@663
  1197
            _forward[u] = true;
kpeter@663
  1198
            _pi[u] = -ART_COST;
kpeter@663
  1199
            _pred[u] = f;
kpeter@663
  1200
            _source[f] = u;
kpeter@663
  1201
            _target[f] = _root;
kpeter@663
  1202
            _cap[f] = INF;
kpeter@663
  1203
            _flow[f] = _supply[u];
kpeter@663
  1204
            _state[f] = STATE_TREE;
kpeter@663
  1205
            _cost[f] = ART_COST;
kpeter@663
  1206
            _source[e] = _root;
kpeter@663
  1207
            _target[e] = u;
kpeter@663
  1208
            _cap[e] = INF;
kpeter@663
  1209
            _flow[e] = 0;
kpeter@663
  1210
            _cost[e] = 0;
kpeter@663
  1211
            _state[e] = STATE_LOWER;
kpeter@663
  1212
            ++f;
kpeter@663
  1213
          }
kpeter@663
  1214
        }
kpeter@663
  1215
        _all_arc_num = f;
kpeter@663
  1216
      }
kpeter@601
  1217
kpeter@601
  1218
      return true;
kpeter@601
  1219
    }
kpeter@601
  1220
kpeter@601
  1221
    // Find the join node
kpeter@601
  1222
    void findJoinNode() {
kpeter@603
  1223
      int u = _source[in_arc];
kpeter@603
  1224
      int v = _target[in_arc];
kpeter@601
  1225
      while (u != v) {
kpeter@604
  1226
        if (_succ_num[u] < _succ_num[v]) {
kpeter@604
  1227
          u = _parent[u];
kpeter@604
  1228
        } else {
kpeter@604
  1229
          v = _parent[v];
kpeter@604
  1230
        }
kpeter@601
  1231
      }
kpeter@601
  1232
      join = u;
kpeter@601
  1233
    }
kpeter@601
  1234
kpeter@601
  1235
    // Find the leaving arc of the cycle and returns true if the
kpeter@601
  1236
    // leaving arc is not the same as the entering arc
kpeter@601
  1237
    bool findLeavingArc() {
kpeter@601
  1238
      // Initialize first and second nodes according to the direction
kpeter@601
  1239
      // of the cycle
kpeter@603
  1240
      if (_state[in_arc] == STATE_LOWER) {
kpeter@603
  1241
        first  = _source[in_arc];
kpeter@603
  1242
        second = _target[in_arc];
kpeter@601
  1243
      } else {
kpeter@603
  1244
        first  = _target[in_arc];
kpeter@603
  1245
        second = _source[in_arc];
kpeter@601
  1246
      }
kpeter@603
  1247
      delta = _cap[in_arc];
kpeter@601
  1248
      int result = 0;
kpeter@641
  1249
      Value d;
kpeter@601
  1250
      int e;
kpeter@601
  1251
kpeter@601
  1252
      // Search the cycle along the path form the first node to the root
kpeter@601
  1253
      for (int u = first; u != join; u = _parent[u]) {
kpeter@601
  1254
        e = _pred[u];
kpeter@640
  1255
        d = _forward[u] ?
kpeter@811
  1256
          _flow[e] : (_cap[e] >= MAX ? INF : _cap[e] - _flow[e]);
kpeter@601
  1257
        if (d < delta) {
kpeter@601
  1258
          delta = d;
kpeter@601
  1259
          u_out = u;
kpeter@601
  1260
          result = 1;
kpeter@601
  1261
        }
kpeter@601
  1262
      }
kpeter@601
  1263
      // Search the cycle along the path form the second node to the root
kpeter@601
  1264
      for (int u = second; u != join; u = _parent[u]) {
kpeter@601
  1265
        e = _pred[u];
alpar@877
  1266
        d = _forward[u] ?
kpeter@811
  1267
          (_cap[e] >= MAX ? INF : _cap[e] - _flow[e]) : _flow[e];
kpeter@601
  1268
        if (d <= delta) {
kpeter@601
  1269
          delta = d;
kpeter@601
  1270
          u_out = u;
kpeter@601
  1271
          result = 2;
kpeter@601
  1272
        }
kpeter@601
  1273
      }
kpeter@601
  1274
kpeter@601
  1275
      if (result == 1) {
kpeter@601
  1276
        u_in = first;
kpeter@601
  1277
        v_in = second;
kpeter@601
  1278
      } else {
kpeter@601
  1279
        u_in = second;
kpeter@601
  1280
        v_in = first;
kpeter@601
  1281
      }
kpeter@601
  1282
      return result != 0;
kpeter@601
  1283
    }
kpeter@601
  1284
kpeter@601
  1285
    // Change _flow and _state vectors
kpeter@601
  1286
    void changeFlow(bool change) {
kpeter@601
  1287
      // Augment along the cycle
kpeter@601
  1288
      if (delta > 0) {
kpeter@641
  1289
        Value val = _state[in_arc] * delta;
kpeter@603
  1290
        _flow[in_arc] += val;
kpeter@603
  1291
        for (int u = _source[in_arc]; u != join; u = _parent[u]) {
kpeter@601
  1292
          _flow[_pred[u]] += _forward[u] ? -val : val;
kpeter@601
  1293
        }
kpeter@603
  1294
        for (int u = _target[in_arc]; u != join; u = _parent[u]) {
kpeter@601
  1295
          _flow[_pred[u]] += _forward[u] ? val : -val;
kpeter@601
  1296
        }
kpeter@601
  1297
      }
kpeter@601
  1298
      // Update the state of the entering and leaving arcs
kpeter@601
  1299
      if (change) {
kpeter@603
  1300
        _state[in_arc] = STATE_TREE;
kpeter@601
  1301
        _state[_pred[u_out]] =
kpeter@601
  1302
          (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
kpeter@601
  1303
      } else {
kpeter@603
  1304
        _state[in_arc] = -_state[in_arc];
kpeter@601
  1305
      }
kpeter@601
  1306
    }
kpeter@601
  1307
kpeter@604
  1308
    // Update the tree structure
kpeter@604
  1309
    void updateTreeStructure() {
kpeter@604
  1310
      int u, w;
kpeter@604
  1311
      int old_rev_thread = _rev_thread[u_out];
kpeter@604
  1312
      int old_succ_num = _succ_num[u_out];
kpeter@604
  1313
      int old_last_succ = _last_succ[u_out];
kpeter@601
  1314
      v_out = _parent[u_out];
kpeter@601
  1315
kpeter@604
  1316
      u = _last_succ[u_in];  // the last successor of u_in
kpeter@604
  1317
      right = _thread[u];    // the node after it
kpeter@604
  1318
kpeter@604
  1319
      // Handle the case when old_rev_thread equals to v_in
kpeter@604
  1320
      // (it also means that join and v_out coincide)
kpeter@604
  1321
      if (old_rev_thread == v_in) {
kpeter@604
  1322
        last = _thread[_last_succ[u_out]];
kpeter@604
  1323
      } else {
kpeter@604
  1324
        last = _thread[v_in];
kpeter@601
  1325
      }
kpeter@601
  1326
kpeter@604
  1327
      // Update _thread and _parent along the stem nodes (i.e. the nodes
kpeter@604
  1328
      // between u_in and u_out, whose parent have to be changed)
kpeter@601
  1329
      _thread[v_in] = stem = u_in;
kpeter@604
  1330
      _dirty_revs.clear();
kpeter@604
  1331
      _dirty_revs.push_back(v_in);
kpeter@601
  1332
      par_stem = v_in;
kpeter@601
  1333
      while (stem != u_out) {
kpeter@604
  1334
        // Insert the next stem node into the thread list
kpeter@604
  1335
        new_stem = _parent[stem];
kpeter@604
  1336
        _thread[u] = new_stem;
kpeter@604
  1337
        _dirty_revs.push_back(u);
kpeter@601
  1338
kpeter@604
  1339
        // Remove the subtree of stem from the thread list
kpeter@604
  1340
        w = _rev_thread[stem];
kpeter@604
  1341
        _thread[w] = right;
kpeter@604
  1342
        _rev_thread[right] = w;
kpeter@601
  1343
kpeter@604
  1344
        // Change the parent node and shift stem nodes
kpeter@601
  1345
        _parent[stem] = par_stem;
kpeter@601
  1346
        par_stem = stem;
kpeter@601
  1347
        stem = new_stem;
kpeter@601
  1348
kpeter@604
  1349
        // Update u and right
kpeter@604
  1350
        u = _last_succ[stem] == _last_succ[par_stem] ?
kpeter@604
  1351
          _rev_thread[par_stem] : _last_succ[stem];
kpeter@601
  1352
        right = _thread[u];
kpeter@601
  1353
      }
kpeter@601
  1354
      _parent[u_out] = par_stem;
kpeter@601
  1355
      _thread[u] = last;
kpeter@604
  1356
      _rev_thread[last] = u;
kpeter@604
  1357
      _last_succ[u_out] = u;
kpeter@601
  1358
kpeter@604
  1359
      // Remove the subtree of u_out from the thread list except for
kpeter@604
  1360
      // the case when old_rev_thread equals to v_in
kpeter@604
  1361
      // (it also means that join and v_out coincide)
kpeter@604
  1362
      if (old_rev_thread != v_in) {
kpeter@604
  1363
        _thread[old_rev_thread] = right;
kpeter@604
  1364
        _rev_thread[right] = old_rev_thread;
kpeter@604
  1365
      }
kpeter@604
  1366
kpeter@604
  1367
      // Update _rev_thread using the new _thread values
kpeter@839
  1368
      for (int i = 0; i != int(_dirty_revs.size()); ++i) {
kpeter@604
  1369
        u = _dirty_revs[i];
kpeter@604
  1370
        _rev_thread[_thread[u]] = u;
kpeter@604
  1371
      }
kpeter@604
  1372
kpeter@604
  1373
      // Update _pred, _forward, _last_succ and _succ_num for the
kpeter@604
  1374
      // stem nodes from u_out to u_in
kpeter@604
  1375
      int tmp_sc = 0, tmp_ls = _last_succ[u_out];
kpeter@604
  1376
      u = u_out;
kpeter@604
  1377
      while (u != u_in) {
kpeter@604
  1378
        w = _parent[u];
kpeter@604
  1379
        _pred[u] = _pred[w];
kpeter@604
  1380
        _forward[u] = !_forward[w];
kpeter@604
  1381
        tmp_sc += _succ_num[u] - _succ_num[w];
kpeter@604
  1382
        _succ_num[u] = tmp_sc;
kpeter@604
  1383
        _last_succ[w] = tmp_ls;
kpeter@604
  1384
        u = w;
kpeter@604
  1385
      }
kpeter@604
  1386
      _pred[u_in] = in_arc;
kpeter@604
  1387
      _forward[u_in] = (u_in == _source[in_arc]);
kpeter@604
  1388
      _succ_num[u_in] = old_succ_num;
kpeter@604
  1389
kpeter@604
  1390
      // Set limits for updating _last_succ form v_in and v_out
kpeter@604
  1391
      // towards the root
kpeter@604
  1392
      int up_limit_in = -1;
kpeter@604
  1393
      int up_limit_out = -1;
kpeter@604
  1394
      if (_last_succ[join] == v_in) {
kpeter@604
  1395
        up_limit_out = join;
kpeter@601
  1396
      } else {
kpeter@604
  1397
        up_limit_in = join;
kpeter@604
  1398
      }
kpeter@604
  1399
kpeter@604
  1400
      // Update _last_succ from v_in towards the root
kpeter@604
  1401
      for (u = v_in; u != up_limit_in && _last_succ[u] == v_in;
kpeter@604
  1402
           u = _parent[u]) {
kpeter@604
  1403
        _last_succ[u] = _last_succ[u_out];
kpeter@604
  1404
      }
kpeter@604
  1405
      // Update _last_succ from v_out towards the root
kpeter@604
  1406
      if (join != old_rev_thread && v_in != old_rev_thread) {
kpeter@604
  1407
        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@604
  1408
             u = _parent[u]) {
kpeter@604
  1409
          _last_succ[u] = old_rev_thread;
kpeter@604
  1410
        }
kpeter@604
  1411
      } else {
kpeter@604
  1412
        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@604
  1413
             u = _parent[u]) {
kpeter@604
  1414
          _last_succ[u] = _last_succ[u_out];
kpeter@604
  1415
        }
kpeter@604
  1416
      }
kpeter@604
  1417
kpeter@604
  1418
      // Update _succ_num from v_in to join
kpeter@604
  1419
      for (u = v_in; u != join; u = _parent[u]) {
kpeter@604
  1420
        _succ_num[u] += old_succ_num;
kpeter@604
  1421
      }
kpeter@604
  1422
      // Update _succ_num from v_out to join
kpeter@604
  1423
      for (u = v_out; u != join; u = _parent[u]) {
kpeter@604
  1424
        _succ_num[u] -= old_succ_num;
kpeter@601
  1425
      }
kpeter@601
  1426
    }
kpeter@601
  1427
kpeter@604
  1428
    // Update potentials
kpeter@604
  1429
    void updatePotential() {
kpeter@607
  1430
      Cost sigma = _forward[u_in] ?
kpeter@601
  1431
        _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
kpeter@601
  1432
        _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
kpeter@608
  1433
      // Update potentials in the subtree, which has been moved
kpeter@608
  1434
      int end = _thread[_last_succ[u_in]];
kpeter@608
  1435
      for (int u = u_in; u != end; u = _thread[u]) {
kpeter@608
  1436
        _pi[u] += sigma;
kpeter@601
  1437
      }
kpeter@601
  1438
    }
kpeter@601
  1439
kpeter@839
  1440
    // Heuristic initial pivots
kpeter@839
  1441
    bool initialPivots() {
kpeter@839
  1442
      Value curr, total = 0;
kpeter@839
  1443
      std::vector<Node> supply_nodes, demand_nodes;
kpeter@839
  1444
      for (NodeIt u(_graph); u != INVALID; ++u) {
kpeter@839
  1445
        curr = _supply[_node_id[u]];
kpeter@839
  1446
        if (curr > 0) {
kpeter@839
  1447
          total += curr;
kpeter@839
  1448
          supply_nodes.push_back(u);
kpeter@839
  1449
        }
kpeter@839
  1450
        else if (curr < 0) {
kpeter@839
  1451
          demand_nodes.push_back(u);
kpeter@839
  1452
        }
kpeter@839
  1453
      }
kpeter@839
  1454
      if (_sum_supply > 0) total -= _sum_supply;
kpeter@839
  1455
      if (total <= 0) return true;
kpeter@839
  1456
kpeter@839
  1457
      IntVector arc_vector;
kpeter@839
  1458
      if (_sum_supply >= 0) {
kpeter@839
  1459
        if (supply_nodes.size() == 1 && demand_nodes.size() == 1) {
kpeter@839
  1460
          // Perform a reverse graph search from the sink to the source
kpeter@839
  1461
          typename GR::template NodeMap<bool> reached(_graph, false);
kpeter@839
  1462
          Node s = supply_nodes[0], t = demand_nodes[0];
kpeter@839
  1463
          std::vector<Node> stack;
kpeter@839
  1464
          reached[t] = true;
kpeter@839
  1465
          stack.push_back(t);
kpeter@839
  1466
          while (!stack.empty()) {
kpeter@839
  1467
            Node u, v = stack.back();
kpeter@839
  1468
            stack.pop_back();
kpeter@839
  1469
            if (v == s) break;
kpeter@839
  1470
            for (InArcIt a(_graph, v); a != INVALID; ++a) {
kpeter@839
  1471
              if (reached[u = _graph.source(a)]) continue;
kpeter@839
  1472
              int j = _arc_id[a];
kpeter@839
  1473
              if (_cap[j] >= total) {
kpeter@839
  1474
                arc_vector.push_back(j);
kpeter@839
  1475
                reached[u] = true;
kpeter@839
  1476
                stack.push_back(u);
kpeter@839
  1477
              }
kpeter@839
  1478
            }
kpeter@839
  1479
          }
kpeter@839
  1480
        } else {
kpeter@839
  1481
          // Find the min. cost incomming arc for each demand node
kpeter@839
  1482
          for (int i = 0; i != int(demand_nodes.size()); ++i) {
kpeter@839
  1483
            Node v = demand_nodes[i];
kpeter@839
  1484
            Cost c, min_cost = std::numeric_limits<Cost>::max();
kpeter@839
  1485
            Arc min_arc = INVALID;
kpeter@839
  1486
            for (InArcIt a(_graph, v); a != INVALID; ++a) {
kpeter@839
  1487
              c = _cost[_arc_id[a]];
kpeter@839
  1488
              if (c < min_cost) {
kpeter@839
  1489
                min_cost = c;
kpeter@839
  1490
                min_arc = a;
kpeter@839
  1491
              }
kpeter@839
  1492
            }
kpeter@839
  1493
            if (min_arc != INVALID) {
kpeter@839
  1494
              arc_vector.push_back(_arc_id[min_arc]);
kpeter@839
  1495
            }
kpeter@839
  1496
          }
kpeter@839
  1497
        }
kpeter@839
  1498
      } else {
kpeter@839
  1499
        // Find the min. cost outgoing arc for each supply node
kpeter@839
  1500
        for (int i = 0; i != int(supply_nodes.size()); ++i) {
kpeter@839
  1501
          Node u = supply_nodes[i];
kpeter@839
  1502
          Cost c, min_cost = std::numeric_limits<Cost>::max();
kpeter@839
  1503
          Arc min_arc = INVALID;
kpeter@839
  1504
          for (OutArcIt a(_graph, u); a != INVALID; ++a) {
kpeter@839
  1505
            c = _cost[_arc_id[a]];
kpeter@839
  1506
            if (c < min_cost) {
kpeter@839
  1507
              min_cost = c;
kpeter@839
  1508
              min_arc = a;
kpeter@839
  1509
            }
kpeter@839
  1510
          }
kpeter@839
  1511
          if (min_arc != INVALID) {
kpeter@839
  1512
            arc_vector.push_back(_arc_id[min_arc]);
kpeter@839
  1513
          }
kpeter@839
  1514
        }
kpeter@839
  1515
      }
kpeter@839
  1516
kpeter@839
  1517
      // Perform heuristic initial pivots
kpeter@839
  1518
      for (int i = 0; i != int(arc_vector.size()); ++i) {
kpeter@839
  1519
        in_arc = arc_vector[i];
kpeter@839
  1520
        if (_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] -
kpeter@839
  1521
            _pi[_target[in_arc]]) >= 0) continue;
kpeter@839
  1522
        findJoinNode();
kpeter@839
  1523
        bool change = findLeavingArc();
kpeter@839
  1524
        if (delta >= MAX) return false;
kpeter@839
  1525
        changeFlow(change);
kpeter@839
  1526
        if (change) {
kpeter@839
  1527
          updateTreeStructure();
kpeter@839
  1528
          updatePotential();
kpeter@839
  1529
        }
kpeter@839
  1530
      }
kpeter@839
  1531
      return true;
kpeter@839
  1532
    }
kpeter@839
  1533
kpeter@601
  1534
    // Execute the algorithm
kpeter@640
  1535
    ProblemType start(PivotRule pivot_rule) {
kpeter@601
  1536
      // Select the pivot rule implementation
kpeter@601
  1537
      switch (pivot_rule) {
kpeter@605
  1538
        case FIRST_ELIGIBLE:
kpeter@601
  1539
          return start<FirstEligiblePivotRule>();
kpeter@605
  1540
        case BEST_ELIGIBLE:
kpeter@601
  1541
          return start<BestEligiblePivotRule>();
kpeter@605
  1542
        case BLOCK_SEARCH:
kpeter@601
  1543
          return start<BlockSearchPivotRule>();
kpeter@605
  1544
        case CANDIDATE_LIST:
kpeter@601
  1545
          return start<CandidateListPivotRule>();
kpeter@605
  1546
        case ALTERING_LIST:
kpeter@601
  1547
          return start<AlteringListPivotRule>();
kpeter@601
  1548
      }
kpeter@640
  1549
      return INFEASIBLE; // avoid warning
kpeter@601
  1550
    }
kpeter@601
  1551
kpeter@605
  1552
    template <typename PivotRuleImpl>
kpeter@640
  1553
    ProblemType start() {
kpeter@605
  1554
      PivotRuleImpl pivot(*this);
kpeter@601
  1555
kpeter@839
  1556
      // Perform heuristic initial pivots
kpeter@839
  1557
      if (!initialPivots()) return UNBOUNDED;
kpeter@839
  1558
kpeter@605
  1559
      // Execute the Network Simplex algorithm
kpeter@601
  1560
      while (pivot.findEnteringArc()) {
kpeter@601
  1561
        findJoinNode();
kpeter@601
  1562
        bool change = findLeavingArc();
kpeter@811
  1563
        if (delta >= MAX) return UNBOUNDED;
kpeter@601
  1564
        changeFlow(change);
kpeter@601
  1565
        if (change) {
kpeter@604
  1566
          updateTreeStructure();
kpeter@604
  1567
          updatePotential();
kpeter@601
  1568
        }
kpeter@601
  1569
      }
alpar@877
  1570
kpeter@640
  1571
      // Check feasibility
kpeter@663
  1572
      for (int e = _search_arc_num; e != _all_arc_num; ++e) {
kpeter@663
  1573
        if (_flow[e] != 0) return INFEASIBLE;
kpeter@640
  1574
      }
kpeter@601
  1575
kpeter@642
  1576
      // Transform the solution and the supply map to the original form
kpeter@642
  1577
      if (_have_lower) {
kpeter@601
  1578
        for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1579
          Value c = _lower[i];
kpeter@642
  1580
          if (c != 0) {
kpeter@642
  1581
            _flow[i] += c;
kpeter@642
  1582
            _supply[_source[i]] += c;
kpeter@642
  1583
            _supply[_target[i]] -= c;
kpeter@642
  1584
          }
kpeter@601
  1585
        }
kpeter@601
  1586
      }
alpar@877
  1587
kpeter@663
  1588
      // Shift potentials to meet the requirements of the GEQ/LEQ type
kpeter@663
  1589
      // optimality conditions
kpeter@663
  1590
      if (_sum_supply == 0) {
kpeter@663
  1591
        if (_stype == GEQ) {
kpeter@888
  1592
          Cost max_pot = -std::numeric_limits<Cost>::max();
kpeter@663
  1593
          for (int i = 0; i != _node_num; ++i) {
kpeter@663
  1594
            if (_pi[i] > max_pot) max_pot = _pi[i];
kpeter@663
  1595
          }
kpeter@663
  1596
          if (max_pot > 0) {
kpeter@663
  1597
            for (int i = 0; i != _node_num; ++i)
kpeter@663
  1598
              _pi[i] -= max_pot;
kpeter@663
  1599
          }
kpeter@663
  1600
        } else {
kpeter@663
  1601
          Cost min_pot = std::numeric_limits<Cost>::max();
kpeter@663
  1602
          for (int i = 0; i != _node_num; ++i) {
kpeter@663
  1603
            if (_pi[i] < min_pot) min_pot = _pi[i];
kpeter@663
  1604
          }
kpeter@663
  1605
          if (min_pot < 0) {
kpeter@663
  1606
            for (int i = 0; i != _node_num; ++i)
kpeter@663
  1607
              _pi[i] -= min_pot;
kpeter@663
  1608
          }
kpeter@663
  1609
        }
kpeter@663
  1610
      }
kpeter@601
  1611
kpeter@640
  1612
      return OPTIMAL;
kpeter@601
  1613
    }
kpeter@601
  1614
kpeter@601
  1615
  }; //class NetworkSimplex
kpeter@601
  1616
kpeter@601
  1617
  ///@}
kpeter@601
  1618
kpeter@601
  1619
} //namespace lemon
kpeter@601
  1620
kpeter@601
  1621
#endif //LEMON_NETWORK_SIMPLEX_H