lemon/network_simplex.h
author Alpar Juttner <alpar@cs.elte.hu>
Tue, 29 Sep 2009 09:25:00 +0200
changeset 732 1f8ad32f088b
parent 729 be48a648d28f
parent 728 e2bdd1a988f3
child 755 134852d7fb0a
child 786 e20173729589
permissions -rw-r--r--
Simple interactive bootstrap script
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2009
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#ifndef LEMON_NETWORK_SIMPLEX_H
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#define LEMON_NETWORK_SIMPLEX_H
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/// \ingroup min_cost_flow_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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  /// This algorithm is a specialized version of the linear programming
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  /// simplex method directly for the minimum cost flow problem.
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  /// It is one of the most efficient solution methods.
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  ///
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  /// In general this class is the fastest implementation available
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  /// in LEMON for the minimum cost flow problem.
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  /// 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 value 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 value 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 value 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 according to our benchmark tests.
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    /// However another pivot rule can be selected using the \ref run()
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    /// function with the proper parameter.
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    enum PivotRule {
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      /// The First Eligible pivot rule.
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      /// The next eligible arc is selected in a wraparound fashion
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      /// in every iteration.
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      FIRST_ELIGIBLE,
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      /// The Best Eligible pivot rule.
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      /// The best eligible arc is selected in every iteration.
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      BEST_ELIGIBLE,
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      /// The Block Search pivot rule.
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      /// A specified number of arcs are examined in every iteration
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      /// in a wraparound fashion and the best eligible arc is selected
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      /// from this block.
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      BLOCK_SEARCH,
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      /// The Candidate List pivot rule.
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      /// In a major iteration a candidate list is built from eligible arcs
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      /// in a wraparound fashion and in the following minor iterations
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      /// the best eligible arc is selected from this list.
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      CANDIDATE_LIST,
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      /// The Altering Candidate List pivot rule.
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      /// It is a modified version of the Candidate List method.
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      /// It keeps only the several best eligible arcs from the former
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      /// candidate list and extends this list in every iteration.
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      ALTERING_LIST
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    };
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  private:
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    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
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    typedef std::vector<int> IntVector;
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    typedef std::vector<bool> BoolVector;
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    typedef std::vector<Value> ValueVector;
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    typedef std::vector<Cost> CostVector;
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    // State constants for arcs
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    enum ArcStateEnum {
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      STATE_UPPER = -1,
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      STATE_TREE  =  0,
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      STATE_LOWER =  1
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    };
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  private:
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    // Data related to the underlying digraph
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    const GR &_graph;
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    int _node_num;
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    int _arc_num;
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    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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    // 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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    IntVector _state;
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    int _root;
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    // Temporary data used in the current pivot iteration
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    int in_arc, join, u_in, v_in, u_out, v_out;
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    int first, second, right, last;
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    int stem, par_stem, new_stem;
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    Value delta;
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  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 IntVector  &_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 IntVector  &_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 IntVector  &_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 = 0.5;
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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
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    class CandidateListPivotRule
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    {
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    private:
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      // References to the NetworkSimplex class
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      const IntVector  &_source;
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      const IntVector  &_target;
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      const CostVector &_cost;
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      const IntVector  &_state;
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      const CostVector &_pi;
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      int &_in_arc;
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      int _search_arc_num;
kpeter@601
   411
kpeter@601
   412
      // Pivot rule data
kpeter@601
   413
      IntVector _candidates;
kpeter@601
   414
      int _list_length, _minor_limit;
kpeter@601
   415
      int _curr_length, _minor_count;
kpeter@601
   416
      int _next_arc;
kpeter@601
   417
kpeter@601
   418
    public:
kpeter@601
   419
kpeter@601
   420
      /// Constructor
kpeter@601
   421
      CandidateListPivotRule(NetworkSimplex &ns) :
kpeter@603
   422
        _source(ns._source), _target(ns._target),
kpeter@601
   423
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@663
   424
        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
kpeter@663
   425
        _next_arc(0)
kpeter@601
   426
      {
kpeter@601
   427
        // The main parameters of the pivot rule
kpeter@727
   428
        const double LIST_LENGTH_FACTOR = 0.25;
kpeter@601
   429
        const int MIN_LIST_LENGTH = 10;
kpeter@601
   430
        const double MINOR_LIMIT_FACTOR = 0.1;
kpeter@601
   431
        const int MIN_MINOR_LIMIT = 3;
kpeter@601
   432
alpar@612
   433
        _list_length = std::max( int(LIST_LENGTH_FACTOR *
kpeter@663
   434
                                     std::sqrt(double(_search_arc_num))),
kpeter@601
   435
                                 MIN_LIST_LENGTH );
kpeter@601
   436
        _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
kpeter@601
   437
                                 MIN_MINOR_LIMIT );
kpeter@601
   438
        _curr_length = _minor_count = 0;
kpeter@601
   439
        _candidates.resize(_list_length);
kpeter@601
   440
      }
kpeter@601
   441
kpeter@601
   442
      /// Find next entering arc
kpeter@601
   443
      bool findEnteringArc() {
kpeter@607
   444
        Cost min, c;
kpeter@727
   445
        int e;
kpeter@601
   446
        if (_curr_length > 0 && _minor_count < _minor_limit) {
kpeter@601
   447
          // Minor iteration: select the best eligible arc from the
kpeter@601
   448
          // current candidate list
kpeter@601
   449
          ++_minor_count;
kpeter@601
   450
          min = 0;
kpeter@601
   451
          for (int i = 0; i < _curr_length; ++i) {
kpeter@601
   452
            e = _candidates[i];
kpeter@601
   453
            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   454
            if (c < min) {
kpeter@601
   455
              min = c;
kpeter@727
   456
              _in_arc = e;
kpeter@601
   457
            }
kpeter@727
   458
            else if (c >= 0) {
kpeter@601
   459
              _candidates[i--] = _candidates[--_curr_length];
kpeter@601
   460
            }
kpeter@601
   461
          }
kpeter@727
   462
          if (min < 0) return true;
kpeter@601
   463
        }
kpeter@601
   464
kpeter@601
   465
        // Major iteration: build a new candidate list
kpeter@601
   466
        min = 0;
kpeter@601
   467
        _curr_length = 0;
kpeter@663
   468
        for (e = _next_arc; e < _search_arc_num; ++e) {
kpeter@601
   469
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   470
          if (c < 0) {
kpeter@601
   471
            _candidates[_curr_length++] = e;
kpeter@601
   472
            if (c < min) {
kpeter@601
   473
              min = c;
kpeter@727
   474
              _in_arc = e;
kpeter@601
   475
            }
kpeter@727
   476
            if (_curr_length == _list_length) goto search_end;
kpeter@601
   477
          }
kpeter@601
   478
        }
kpeter@727
   479
        for (e = 0; e < _next_arc; ++e) {
kpeter@727
   480
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@727
   481
          if (c < 0) {
kpeter@727
   482
            _candidates[_curr_length++] = e;
kpeter@727
   483
            if (c < min) {
kpeter@727
   484
              min = c;
kpeter@727
   485
              _in_arc = e;
kpeter@601
   486
            }
kpeter@727
   487
            if (_curr_length == _list_length) goto search_end;
kpeter@601
   488
          }
kpeter@601
   489
        }
kpeter@601
   490
        if (_curr_length == 0) return false;
kpeter@727
   491
      
kpeter@727
   492
      search_end:        
kpeter@601
   493
        _minor_count = 1;
kpeter@601
   494
        _next_arc = e;
kpeter@601
   495
        return true;
kpeter@601
   496
      }
kpeter@601
   497
kpeter@601
   498
    }; //class CandidateListPivotRule
kpeter@601
   499
kpeter@601
   500
kpeter@605
   501
    // Implementation of the Altering Candidate List pivot rule
kpeter@601
   502
    class AlteringListPivotRule
kpeter@601
   503
    {
kpeter@601
   504
    private:
kpeter@601
   505
kpeter@601
   506
      // References to the NetworkSimplex class
kpeter@601
   507
      const IntVector  &_source;
kpeter@601
   508
      const IntVector  &_target;
kpeter@607
   509
      const CostVector &_cost;
kpeter@601
   510
      const IntVector  &_state;
kpeter@607
   511
      const CostVector &_pi;
kpeter@601
   512
      int &_in_arc;
kpeter@663
   513
      int _search_arc_num;
kpeter@601
   514
kpeter@601
   515
      // Pivot rule data
kpeter@601
   516
      int _block_size, _head_length, _curr_length;
kpeter@601
   517
      int _next_arc;
kpeter@601
   518
      IntVector _candidates;
kpeter@607
   519
      CostVector _cand_cost;
kpeter@601
   520
kpeter@601
   521
      // Functor class to compare arcs during sort of the candidate list
kpeter@601
   522
      class SortFunc
kpeter@601
   523
      {
kpeter@601
   524
      private:
kpeter@607
   525
        const CostVector &_map;
kpeter@601
   526
      public:
kpeter@607
   527
        SortFunc(const CostVector &map) : _map(map) {}
kpeter@601
   528
        bool operator()(int left, int right) {
kpeter@601
   529
          return _map[left] > _map[right];
kpeter@601
   530
        }
kpeter@601
   531
      };
kpeter@601
   532
kpeter@601
   533
      SortFunc _sort_func;
kpeter@601
   534
kpeter@601
   535
    public:
kpeter@601
   536
kpeter@605
   537
      // Constructor
kpeter@601
   538
      AlteringListPivotRule(NetworkSimplex &ns) :
kpeter@603
   539
        _source(ns._source), _target(ns._target),
kpeter@601
   540
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@663
   541
        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
kpeter@663
   542
        _next_arc(0), _cand_cost(ns._search_arc_num), _sort_func(_cand_cost)
kpeter@601
   543
      {
kpeter@601
   544
        // The main parameters of the pivot rule
kpeter@727
   545
        const double BLOCK_SIZE_FACTOR = 1.0;
kpeter@601
   546
        const int MIN_BLOCK_SIZE = 10;
kpeter@601
   547
        const double HEAD_LENGTH_FACTOR = 0.1;
kpeter@601
   548
        const int MIN_HEAD_LENGTH = 3;
kpeter@601
   549
alpar@612
   550
        _block_size = std::max( int(BLOCK_SIZE_FACTOR *
kpeter@663
   551
                                    std::sqrt(double(_search_arc_num))),
kpeter@601
   552
                                MIN_BLOCK_SIZE );
kpeter@601
   553
        _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),
kpeter@601
   554
                                 MIN_HEAD_LENGTH );
kpeter@601
   555
        _candidates.resize(_head_length + _block_size);
kpeter@601
   556
        _curr_length = 0;
kpeter@601
   557
      }
kpeter@601
   558
kpeter@605
   559
      // Find next entering arc
kpeter@601
   560
      bool findEnteringArc() {
kpeter@601
   561
        // Check the current candidate list
kpeter@601
   562
        int e;
kpeter@601
   563
        for (int i = 0; i < _curr_length; ++i) {
kpeter@601
   564
          e = _candidates[i];
kpeter@601
   565
          _cand_cost[e] = _state[e] *
kpeter@601
   566
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   567
          if (_cand_cost[e] >= 0) {
kpeter@601
   568
            _candidates[i--] = _candidates[--_curr_length];
kpeter@601
   569
          }
kpeter@601
   570
        }
kpeter@601
   571
kpeter@601
   572
        // Extend the list
kpeter@601
   573
        int cnt = _block_size;
kpeter@601
   574
        int limit = _head_length;
kpeter@601
   575
kpeter@727
   576
        for (e = _next_arc; e < _search_arc_num; ++e) {
kpeter@601
   577
          _cand_cost[e] = _state[e] *
kpeter@601
   578
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   579
          if (_cand_cost[e] < 0) {
kpeter@601
   580
            _candidates[_curr_length++] = e;
kpeter@601
   581
          }
kpeter@601
   582
          if (--cnt == 0) {
kpeter@727
   583
            if (_curr_length > limit) goto search_end;
kpeter@601
   584
            limit = 0;
kpeter@601
   585
            cnt = _block_size;
kpeter@601
   586
          }
kpeter@601
   587
        }
kpeter@727
   588
        for (e = 0; e < _next_arc; ++e) {
kpeter@727
   589
          _cand_cost[e] = _state[e] *
kpeter@727
   590
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@727
   591
          if (_cand_cost[e] < 0) {
kpeter@727
   592
            _candidates[_curr_length++] = e;
kpeter@727
   593
          }
kpeter@727
   594
          if (--cnt == 0) {
kpeter@727
   595
            if (_curr_length > limit) goto search_end;
kpeter@727
   596
            limit = 0;
kpeter@727
   597
            cnt = _block_size;
kpeter@601
   598
          }
kpeter@601
   599
        }
kpeter@601
   600
        if (_curr_length == 0) return false;
kpeter@727
   601
        
kpeter@727
   602
      search_end:
kpeter@601
   603
kpeter@601
   604
        // Make heap of the candidate list (approximating a partial sort)
kpeter@601
   605
        make_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@601
   606
                   _sort_func );
kpeter@601
   607
kpeter@601
   608
        // Pop the first element of the heap
kpeter@601
   609
        _in_arc = _candidates[0];
kpeter@727
   610
        _next_arc = e;
kpeter@601
   611
        pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@601
   612
                  _sort_func );
kpeter@601
   613
        _curr_length = std::min(_head_length, _curr_length - 1);
kpeter@601
   614
        return true;
kpeter@601
   615
      }
kpeter@601
   616
kpeter@601
   617
    }; //class AlteringListPivotRule
kpeter@601
   618
kpeter@601
   619
  public:
kpeter@601
   620
kpeter@605
   621
    /// \brief Constructor.
kpeter@601
   622
    ///
kpeter@609
   623
    /// The constructor of the class.
kpeter@601
   624
    ///
kpeter@603
   625
    /// \param graph The digraph the algorithm runs on.
kpeter@728
   626
    /// \param arc_mixing Indicate if the arcs have to be stored in a
kpeter@728
   627
    /// mixed order in the internal data structure. 
kpeter@728
   628
    /// In special cases, it could lead to better overall performance,
kpeter@728
   629
    /// but it is usually slower. Therefore it is disabled by default.
kpeter@728
   630
    NetworkSimplex(const GR& graph, bool arc_mixing = false) :
kpeter@642
   631
      _graph(graph), _node_id(graph), _arc_id(graph),
kpeter@641
   632
      INF(std::numeric_limits<Value>::has_infinity ?
kpeter@641
   633
          std::numeric_limits<Value>::infinity() :
kpeter@641
   634
          std::numeric_limits<Value>::max())
kpeter@605
   635
    {
kpeter@640
   636
      // Check the value types
kpeter@641
   637
      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
kpeter@640
   638
        "The flow type of NetworkSimplex must be signed");
kpeter@640
   639
      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
kpeter@640
   640
        "The cost type of NetworkSimplex must be signed");
kpeter@642
   641
        
kpeter@642
   642
      // Resize vectors
kpeter@642
   643
      _node_num = countNodes(_graph);
kpeter@642
   644
      _arc_num = countArcs(_graph);
kpeter@642
   645
      int all_node_num = _node_num + 1;
kpeter@663
   646
      int max_arc_num = _arc_num + 2 * _node_num;
kpeter@601
   647
kpeter@663
   648
      _source.resize(max_arc_num);
kpeter@663
   649
      _target.resize(max_arc_num);
kpeter@642
   650
kpeter@663
   651
      _lower.resize(_arc_num);
kpeter@663
   652
      _upper.resize(_arc_num);
kpeter@663
   653
      _cap.resize(max_arc_num);
kpeter@663
   654
      _cost.resize(max_arc_num);
kpeter@642
   655
      _supply.resize(all_node_num);
kpeter@663
   656
      _flow.resize(max_arc_num);
kpeter@642
   657
      _pi.resize(all_node_num);
kpeter@642
   658
kpeter@642
   659
      _parent.resize(all_node_num);
kpeter@642
   660
      _pred.resize(all_node_num);
kpeter@642
   661
      _forward.resize(all_node_num);
kpeter@642
   662
      _thread.resize(all_node_num);
kpeter@642
   663
      _rev_thread.resize(all_node_num);
kpeter@642
   664
      _succ_num.resize(all_node_num);
kpeter@642
   665
      _last_succ.resize(all_node_num);
kpeter@663
   666
      _state.resize(max_arc_num);
kpeter@642
   667
kpeter@728
   668
      // Copy the graph
kpeter@642
   669
      int i = 0;
kpeter@642
   670
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@642
   671
        _node_id[n] = i;
kpeter@642
   672
      }
kpeter@728
   673
      if (arc_mixing) {
kpeter@728
   674
        // Store the arcs in a mixed order
kpeter@728
   675
        int k = std::max(int(std::sqrt(double(_arc_num))), 10);
kpeter@728
   676
        int i = 0, j = 0;
kpeter@728
   677
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@728
   678
          _arc_id[a] = i;
kpeter@728
   679
          _source[i] = _node_id[_graph.source(a)];
kpeter@728
   680
          _target[i] = _node_id[_graph.target(a)];
kpeter@728
   681
          if ((i += k) >= _arc_num) i = ++j;
kpeter@728
   682
        }
kpeter@728
   683
      } else {
kpeter@728
   684
        // Store the arcs in the original order
kpeter@728
   685
        int i = 0;
kpeter@728
   686
        for (ArcIt a(_graph); a != INVALID; ++a, ++i) {
kpeter@728
   687
          _arc_id[a] = i;
kpeter@728
   688
          _source[i] = _node_id[_graph.source(a)];
kpeter@728
   689
          _target[i] = _node_id[_graph.target(a)];
kpeter@728
   690
        }
kpeter@642
   691
      }
kpeter@642
   692
      
kpeter@729
   693
      // Reset parameters
kpeter@729
   694
      reset();
kpeter@601
   695
    }
kpeter@601
   696
kpeter@609
   697
    /// \name Parameters
kpeter@609
   698
    /// The parameters of the algorithm can be specified using these
kpeter@609
   699
    /// functions.
kpeter@609
   700
kpeter@609
   701
    /// @{
kpeter@609
   702
kpeter@605
   703
    /// \brief Set the lower bounds on the arcs.
kpeter@605
   704
    ///
kpeter@605
   705
    /// This function sets the lower bounds on the arcs.
kpeter@640
   706
    /// If it is not used before calling \ref run(), the lower bounds
kpeter@640
   707
    /// will be set to zero on all arcs.
kpeter@605
   708
    ///
kpeter@605
   709
    /// \param map An arc map storing the lower bounds.
kpeter@641
   710
    /// Its \c Value type must be convertible to the \c Value type
kpeter@605
   711
    /// of the algorithm.
kpeter@605
   712
    ///
kpeter@605
   713
    /// \return <tt>(*this)</tt>
kpeter@640
   714
    template <typename LowerMap>
kpeter@640
   715
    NetworkSimplex& lowerMap(const LowerMap& map) {
kpeter@642
   716
      _have_lower = true;
kpeter@605
   717
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   718
        _lower[_arc_id[a]] = map[a];
kpeter@605
   719
      }
kpeter@605
   720
      return *this;
kpeter@605
   721
    }
kpeter@605
   722
kpeter@605
   723
    /// \brief Set the upper bounds (capacities) on the arcs.
kpeter@605
   724
    ///
kpeter@605
   725
    /// This function sets the upper bounds (capacities) on the arcs.
kpeter@640
   726
    /// If it is not used before calling \ref run(), the upper bounds
kpeter@640
   727
    /// will be set to \ref INF on all arcs (i.e. the flow value will be
kpeter@640
   728
    /// unbounded from above on each arc).
kpeter@605
   729
    ///
kpeter@605
   730
    /// \param map An arc map storing the upper bounds.
kpeter@641
   731
    /// Its \c Value type must be convertible to the \c Value type
kpeter@605
   732
    /// of the algorithm.
kpeter@605
   733
    ///
kpeter@605
   734
    /// \return <tt>(*this)</tt>
kpeter@640
   735
    template<typename UpperMap>
kpeter@640
   736
    NetworkSimplex& upperMap(const UpperMap& map) {
kpeter@605
   737
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   738
        _upper[_arc_id[a]] = map[a];
kpeter@605
   739
      }
kpeter@605
   740
      return *this;
kpeter@605
   741
    }
kpeter@605
   742
kpeter@605
   743
    /// \brief Set the costs of the arcs.
kpeter@605
   744
    ///
kpeter@605
   745
    /// This function sets the costs of the arcs.
kpeter@605
   746
    /// If it is not used before calling \ref run(), the costs
kpeter@605
   747
    /// will be set to \c 1 on all arcs.
kpeter@605
   748
    ///
kpeter@605
   749
    /// \param map An arc map storing the costs.
kpeter@607
   750
    /// Its \c Value type must be convertible to the \c Cost type
kpeter@605
   751
    /// of the algorithm.
kpeter@605
   752
    ///
kpeter@605
   753
    /// \return <tt>(*this)</tt>
kpeter@640
   754
    template<typename CostMap>
kpeter@640
   755
    NetworkSimplex& costMap(const CostMap& map) {
kpeter@605
   756
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   757
        _cost[_arc_id[a]] = map[a];
kpeter@605
   758
      }
kpeter@605
   759
      return *this;
kpeter@605
   760
    }
kpeter@605
   761
kpeter@605
   762
    /// \brief Set the supply values of the nodes.
kpeter@605
   763
    ///
kpeter@605
   764
    /// This function sets the supply values of the nodes.
kpeter@605
   765
    /// If neither this function nor \ref stSupply() is used before
kpeter@605
   766
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@605
   767
    ///
kpeter@605
   768
    /// \param map A node map storing the supply values.
kpeter@641
   769
    /// Its \c Value type must be convertible to the \c Value type
kpeter@605
   770
    /// of the algorithm.
kpeter@605
   771
    ///
kpeter@605
   772
    /// \return <tt>(*this)</tt>
kpeter@640
   773
    template<typename SupplyMap>
kpeter@640
   774
    NetworkSimplex& supplyMap(const SupplyMap& map) {
kpeter@605
   775
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@642
   776
        _supply[_node_id[n]] = map[n];
kpeter@605
   777
      }
kpeter@605
   778
      return *this;
kpeter@605
   779
    }
kpeter@605
   780
kpeter@605
   781
    /// \brief Set single source and target nodes and a supply value.
kpeter@605
   782
    ///
kpeter@605
   783
    /// This function sets a single source node and a single target node
kpeter@605
   784
    /// and the required flow value.
kpeter@605
   785
    /// If neither this function nor \ref supplyMap() is used before
kpeter@605
   786
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@605
   787
    ///
kpeter@640
   788
    /// Using this function has the same effect as using \ref supplyMap()
kpeter@640
   789
    /// with such a map in which \c k is assigned to \c s, \c -k is
kpeter@640
   790
    /// assigned to \c t and all other nodes have zero supply value.
kpeter@640
   791
    ///
kpeter@605
   792
    /// \param s The source node.
kpeter@605
   793
    /// \param t The target node.
kpeter@605
   794
    /// \param k The required amount of flow from node \c s to node \c t
kpeter@605
   795
    /// (i.e. the supply of \c s and the demand of \c t).
kpeter@605
   796
    ///
kpeter@605
   797
    /// \return <tt>(*this)</tt>
kpeter@641
   798
    NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) {
kpeter@642
   799
      for (int i = 0; i != _node_num; ++i) {
kpeter@642
   800
        _supply[i] = 0;
kpeter@642
   801
      }
kpeter@642
   802
      _supply[_node_id[s]] =  k;
kpeter@642
   803
      _supply[_node_id[t]] = -k;
kpeter@605
   804
      return *this;
kpeter@605
   805
    }
kpeter@609
   806
    
kpeter@640
   807
    /// \brief Set the type of the supply constraints.
kpeter@609
   808
    ///
kpeter@640
   809
    /// This function sets the type of the supply/demand constraints.
kpeter@640
   810
    /// If it is not used before calling \ref run(), the \ref GEQ supply
kpeter@609
   811
    /// type will be used.
kpeter@609
   812
    ///
kpeter@640
   813
    /// For more information see \ref SupplyType.
kpeter@609
   814
    ///
kpeter@609
   815
    /// \return <tt>(*this)</tt>
kpeter@640
   816
    NetworkSimplex& supplyType(SupplyType supply_type) {
kpeter@640
   817
      _stype = supply_type;
kpeter@609
   818
      return *this;
kpeter@609
   819
    }
kpeter@605
   820
kpeter@609
   821
    /// @}
kpeter@601
   822
kpeter@605
   823
    /// \name Execution Control
kpeter@605
   824
    /// The algorithm can be executed using \ref run().
kpeter@605
   825
kpeter@601
   826
    /// @{
kpeter@601
   827
kpeter@601
   828
    /// \brief Run the algorithm.
kpeter@601
   829
    ///
kpeter@601
   830
    /// This function runs the algorithm.
kpeter@609
   831
    /// The paramters can be specified using functions \ref lowerMap(),
kpeter@640
   832
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), 
kpeter@642
   833
    /// \ref supplyType().
kpeter@609
   834
    /// For example,
kpeter@605
   835
    /// \code
kpeter@605
   836
    ///   NetworkSimplex<ListDigraph> ns(graph);
kpeter@640
   837
    ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@605
   838
    ///     .supplyMap(sup).run();
kpeter@605
   839
    /// \endcode
kpeter@601
   840
    ///
kpeter@606
   841
    /// This function can be called more than once. All the parameters
kpeter@606
   842
    /// that have been given are kept for the next call, unless
kpeter@606
   843
    /// \ref reset() is called, thus only the modified parameters
kpeter@606
   844
    /// have to be set again. See \ref reset() for examples.
kpeter@642
   845
    /// However the underlying digraph must not be modified after this
kpeter@642
   846
    /// class have been constructed, since it copies and extends the graph.
kpeter@606
   847
    ///
kpeter@605
   848
    /// \param pivot_rule The pivot rule that will be used during the
kpeter@605
   849
    /// algorithm. For more information see \ref PivotRule.
kpeter@601
   850
    ///
kpeter@640
   851
    /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@640
   852
    /// \n \c OPTIMAL if the problem has optimal solution
kpeter@640
   853
    /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@640
   854
    /// optimal flow and node potentials (primal and dual solutions),
kpeter@640
   855
    /// \n \c UNBOUNDED if the objective function of the problem is
kpeter@640
   856
    /// unbounded, i.e. there is a directed cycle having negative total
kpeter@640
   857
    /// cost and infinite upper bound.
kpeter@640
   858
    ///
kpeter@640
   859
    /// \see ProblemType, PivotRule
kpeter@640
   860
    ProblemType run(PivotRule pivot_rule = BLOCK_SEARCH) {
kpeter@640
   861
      if (!init()) return INFEASIBLE;
kpeter@640
   862
      return start(pivot_rule);
kpeter@601
   863
    }
kpeter@601
   864
kpeter@606
   865
    /// \brief Reset all the parameters that have been given before.
kpeter@606
   866
    ///
kpeter@606
   867
    /// This function resets all the paramaters that have been given
kpeter@609
   868
    /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@642
   869
    /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType().
kpeter@606
   870
    ///
kpeter@606
   871
    /// It is useful for multiple run() calls. If this function is not
kpeter@606
   872
    /// used, all the parameters given before are kept for the next
kpeter@606
   873
    /// \ref run() call.
kpeter@642
   874
    /// However the underlying digraph must not be modified after this
kpeter@642
   875
    /// class have been constructed, since it copies and extends the graph.
kpeter@606
   876
    ///
kpeter@606
   877
    /// For example,
kpeter@606
   878
    /// \code
kpeter@606
   879
    ///   NetworkSimplex<ListDigraph> ns(graph);
kpeter@606
   880
    ///
kpeter@606
   881
    ///   // First run
kpeter@640
   882
    ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@606
   883
    ///     .supplyMap(sup).run();
kpeter@606
   884
    ///
kpeter@606
   885
    ///   // Run again with modified cost map (reset() is not called,
kpeter@606
   886
    ///   // so only the cost map have to be set again)
kpeter@606
   887
    ///   cost[e] += 100;
kpeter@606
   888
    ///   ns.costMap(cost).run();
kpeter@606
   889
    ///
kpeter@606
   890
    ///   // Run again from scratch using reset()
kpeter@606
   891
    ///   // (the lower bounds will be set to zero on all arcs)
kpeter@606
   892
    ///   ns.reset();
kpeter@640
   893
    ///   ns.upperMap(capacity).costMap(cost)
kpeter@606
   894
    ///     .supplyMap(sup).run();
kpeter@606
   895
    /// \endcode
kpeter@606
   896
    ///
kpeter@606
   897
    /// \return <tt>(*this)</tt>
kpeter@606
   898
    NetworkSimplex& reset() {
kpeter@642
   899
      for (int i = 0; i != _node_num; ++i) {
kpeter@642
   900
        _supply[i] = 0;
kpeter@642
   901
      }
kpeter@642
   902
      for (int i = 0; i != _arc_num; ++i) {
kpeter@642
   903
        _lower[i] = 0;
kpeter@642
   904
        _upper[i] = INF;
kpeter@642
   905
        _cost[i] = 1;
kpeter@642
   906
      }
kpeter@642
   907
      _have_lower = false;
kpeter@640
   908
      _stype = GEQ;
kpeter@606
   909
      return *this;
kpeter@606
   910
    }
kpeter@606
   911
kpeter@601
   912
    /// @}
kpeter@601
   913
kpeter@601
   914
    /// \name Query Functions
kpeter@601
   915
    /// The results of the algorithm can be obtained using these
kpeter@601
   916
    /// functions.\n
kpeter@605
   917
    /// The \ref run() function must be called before using them.
kpeter@605
   918
kpeter@601
   919
    /// @{
kpeter@601
   920
kpeter@605
   921
    /// \brief Return the total cost of the found flow.
kpeter@605
   922
    ///
kpeter@605
   923
    /// This function returns the total cost of the found flow.
kpeter@640
   924
    /// Its complexity is O(e).
kpeter@605
   925
    ///
kpeter@605
   926
    /// \note The return type of the function can be specified as a
kpeter@605
   927
    /// template parameter. For example,
kpeter@605
   928
    /// \code
kpeter@605
   929
    ///   ns.totalCost<double>();
kpeter@605
   930
    /// \endcode
kpeter@607
   931
    /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@605
   932
    /// type of the algorithm, which is the default return type of the
kpeter@605
   933
    /// function.
kpeter@605
   934
    ///
kpeter@605
   935
    /// \pre \ref run() must be called before using this function.
kpeter@642
   936
    template <typename Number>
kpeter@642
   937
    Number totalCost() const {
kpeter@642
   938
      Number c = 0;
kpeter@642
   939
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   940
        int i = _arc_id[a];
kpeter@642
   941
        c += Number(_flow[i]) * Number(_cost[i]);
kpeter@605
   942
      }
kpeter@605
   943
      return c;
kpeter@605
   944
    }
kpeter@605
   945
kpeter@605
   946
#ifndef DOXYGEN
kpeter@607
   947
    Cost totalCost() const {
kpeter@607
   948
      return totalCost<Cost>();
kpeter@605
   949
    }
kpeter@605
   950
#endif
kpeter@605
   951
kpeter@605
   952
    /// \brief Return the flow on the given arc.
kpeter@605
   953
    ///
kpeter@605
   954
    /// This function returns the flow on the given arc.
kpeter@605
   955
    ///
kpeter@605
   956
    /// \pre \ref run() must be called before using this function.
kpeter@641
   957
    Value flow(const Arc& a) const {
kpeter@642
   958
      return _flow[_arc_id[a]];
kpeter@605
   959
    }
kpeter@605
   960
kpeter@642
   961
    /// \brief Return the flow map (the primal solution).
kpeter@601
   962
    ///
kpeter@642
   963
    /// This function copies the flow value on each arc into the given
kpeter@642
   964
    /// map. The \c Value type of the algorithm must be convertible to
kpeter@642
   965
    /// the \c Value type of the map.
kpeter@601
   966
    ///
kpeter@601
   967
    /// \pre \ref run() must be called before using this function.
kpeter@642
   968
    template <typename FlowMap>
kpeter@642
   969
    void flowMap(FlowMap &map) const {
kpeter@642
   970
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   971
        map.set(a, _flow[_arc_id[a]]);
kpeter@642
   972
      }
kpeter@601
   973
    }
kpeter@601
   974
kpeter@605
   975
    /// \brief Return the potential (dual value) of the given node.
kpeter@605
   976
    ///
kpeter@605
   977
    /// This function returns the potential (dual value) of the
kpeter@605
   978
    /// given node.
kpeter@605
   979
    ///
kpeter@605
   980
    /// \pre \ref run() must be called before using this function.
kpeter@607
   981
    Cost potential(const Node& n) const {
kpeter@642
   982
      return _pi[_node_id[n]];
kpeter@605
   983
    }
kpeter@605
   984
kpeter@642
   985
    /// \brief Return the potential map (the dual solution).
kpeter@601
   986
    ///
kpeter@642
   987
    /// This function copies the potential (dual value) of each node
kpeter@642
   988
    /// into the given map.
kpeter@642
   989
    /// The \c Cost type of the algorithm must be convertible to the
kpeter@642
   990
    /// \c Value type of the map.
kpeter@601
   991
    ///
kpeter@601
   992
    /// \pre \ref run() must be called before using this function.
kpeter@642
   993
    template <typename PotentialMap>
kpeter@642
   994
    void potentialMap(PotentialMap &map) const {
kpeter@642
   995
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@642
   996
        map.set(n, _pi[_node_id[n]]);
kpeter@642
   997
      }
kpeter@601
   998
    }
kpeter@601
   999
kpeter@601
  1000
    /// @}
kpeter@601
  1001
kpeter@601
  1002
  private:
kpeter@601
  1003
kpeter@601
  1004
    // Initialize internal data structures
kpeter@601
  1005
    bool init() {
kpeter@605
  1006
      if (_node_num == 0) return false;
kpeter@601
  1007
kpeter@642
  1008
      // Check the sum of supply values
kpeter@642
  1009
      _sum_supply = 0;
kpeter@642
  1010
      for (int i = 0; i != _node_num; ++i) {
kpeter@642
  1011
        _sum_supply += _supply[i];
kpeter@642
  1012
      }
alpar@643
  1013
      if ( !((_stype == GEQ && _sum_supply <= 0) ||
alpar@643
  1014
             (_stype == LEQ && _sum_supply >= 0)) ) return false;
kpeter@601
  1015
kpeter@642
  1016
      // Remove non-zero lower bounds
kpeter@642
  1017
      if (_have_lower) {
kpeter@642
  1018
        for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1019
          Value c = _lower[i];
kpeter@642
  1020
          if (c >= 0) {
kpeter@642
  1021
            _cap[i] = _upper[i] < INF ? _upper[i] - c : INF;
kpeter@642
  1022
          } else {
kpeter@642
  1023
            _cap[i] = _upper[i] < INF + c ? _upper[i] - c : INF;
kpeter@642
  1024
          }
kpeter@642
  1025
          _supply[_source[i]] -= c;
kpeter@642
  1026
          _supply[_target[i]] += c;
kpeter@642
  1027
        }
kpeter@642
  1028
      } else {
kpeter@642
  1029
        for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1030
          _cap[i] = _upper[i];
kpeter@642
  1031
        }
kpeter@605
  1032
      }
kpeter@601
  1033
kpeter@609
  1034
      // Initialize artifical cost
kpeter@640
  1035
      Cost ART_COST;
kpeter@609
  1036
      if (std::numeric_limits<Cost>::is_exact) {
kpeter@663
  1037
        ART_COST = std::numeric_limits<Cost>::max() / 2 + 1;
kpeter@609
  1038
      } else {
kpeter@640
  1039
        ART_COST = std::numeric_limits<Cost>::min();
kpeter@609
  1040
        for (int i = 0; i != _arc_num; ++i) {
kpeter@640
  1041
          if (_cost[i] > ART_COST) ART_COST = _cost[i];
kpeter@609
  1042
        }
kpeter@640
  1043
        ART_COST = (ART_COST + 1) * _node_num;
kpeter@609
  1044
      }
kpeter@609
  1045
kpeter@642
  1046
      // Initialize arc maps
kpeter@642
  1047
      for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1048
        _flow[i] = 0;
kpeter@642
  1049
        _state[i] = STATE_LOWER;
kpeter@642
  1050
      }
kpeter@642
  1051
      
kpeter@601
  1052
      // Set data for the artificial root node
kpeter@601
  1053
      _root = _node_num;
kpeter@601
  1054
      _parent[_root] = -1;
kpeter@601
  1055
      _pred[_root] = -1;
kpeter@601
  1056
      _thread[_root] = 0;
kpeter@604
  1057
      _rev_thread[0] = _root;
kpeter@642
  1058
      _succ_num[_root] = _node_num + 1;
kpeter@604
  1059
      _last_succ[_root] = _root - 1;
kpeter@640
  1060
      _supply[_root] = -_sum_supply;
kpeter@663
  1061
      _pi[_root] = 0;
kpeter@601
  1062
kpeter@601
  1063
      // Add artificial arcs and initialize the spanning tree data structure
kpeter@663
  1064
      if (_sum_supply == 0) {
kpeter@663
  1065
        // EQ supply constraints
kpeter@663
  1066
        _search_arc_num = _arc_num;
kpeter@663
  1067
        _all_arc_num = _arc_num + _node_num;
kpeter@663
  1068
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@663
  1069
          _parent[u] = _root;
kpeter@663
  1070
          _pred[u] = e;
kpeter@663
  1071
          _thread[u] = u + 1;
kpeter@663
  1072
          _rev_thread[u + 1] = u;
kpeter@663
  1073
          _succ_num[u] = 1;
kpeter@663
  1074
          _last_succ[u] = u;
kpeter@663
  1075
          _cap[e] = INF;
kpeter@663
  1076
          _state[e] = STATE_TREE;
kpeter@663
  1077
          if (_supply[u] >= 0) {
kpeter@663
  1078
            _forward[u] = true;
kpeter@663
  1079
            _pi[u] = 0;
kpeter@663
  1080
            _source[e] = u;
kpeter@663
  1081
            _target[e] = _root;
kpeter@663
  1082
            _flow[e] = _supply[u];
kpeter@663
  1083
            _cost[e] = 0;
kpeter@663
  1084
          } else {
kpeter@663
  1085
            _forward[u] = false;
kpeter@663
  1086
            _pi[u] = ART_COST;
kpeter@663
  1087
            _source[e] = _root;
kpeter@663
  1088
            _target[e] = u;
kpeter@663
  1089
            _flow[e] = -_supply[u];
kpeter@663
  1090
            _cost[e] = ART_COST;
kpeter@663
  1091
          }
kpeter@601
  1092
        }
kpeter@601
  1093
      }
kpeter@663
  1094
      else if (_sum_supply > 0) {
kpeter@663
  1095
        // LEQ supply constraints
kpeter@663
  1096
        _search_arc_num = _arc_num + _node_num;
kpeter@663
  1097
        int f = _arc_num + _node_num;
kpeter@663
  1098
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@663
  1099
          _parent[u] = _root;
kpeter@663
  1100
          _thread[u] = u + 1;
kpeter@663
  1101
          _rev_thread[u + 1] = u;
kpeter@663
  1102
          _succ_num[u] = 1;
kpeter@663
  1103
          _last_succ[u] = u;
kpeter@663
  1104
          if (_supply[u] >= 0) {
kpeter@663
  1105
            _forward[u] = true;
kpeter@663
  1106
            _pi[u] = 0;
kpeter@663
  1107
            _pred[u] = e;
kpeter@663
  1108
            _source[e] = u;
kpeter@663
  1109
            _target[e] = _root;
kpeter@663
  1110
            _cap[e] = INF;
kpeter@663
  1111
            _flow[e] = _supply[u];
kpeter@663
  1112
            _cost[e] = 0;
kpeter@663
  1113
            _state[e] = STATE_TREE;
kpeter@663
  1114
          } else {
kpeter@663
  1115
            _forward[u] = false;
kpeter@663
  1116
            _pi[u] = ART_COST;
kpeter@663
  1117
            _pred[u] = f;
kpeter@663
  1118
            _source[f] = _root;
kpeter@663
  1119
            _target[f] = u;
kpeter@663
  1120
            _cap[f] = INF;
kpeter@663
  1121
            _flow[f] = -_supply[u];
kpeter@663
  1122
            _cost[f] = ART_COST;
kpeter@663
  1123
            _state[f] = STATE_TREE;
kpeter@663
  1124
            _source[e] = u;
kpeter@663
  1125
            _target[e] = _root;
kpeter@663
  1126
            _cap[e] = INF;
kpeter@663
  1127
            _flow[e] = 0;
kpeter@663
  1128
            _cost[e] = 0;
kpeter@663
  1129
            _state[e] = STATE_LOWER;
kpeter@663
  1130
            ++f;
kpeter@663
  1131
          }
kpeter@663
  1132
        }
kpeter@663
  1133
        _all_arc_num = f;
kpeter@663
  1134
      }
kpeter@663
  1135
      else {
kpeter@663
  1136
        // GEQ 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] = false;
kpeter@663
  1147
            _pi[u] = 0;
kpeter@663
  1148
            _pred[u] = e;
kpeter@663
  1149
            _source[e] = _root;
kpeter@663
  1150
            _target[e] = u;
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] = true;
kpeter@663
  1157
            _pi[u] = -ART_COST;
kpeter@663
  1158
            _pred[u] = f;
kpeter@663
  1159
            _source[f] = u;
kpeter@663
  1160
            _target[f] = _root;
kpeter@663
  1161
            _cap[f] = INF;
kpeter@663
  1162
            _flow[f] = _supply[u];
kpeter@663
  1163
            _state[f] = STATE_TREE;
kpeter@663
  1164
            _cost[f] = ART_COST;
kpeter@663
  1165
            _source[e] = _root;
kpeter@663
  1166
            _target[e] = u;
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@601
  1176
kpeter@601
  1177
      return true;
kpeter@601
  1178
    }
kpeter@601
  1179
kpeter@601
  1180
    // Find the join node
kpeter@601
  1181
    void findJoinNode() {
kpeter@603
  1182
      int u = _source[in_arc];
kpeter@603
  1183
      int v = _target[in_arc];
kpeter@601
  1184
      while (u != v) {
kpeter@604
  1185
        if (_succ_num[u] < _succ_num[v]) {
kpeter@604
  1186
          u = _parent[u];
kpeter@604
  1187
        } else {
kpeter@604
  1188
          v = _parent[v];
kpeter@604
  1189
        }
kpeter@601
  1190
      }
kpeter@601
  1191
      join = u;
kpeter@601
  1192
    }
kpeter@601
  1193
kpeter@601
  1194
    // Find the leaving arc of the cycle and returns true if the
kpeter@601
  1195
    // leaving arc is not the same as the entering arc
kpeter@601
  1196
    bool findLeavingArc() {
kpeter@601
  1197
      // Initialize first and second nodes according to the direction
kpeter@601
  1198
      // of the cycle
kpeter@603
  1199
      if (_state[in_arc] == STATE_LOWER) {
kpeter@603
  1200
        first  = _source[in_arc];
kpeter@603
  1201
        second = _target[in_arc];
kpeter@601
  1202
      } else {
kpeter@603
  1203
        first  = _target[in_arc];
kpeter@603
  1204
        second = _source[in_arc];
kpeter@601
  1205
      }
kpeter@603
  1206
      delta = _cap[in_arc];
kpeter@601
  1207
      int result = 0;
kpeter@641
  1208
      Value d;
kpeter@601
  1209
      int e;
kpeter@601
  1210
kpeter@601
  1211
      // Search the cycle along the path form the first node to the root
kpeter@601
  1212
      for (int u = first; u != join; u = _parent[u]) {
kpeter@601
  1213
        e = _pred[u];
kpeter@640
  1214
        d = _forward[u] ?
kpeter@640
  1215
          _flow[e] : (_cap[e] == INF ? INF : _cap[e] - _flow[e]);
kpeter@601
  1216
        if (d < delta) {
kpeter@601
  1217
          delta = d;
kpeter@601
  1218
          u_out = u;
kpeter@601
  1219
          result = 1;
kpeter@601
  1220
        }
kpeter@601
  1221
      }
kpeter@601
  1222
      // Search the cycle along the path form the second node to the root
kpeter@601
  1223
      for (int u = second; u != join; u = _parent[u]) {
kpeter@601
  1224
        e = _pred[u];
kpeter@640
  1225
        d = _forward[u] ? 
kpeter@640
  1226
          (_cap[e] == INF ? INF : _cap[e] - _flow[e]) : _flow[e];
kpeter@601
  1227
        if (d <= delta) {
kpeter@601
  1228
          delta = d;
kpeter@601
  1229
          u_out = u;
kpeter@601
  1230
          result = 2;
kpeter@601
  1231
        }
kpeter@601
  1232
      }
kpeter@601
  1233
kpeter@601
  1234
      if (result == 1) {
kpeter@601
  1235
        u_in = first;
kpeter@601
  1236
        v_in = second;
kpeter@601
  1237
      } else {
kpeter@601
  1238
        u_in = second;
kpeter@601
  1239
        v_in = first;
kpeter@601
  1240
      }
kpeter@601
  1241
      return result != 0;
kpeter@601
  1242
    }
kpeter@601
  1243
kpeter@601
  1244
    // Change _flow and _state vectors
kpeter@601
  1245
    void changeFlow(bool change) {
kpeter@601
  1246
      // Augment along the cycle
kpeter@601
  1247
      if (delta > 0) {
kpeter@641
  1248
        Value val = _state[in_arc] * delta;
kpeter@603
  1249
        _flow[in_arc] += val;
kpeter@603
  1250
        for (int u = _source[in_arc]; u != join; u = _parent[u]) {
kpeter@601
  1251
          _flow[_pred[u]] += _forward[u] ? -val : val;
kpeter@601
  1252
        }
kpeter@603
  1253
        for (int u = _target[in_arc]; u != join; u = _parent[u]) {
kpeter@601
  1254
          _flow[_pred[u]] += _forward[u] ? val : -val;
kpeter@601
  1255
        }
kpeter@601
  1256
      }
kpeter@601
  1257
      // Update the state of the entering and leaving arcs
kpeter@601
  1258
      if (change) {
kpeter@603
  1259
        _state[in_arc] = STATE_TREE;
kpeter@601
  1260
        _state[_pred[u_out]] =
kpeter@601
  1261
          (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
kpeter@601
  1262
      } else {
kpeter@603
  1263
        _state[in_arc] = -_state[in_arc];
kpeter@601
  1264
      }
kpeter@601
  1265
    }
kpeter@601
  1266
kpeter@604
  1267
    // Update the tree structure
kpeter@604
  1268
    void updateTreeStructure() {
kpeter@604
  1269
      int u, w;
kpeter@604
  1270
      int old_rev_thread = _rev_thread[u_out];
kpeter@604
  1271
      int old_succ_num = _succ_num[u_out];
kpeter@604
  1272
      int old_last_succ = _last_succ[u_out];
kpeter@601
  1273
      v_out = _parent[u_out];
kpeter@601
  1274
kpeter@604
  1275
      u = _last_succ[u_in];  // the last successor of u_in
kpeter@604
  1276
      right = _thread[u];    // the node after it
kpeter@604
  1277
kpeter@604
  1278
      // Handle the case when old_rev_thread equals to v_in
kpeter@604
  1279
      // (it also means that join and v_out coincide)
kpeter@604
  1280
      if (old_rev_thread == v_in) {
kpeter@604
  1281
        last = _thread[_last_succ[u_out]];
kpeter@604
  1282
      } else {
kpeter@604
  1283
        last = _thread[v_in];
kpeter@601
  1284
      }
kpeter@601
  1285
kpeter@604
  1286
      // Update _thread and _parent along the stem nodes (i.e. the nodes
kpeter@604
  1287
      // between u_in and u_out, whose parent have to be changed)
kpeter@601
  1288
      _thread[v_in] = stem = u_in;
kpeter@604
  1289
      _dirty_revs.clear();
kpeter@604
  1290
      _dirty_revs.push_back(v_in);
kpeter@601
  1291
      par_stem = v_in;
kpeter@601
  1292
      while (stem != u_out) {
kpeter@604
  1293
        // Insert the next stem node into the thread list
kpeter@604
  1294
        new_stem = _parent[stem];
kpeter@604
  1295
        _thread[u] = new_stem;
kpeter@604
  1296
        _dirty_revs.push_back(u);
kpeter@601
  1297
kpeter@604
  1298
        // Remove the subtree of stem from the thread list
kpeter@604
  1299
        w = _rev_thread[stem];
kpeter@604
  1300
        _thread[w] = right;
kpeter@604
  1301
        _rev_thread[right] = w;
kpeter@601
  1302
kpeter@604
  1303
        // Change the parent node and shift stem nodes
kpeter@601
  1304
        _parent[stem] = par_stem;
kpeter@601
  1305
        par_stem = stem;
kpeter@601
  1306
        stem = new_stem;
kpeter@601
  1307
kpeter@604
  1308
        // Update u and right
kpeter@604
  1309
        u = _last_succ[stem] == _last_succ[par_stem] ?
kpeter@604
  1310
          _rev_thread[par_stem] : _last_succ[stem];
kpeter@601
  1311
        right = _thread[u];
kpeter@601
  1312
      }
kpeter@601
  1313
      _parent[u_out] = par_stem;
kpeter@601
  1314
      _thread[u] = last;
kpeter@604
  1315
      _rev_thread[last] = u;
kpeter@604
  1316
      _last_succ[u_out] = u;
kpeter@601
  1317
kpeter@604
  1318
      // Remove the subtree of u_out from the thread list except for
kpeter@604
  1319
      // 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
        _thread[old_rev_thread] = right;
kpeter@604
  1323
        _rev_thread[right] = old_rev_thread;
kpeter@604
  1324
      }
kpeter@604
  1325
kpeter@604
  1326
      // Update _rev_thread using the new _thread values
kpeter@604
  1327
      for (int i = 0; i < int(_dirty_revs.size()); ++i) {
kpeter@604
  1328
        u = _dirty_revs[i];
kpeter@604
  1329
        _rev_thread[_thread[u]] = u;
kpeter@604
  1330
      }
kpeter@604
  1331
kpeter@604
  1332
      // Update _pred, _forward, _last_succ and _succ_num for the
kpeter@604
  1333
      // stem nodes from u_out to u_in
kpeter@604
  1334
      int tmp_sc = 0, tmp_ls = _last_succ[u_out];
kpeter@604
  1335
      u = u_out;
kpeter@604
  1336
      while (u != u_in) {
kpeter@604
  1337
        w = _parent[u];
kpeter@604
  1338
        _pred[u] = _pred[w];
kpeter@604
  1339
        _forward[u] = !_forward[w];
kpeter@604
  1340
        tmp_sc += _succ_num[u] - _succ_num[w];
kpeter@604
  1341
        _succ_num[u] = tmp_sc;
kpeter@604
  1342
        _last_succ[w] = tmp_ls;
kpeter@604
  1343
        u = w;
kpeter@604
  1344
      }
kpeter@604
  1345
      _pred[u_in] = in_arc;
kpeter@604
  1346
      _forward[u_in] = (u_in == _source[in_arc]);
kpeter@604
  1347
      _succ_num[u_in] = old_succ_num;
kpeter@604
  1348
kpeter@604
  1349
      // Set limits for updating _last_succ form v_in and v_out
kpeter@604
  1350
      // towards the root
kpeter@604
  1351
      int up_limit_in = -1;
kpeter@604
  1352
      int up_limit_out = -1;
kpeter@604
  1353
      if (_last_succ[join] == v_in) {
kpeter@604
  1354
        up_limit_out = join;
kpeter@601
  1355
      } else {
kpeter@604
  1356
        up_limit_in = join;
kpeter@604
  1357
      }
kpeter@604
  1358
kpeter@604
  1359
      // Update _last_succ from v_in towards the root
kpeter@604
  1360
      for (u = v_in; u != up_limit_in && _last_succ[u] == v_in;
kpeter@604
  1361
           u = _parent[u]) {
kpeter@604
  1362
        _last_succ[u] = _last_succ[u_out];
kpeter@604
  1363
      }
kpeter@604
  1364
      // Update _last_succ from v_out towards the root
kpeter@604
  1365
      if (join != old_rev_thread && v_in != old_rev_thread) {
kpeter@604
  1366
        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@604
  1367
             u = _parent[u]) {
kpeter@604
  1368
          _last_succ[u] = old_rev_thread;
kpeter@604
  1369
        }
kpeter@604
  1370
      } else {
kpeter@604
  1371
        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@604
  1372
             u = _parent[u]) {
kpeter@604
  1373
          _last_succ[u] = _last_succ[u_out];
kpeter@604
  1374
        }
kpeter@604
  1375
      }
kpeter@604
  1376
kpeter@604
  1377
      // Update _succ_num from v_in to join
kpeter@604
  1378
      for (u = v_in; u != join; u = _parent[u]) {
kpeter@604
  1379
        _succ_num[u] += old_succ_num;
kpeter@604
  1380
      }
kpeter@604
  1381
      // Update _succ_num from v_out to join
kpeter@604
  1382
      for (u = v_out; u != join; u = _parent[u]) {
kpeter@604
  1383
        _succ_num[u] -= old_succ_num;
kpeter@601
  1384
      }
kpeter@601
  1385
    }
kpeter@601
  1386
kpeter@604
  1387
    // Update potentials
kpeter@604
  1388
    void updatePotential() {
kpeter@607
  1389
      Cost sigma = _forward[u_in] ?
kpeter@601
  1390
        _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
kpeter@601
  1391
        _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
kpeter@608
  1392
      // Update potentials in the subtree, which has been moved
kpeter@608
  1393
      int end = _thread[_last_succ[u_in]];
kpeter@608
  1394
      for (int u = u_in; u != end; u = _thread[u]) {
kpeter@608
  1395
        _pi[u] += sigma;
kpeter@601
  1396
      }
kpeter@601
  1397
    }
kpeter@601
  1398
kpeter@601
  1399
    // Execute the algorithm
kpeter@640
  1400
    ProblemType start(PivotRule pivot_rule) {
kpeter@601
  1401
      // Select the pivot rule implementation
kpeter@601
  1402
      switch (pivot_rule) {
kpeter@605
  1403
        case FIRST_ELIGIBLE:
kpeter@601
  1404
          return start<FirstEligiblePivotRule>();
kpeter@605
  1405
        case BEST_ELIGIBLE:
kpeter@601
  1406
          return start<BestEligiblePivotRule>();
kpeter@605
  1407
        case BLOCK_SEARCH:
kpeter@601
  1408
          return start<BlockSearchPivotRule>();
kpeter@605
  1409
        case CANDIDATE_LIST:
kpeter@601
  1410
          return start<CandidateListPivotRule>();
kpeter@605
  1411
        case ALTERING_LIST:
kpeter@601
  1412
          return start<AlteringListPivotRule>();
kpeter@601
  1413
      }
kpeter@640
  1414
      return INFEASIBLE; // avoid warning
kpeter@601
  1415
    }
kpeter@601
  1416
kpeter@605
  1417
    template <typename PivotRuleImpl>
kpeter@640
  1418
    ProblemType start() {
kpeter@605
  1419
      PivotRuleImpl pivot(*this);
kpeter@601
  1420
kpeter@605
  1421
      // Execute the Network Simplex algorithm
kpeter@601
  1422
      while (pivot.findEnteringArc()) {
kpeter@601
  1423
        findJoinNode();
kpeter@601
  1424
        bool change = findLeavingArc();
kpeter@640
  1425
        if (delta >= INF) return UNBOUNDED;
kpeter@601
  1426
        changeFlow(change);
kpeter@601
  1427
        if (change) {
kpeter@604
  1428
          updateTreeStructure();
kpeter@604
  1429
          updatePotential();
kpeter@601
  1430
        }
kpeter@601
  1431
      }
kpeter@640
  1432
      
kpeter@640
  1433
      // Check feasibility
kpeter@663
  1434
      for (int e = _search_arc_num; e != _all_arc_num; ++e) {
kpeter@663
  1435
        if (_flow[e] != 0) return INFEASIBLE;
kpeter@640
  1436
      }
kpeter@601
  1437
kpeter@642
  1438
      // Transform the solution and the supply map to the original form
kpeter@642
  1439
      if (_have_lower) {
kpeter@601
  1440
        for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1441
          Value c = _lower[i];
kpeter@642
  1442
          if (c != 0) {
kpeter@642
  1443
            _flow[i] += c;
kpeter@642
  1444
            _supply[_source[i]] += c;
kpeter@642
  1445
            _supply[_target[i]] -= c;
kpeter@642
  1446
          }
kpeter@601
  1447
        }
kpeter@601
  1448
      }
kpeter@663
  1449
      
kpeter@663
  1450
      // Shift potentials to meet the requirements of the GEQ/LEQ type
kpeter@663
  1451
      // optimality conditions
kpeter@663
  1452
      if (_sum_supply == 0) {
kpeter@663
  1453
        if (_stype == GEQ) {
kpeter@663
  1454
          Cost max_pot = std::numeric_limits<Cost>::min();
kpeter@663
  1455
          for (int i = 0; i != _node_num; ++i) {
kpeter@663
  1456
            if (_pi[i] > max_pot) max_pot = _pi[i];
kpeter@663
  1457
          }
kpeter@663
  1458
          if (max_pot > 0) {
kpeter@663
  1459
            for (int i = 0; i != _node_num; ++i)
kpeter@663
  1460
              _pi[i] -= max_pot;
kpeter@663
  1461
          }
kpeter@663
  1462
        } else {
kpeter@663
  1463
          Cost min_pot = std::numeric_limits<Cost>::max();
kpeter@663
  1464
          for (int i = 0; i != _node_num; ++i) {
kpeter@663
  1465
            if (_pi[i] < min_pot) min_pot = _pi[i];
kpeter@663
  1466
          }
kpeter@663
  1467
          if (min_pot < 0) {
kpeter@663
  1468
            for (int i = 0; i != _node_num; ++i)
kpeter@663
  1469
              _pi[i] -= min_pot;
kpeter@663
  1470
          }
kpeter@663
  1471
        }
kpeter@663
  1472
      }
kpeter@601
  1473
kpeter@640
  1474
      return OPTIMAL;
kpeter@601
  1475
    }
kpeter@601
  1476
kpeter@601
  1477
  }; //class NetworkSimplex
kpeter@601
  1478
kpeter@601
  1479
  ///@}
kpeter@601
  1480
kpeter@601
  1481
} //namespace lemon
kpeter@601
  1482
kpeter@601
  1483
#endif //LEMON_NETWORK_SIMPLEX_H