lemon/network_simplex.h
author Balazs Dezso <deba@inf.elte.hu>
Thu, 04 Mar 2010 15:20:59 +0100
changeset 951 41d7ac528c3a
parent 690 f3792d5bb294
child 774 cab85bd7859b
child 776 be48a648d28f
child 976 5205145fabf6
permissions -rw-r--r--
Uniforming primal scale to 2 (#314)
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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<Arc> ArcVector;
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    typedef std::vector<Node> NodeVector;
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    typedef std::vector<int> IntVector;
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    typedef std::vector<bool> BoolVector;
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    typedef std::vector<Value> ValueVector;
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    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, min_arc = _next_arc;
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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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            min_arc = e;
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          }
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          if (--cnt == 0) {
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            if (min < 0) break;
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            cnt = _block_size;
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          }
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        }
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        if (min == 0 || cnt > 0) {
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          for (e = 0; e < _next_arc; ++e) {
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            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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            if (c < min) {
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              min = c;
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              min_arc = e;
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            }
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            if (--cnt == 0) {
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              if (min < 0) break;
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              cnt = _block_size;
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            }
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          }
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        }
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        if (min >= 0) return false;
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        _in_arc = min_arc;
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        _next_arc = e;
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        return true;
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      }
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    }; //class BlockSearchPivotRule
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    // Implementation of the Candidate List pivot rule
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    class CandidateListPivotRule
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    {
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    private:
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      // References to the NetworkSimplex class
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      const IntVector  &_source;
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      const IntVector  &_target;
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   409
      const CostVector &_cost;
kpeter@648
   410
      const IntVector  &_state;
kpeter@654
   411
      const CostVector &_pi;
kpeter@648
   412
      int &_in_arc;
kpeter@710
   413
      int _search_arc_num;
kpeter@648
   414
kpeter@648
   415
      // Pivot rule data
kpeter@648
   416
      IntVector _candidates;
kpeter@648
   417
      int _list_length, _minor_limit;
kpeter@648
   418
      int _curr_length, _minor_count;
kpeter@648
   419
      int _next_arc;
kpeter@648
   420
kpeter@648
   421
    public:
kpeter@648
   422
kpeter@648
   423
      /// Constructor
kpeter@648
   424
      CandidateListPivotRule(NetworkSimplex &ns) :
kpeter@650
   425
        _source(ns._source), _target(ns._target),
kpeter@648
   426
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@710
   427
        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
kpeter@710
   428
        _next_arc(0)
kpeter@648
   429
      {
kpeter@648
   430
        // The main parameters of the pivot rule
kpeter@648
   431
        const double LIST_LENGTH_FACTOR = 1.0;
kpeter@648
   432
        const int MIN_LIST_LENGTH = 10;
kpeter@648
   433
        const double MINOR_LIMIT_FACTOR = 0.1;
kpeter@648
   434
        const int MIN_MINOR_LIMIT = 3;
kpeter@648
   435
alpar@659
   436
        _list_length = std::max( int(LIST_LENGTH_FACTOR *
kpeter@710
   437
                                     std::sqrt(double(_search_arc_num))),
kpeter@648
   438
                                 MIN_LIST_LENGTH );
kpeter@648
   439
        _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
kpeter@648
   440
                                 MIN_MINOR_LIMIT );
kpeter@648
   441
        _curr_length = _minor_count = 0;
kpeter@648
   442
        _candidates.resize(_list_length);
kpeter@648
   443
      }
kpeter@648
   444
kpeter@648
   445
      /// Find next entering arc
kpeter@648
   446
      bool findEnteringArc() {
kpeter@654
   447
        Cost min, c;
kpeter@648
   448
        int e, min_arc = _next_arc;
kpeter@648
   449
        if (_curr_length > 0 && _minor_count < _minor_limit) {
kpeter@648
   450
          // Minor iteration: select the best eligible arc from the
kpeter@648
   451
          // current candidate list
kpeter@648
   452
          ++_minor_count;
kpeter@648
   453
          min = 0;
kpeter@648
   454
          for (int i = 0; i < _curr_length; ++i) {
kpeter@648
   455
            e = _candidates[i];
kpeter@648
   456
            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   457
            if (c < min) {
kpeter@648
   458
              min = c;
kpeter@648
   459
              min_arc = e;
kpeter@648
   460
            }
kpeter@648
   461
            if (c >= 0) {
kpeter@648
   462
              _candidates[i--] = _candidates[--_curr_length];
kpeter@648
   463
            }
kpeter@648
   464
          }
kpeter@648
   465
          if (min < 0) {
kpeter@648
   466
            _in_arc = min_arc;
kpeter@648
   467
            return true;
kpeter@648
   468
          }
kpeter@648
   469
        }
kpeter@648
   470
kpeter@648
   471
        // Major iteration: build a new candidate list
kpeter@648
   472
        min = 0;
kpeter@648
   473
        _curr_length = 0;
kpeter@710
   474
        for (e = _next_arc; e < _search_arc_num; ++e) {
kpeter@648
   475
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   476
          if (c < 0) {
kpeter@648
   477
            _candidates[_curr_length++] = e;
kpeter@648
   478
            if (c < min) {
kpeter@648
   479
              min = c;
kpeter@648
   480
              min_arc = e;
kpeter@648
   481
            }
kpeter@648
   482
            if (_curr_length == _list_length) break;
kpeter@648
   483
          }
kpeter@648
   484
        }
kpeter@648
   485
        if (_curr_length < _list_length) {
kpeter@648
   486
          for (e = 0; e < _next_arc; ++e) {
kpeter@648
   487
            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   488
            if (c < 0) {
kpeter@648
   489
              _candidates[_curr_length++] = e;
kpeter@648
   490
              if (c < min) {
kpeter@648
   491
                min = c;
kpeter@648
   492
                min_arc = e;
kpeter@648
   493
              }
kpeter@648
   494
              if (_curr_length == _list_length) break;
kpeter@648
   495
            }
kpeter@648
   496
          }
kpeter@648
   497
        }
kpeter@648
   498
        if (_curr_length == 0) return false;
kpeter@648
   499
        _minor_count = 1;
kpeter@648
   500
        _in_arc = min_arc;
kpeter@648
   501
        _next_arc = e;
kpeter@648
   502
        return true;
kpeter@648
   503
      }
kpeter@648
   504
kpeter@648
   505
    }; //class CandidateListPivotRule
kpeter@648
   506
kpeter@648
   507
kpeter@652
   508
    // Implementation of the Altering Candidate List pivot rule
kpeter@648
   509
    class AlteringListPivotRule
kpeter@648
   510
    {
kpeter@648
   511
    private:
kpeter@648
   512
kpeter@648
   513
      // References to the NetworkSimplex class
kpeter@648
   514
      const IntVector  &_source;
kpeter@648
   515
      const IntVector  &_target;
kpeter@654
   516
      const CostVector &_cost;
kpeter@648
   517
      const IntVector  &_state;
kpeter@654
   518
      const CostVector &_pi;
kpeter@648
   519
      int &_in_arc;
kpeter@710
   520
      int _search_arc_num;
kpeter@648
   521
kpeter@648
   522
      // Pivot rule data
kpeter@648
   523
      int _block_size, _head_length, _curr_length;
kpeter@648
   524
      int _next_arc;
kpeter@648
   525
      IntVector _candidates;
kpeter@654
   526
      CostVector _cand_cost;
kpeter@648
   527
kpeter@648
   528
      // Functor class to compare arcs during sort of the candidate list
kpeter@648
   529
      class SortFunc
kpeter@648
   530
      {
kpeter@648
   531
      private:
kpeter@654
   532
        const CostVector &_map;
kpeter@648
   533
      public:
kpeter@654
   534
        SortFunc(const CostVector &map) : _map(map) {}
kpeter@648
   535
        bool operator()(int left, int right) {
kpeter@648
   536
          return _map[left] > _map[right];
kpeter@648
   537
        }
kpeter@648
   538
      };
kpeter@648
   539
kpeter@648
   540
      SortFunc _sort_func;
kpeter@648
   541
kpeter@648
   542
    public:
kpeter@648
   543
kpeter@652
   544
      // Constructor
kpeter@648
   545
      AlteringListPivotRule(NetworkSimplex &ns) :
kpeter@650
   546
        _source(ns._source), _target(ns._target),
kpeter@648
   547
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@710
   548
        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
kpeter@710
   549
        _next_arc(0), _cand_cost(ns._search_arc_num), _sort_func(_cand_cost)
kpeter@648
   550
      {
kpeter@648
   551
        // The main parameters of the pivot rule
kpeter@648
   552
        const double BLOCK_SIZE_FACTOR = 1.5;
kpeter@648
   553
        const int MIN_BLOCK_SIZE = 10;
kpeter@648
   554
        const double HEAD_LENGTH_FACTOR = 0.1;
kpeter@648
   555
        const int MIN_HEAD_LENGTH = 3;
kpeter@648
   556
alpar@659
   557
        _block_size = std::max( int(BLOCK_SIZE_FACTOR *
kpeter@710
   558
                                    std::sqrt(double(_search_arc_num))),
kpeter@648
   559
                                MIN_BLOCK_SIZE );
kpeter@648
   560
        _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),
kpeter@648
   561
                                 MIN_HEAD_LENGTH );
kpeter@648
   562
        _candidates.resize(_head_length + _block_size);
kpeter@648
   563
        _curr_length = 0;
kpeter@648
   564
      }
kpeter@648
   565
kpeter@652
   566
      // Find next entering arc
kpeter@648
   567
      bool findEnteringArc() {
kpeter@648
   568
        // Check the current candidate list
kpeter@648
   569
        int e;
kpeter@648
   570
        for (int i = 0; i < _curr_length; ++i) {
kpeter@648
   571
          e = _candidates[i];
kpeter@648
   572
          _cand_cost[e] = _state[e] *
kpeter@648
   573
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   574
          if (_cand_cost[e] >= 0) {
kpeter@648
   575
            _candidates[i--] = _candidates[--_curr_length];
kpeter@648
   576
          }
kpeter@648
   577
        }
kpeter@648
   578
kpeter@648
   579
        // Extend the list
kpeter@648
   580
        int cnt = _block_size;
kpeter@650
   581
        int last_arc = 0;
kpeter@648
   582
        int limit = _head_length;
kpeter@648
   583
kpeter@710
   584
        for (int e = _next_arc; e < _search_arc_num; ++e) {
kpeter@648
   585
          _cand_cost[e] = _state[e] *
kpeter@648
   586
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   587
          if (_cand_cost[e] < 0) {
kpeter@648
   588
            _candidates[_curr_length++] = e;
kpeter@650
   589
            last_arc = e;
kpeter@648
   590
          }
kpeter@648
   591
          if (--cnt == 0) {
kpeter@648
   592
            if (_curr_length > limit) break;
kpeter@648
   593
            limit = 0;
kpeter@648
   594
            cnt = _block_size;
kpeter@648
   595
          }
kpeter@648
   596
        }
kpeter@648
   597
        if (_curr_length <= limit) {
kpeter@648
   598
          for (int e = 0; e < _next_arc; ++e) {
kpeter@648
   599
            _cand_cost[e] = _state[e] *
kpeter@648
   600
              (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   601
            if (_cand_cost[e] < 0) {
kpeter@648
   602
              _candidates[_curr_length++] = e;
kpeter@650
   603
              last_arc = e;
kpeter@648
   604
            }
kpeter@648
   605
            if (--cnt == 0) {
kpeter@648
   606
              if (_curr_length > limit) break;
kpeter@648
   607
              limit = 0;
kpeter@648
   608
              cnt = _block_size;
kpeter@648
   609
            }
kpeter@648
   610
          }
kpeter@648
   611
        }
kpeter@648
   612
        if (_curr_length == 0) return false;
kpeter@650
   613
        _next_arc = last_arc + 1;
kpeter@648
   614
kpeter@648
   615
        // Make heap of the candidate list (approximating a partial sort)
kpeter@648
   616
        make_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@648
   617
                   _sort_func );
kpeter@648
   618
kpeter@648
   619
        // Pop the first element of the heap
kpeter@648
   620
        _in_arc = _candidates[0];
kpeter@648
   621
        pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@648
   622
                  _sort_func );
kpeter@648
   623
        _curr_length = std::min(_head_length, _curr_length - 1);
kpeter@648
   624
        return true;
kpeter@648
   625
      }
kpeter@648
   626
kpeter@648
   627
    }; //class AlteringListPivotRule
kpeter@648
   628
kpeter@648
   629
  public:
kpeter@648
   630
kpeter@652
   631
    /// \brief Constructor.
kpeter@648
   632
    ///
kpeter@656
   633
    /// The constructor of the class.
kpeter@648
   634
    ///
kpeter@650
   635
    /// \param graph The digraph the algorithm runs on.
kpeter@652
   636
    NetworkSimplex(const GR& graph) :
kpeter@689
   637
      _graph(graph), _node_id(graph), _arc_id(graph),
kpeter@688
   638
      INF(std::numeric_limits<Value>::has_infinity ?
kpeter@688
   639
          std::numeric_limits<Value>::infinity() :
kpeter@688
   640
          std::numeric_limits<Value>::max())
kpeter@652
   641
    {
kpeter@687
   642
      // Check the value types
kpeter@688
   643
      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
kpeter@687
   644
        "The flow type of NetworkSimplex must be signed");
kpeter@687
   645
      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
kpeter@687
   646
        "The cost type of NetworkSimplex must be signed");
kpeter@689
   647
        
kpeter@689
   648
      // Resize vectors
kpeter@689
   649
      _node_num = countNodes(_graph);
kpeter@689
   650
      _arc_num = countArcs(_graph);
kpeter@689
   651
      int all_node_num = _node_num + 1;
kpeter@710
   652
      int max_arc_num = _arc_num + 2 * _node_num;
kpeter@648
   653
kpeter@710
   654
      _source.resize(max_arc_num);
kpeter@710
   655
      _target.resize(max_arc_num);
kpeter@689
   656
kpeter@710
   657
      _lower.resize(_arc_num);
kpeter@710
   658
      _upper.resize(_arc_num);
kpeter@710
   659
      _cap.resize(max_arc_num);
kpeter@710
   660
      _cost.resize(max_arc_num);
kpeter@689
   661
      _supply.resize(all_node_num);
kpeter@710
   662
      _flow.resize(max_arc_num);
kpeter@689
   663
      _pi.resize(all_node_num);
kpeter@689
   664
kpeter@689
   665
      _parent.resize(all_node_num);
kpeter@689
   666
      _pred.resize(all_node_num);
kpeter@689
   667
      _forward.resize(all_node_num);
kpeter@689
   668
      _thread.resize(all_node_num);
kpeter@689
   669
      _rev_thread.resize(all_node_num);
kpeter@689
   670
      _succ_num.resize(all_node_num);
kpeter@689
   671
      _last_succ.resize(all_node_num);
kpeter@710
   672
      _state.resize(max_arc_num);
kpeter@689
   673
kpeter@689
   674
      // Copy the graph (store the arcs in a mixed order)
kpeter@689
   675
      int i = 0;
kpeter@689
   676
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@689
   677
        _node_id[n] = i;
kpeter@689
   678
      }
kpeter@689
   679
      int k = std::max(int(std::sqrt(double(_arc_num))), 10);
kpeter@689
   680
      i = 0;
kpeter@689
   681
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@689
   682
        _arc_id[a] = i;
kpeter@689
   683
        _source[i] = _node_id[_graph.source(a)];
kpeter@689
   684
        _target[i] = _node_id[_graph.target(a)];
kpeter@689
   685
        if ((i += k) >= _arc_num) i = (i % k) + 1;
kpeter@689
   686
      }
kpeter@689
   687
      
kpeter@689
   688
      // Initialize maps
kpeter@689
   689
      for (int i = 0; i != _node_num; ++i) {
kpeter@689
   690
        _supply[i] = 0;
kpeter@689
   691
      }
kpeter@689
   692
      for (int i = 0; i != _arc_num; ++i) {
kpeter@689
   693
        _lower[i] = 0;
kpeter@689
   694
        _upper[i] = INF;
kpeter@689
   695
        _cost[i] = 1;
kpeter@689
   696
      }
kpeter@689
   697
      _have_lower = false;
kpeter@689
   698
      _stype = GEQ;
kpeter@648
   699
    }
kpeter@648
   700
kpeter@656
   701
    /// \name Parameters
kpeter@656
   702
    /// The parameters of the algorithm can be specified using these
kpeter@656
   703
    /// functions.
kpeter@656
   704
kpeter@656
   705
    /// @{
kpeter@656
   706
kpeter@652
   707
    /// \brief Set the lower bounds on the arcs.
kpeter@652
   708
    ///
kpeter@652
   709
    /// This function sets the lower bounds on the arcs.
kpeter@687
   710
    /// If it is not used before calling \ref run(), the lower bounds
kpeter@687
   711
    /// will be set to zero on all arcs.
kpeter@652
   712
    ///
kpeter@652
   713
    /// \param map An arc map storing the lower bounds.
kpeter@688
   714
    /// Its \c Value type must be convertible to the \c Value type
kpeter@652
   715
    /// of the algorithm.
kpeter@652
   716
    ///
kpeter@652
   717
    /// \return <tt>(*this)</tt>
kpeter@687
   718
    template <typename LowerMap>
kpeter@687
   719
    NetworkSimplex& lowerMap(const LowerMap& map) {
kpeter@689
   720
      _have_lower = true;
kpeter@652
   721
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@689
   722
        _lower[_arc_id[a]] = map[a];
kpeter@652
   723
      }
kpeter@652
   724
      return *this;
kpeter@652
   725
    }
kpeter@652
   726
kpeter@652
   727
    /// \brief Set the upper bounds (capacities) on the arcs.
kpeter@652
   728
    ///
kpeter@652
   729
    /// This function sets the upper bounds (capacities) on the arcs.
kpeter@687
   730
    /// If it is not used before calling \ref run(), the upper bounds
kpeter@687
   731
    /// will be set to \ref INF on all arcs (i.e. the flow value will be
kpeter@687
   732
    /// unbounded from above on each arc).
kpeter@652
   733
    ///
kpeter@652
   734
    /// \param map An arc map storing the upper bounds.
kpeter@688
   735
    /// Its \c Value type must be convertible to the \c Value type
kpeter@652
   736
    /// of the algorithm.
kpeter@652
   737
    ///
kpeter@652
   738
    /// \return <tt>(*this)</tt>
kpeter@687
   739
    template<typename UpperMap>
kpeter@687
   740
    NetworkSimplex& upperMap(const UpperMap& map) {
kpeter@652
   741
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@689
   742
        _upper[_arc_id[a]] = map[a];
kpeter@652
   743
      }
kpeter@652
   744
      return *this;
kpeter@652
   745
    }
kpeter@652
   746
kpeter@652
   747
    /// \brief Set the costs of the arcs.
kpeter@652
   748
    ///
kpeter@652
   749
    /// This function sets the costs of the arcs.
kpeter@652
   750
    /// If it is not used before calling \ref run(), the costs
kpeter@652
   751
    /// will be set to \c 1 on all arcs.
kpeter@652
   752
    ///
kpeter@652
   753
    /// \param map An arc map storing the costs.
kpeter@654
   754
    /// Its \c Value type must be convertible to the \c Cost type
kpeter@652
   755
    /// of the algorithm.
kpeter@652
   756
    ///
kpeter@652
   757
    /// \return <tt>(*this)</tt>
kpeter@687
   758
    template<typename CostMap>
kpeter@687
   759
    NetworkSimplex& costMap(const CostMap& map) {
kpeter@652
   760
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@689
   761
        _cost[_arc_id[a]] = map[a];
kpeter@652
   762
      }
kpeter@652
   763
      return *this;
kpeter@652
   764
    }
kpeter@652
   765
kpeter@652
   766
    /// \brief Set the supply values of the nodes.
kpeter@652
   767
    ///
kpeter@652
   768
    /// This function sets the supply values of the nodes.
kpeter@652
   769
    /// If neither this function nor \ref stSupply() is used before
kpeter@652
   770
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@652
   771
    /// (It makes sense only if non-zero lower bounds are given.)
kpeter@652
   772
    ///
kpeter@652
   773
    /// \param map A node map storing the supply values.
kpeter@688
   774
    /// Its \c Value type must be convertible to the \c Value type
kpeter@652
   775
    /// of the algorithm.
kpeter@652
   776
    ///
kpeter@652
   777
    /// \return <tt>(*this)</tt>
kpeter@687
   778
    template<typename SupplyMap>
kpeter@687
   779
    NetworkSimplex& supplyMap(const SupplyMap& map) {
kpeter@652
   780
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@689
   781
        _supply[_node_id[n]] = map[n];
kpeter@652
   782
      }
kpeter@652
   783
      return *this;
kpeter@652
   784
    }
kpeter@652
   785
kpeter@652
   786
    /// \brief Set single source and target nodes and a supply value.
kpeter@652
   787
    ///
kpeter@652
   788
    /// This function sets a single source node and a single target node
kpeter@652
   789
    /// and the required flow value.
kpeter@652
   790
    /// If neither this function nor \ref supplyMap() is used before
kpeter@652
   791
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@652
   792
    /// (It makes sense only if non-zero lower bounds are given.)
kpeter@652
   793
    ///
kpeter@687
   794
    /// Using this function has the same effect as using \ref supplyMap()
kpeter@687
   795
    /// with such a map in which \c k is assigned to \c s, \c -k is
kpeter@687
   796
    /// assigned to \c t and all other nodes have zero supply value.
kpeter@687
   797
    ///
kpeter@652
   798
    /// \param s The source node.
kpeter@652
   799
    /// \param t The target node.
kpeter@652
   800
    /// \param k The required amount of flow from node \c s to node \c t
kpeter@652
   801
    /// (i.e. the supply of \c s and the demand of \c t).
kpeter@652
   802
    ///
kpeter@652
   803
    /// \return <tt>(*this)</tt>
kpeter@688
   804
    NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) {
kpeter@689
   805
      for (int i = 0; i != _node_num; ++i) {
kpeter@689
   806
        _supply[i] = 0;
kpeter@689
   807
      }
kpeter@689
   808
      _supply[_node_id[s]] =  k;
kpeter@689
   809
      _supply[_node_id[t]] = -k;
kpeter@652
   810
      return *this;
kpeter@652
   811
    }
kpeter@656
   812
    
kpeter@687
   813
    /// \brief Set the type of the supply constraints.
kpeter@656
   814
    ///
kpeter@687
   815
    /// This function sets the type of the supply/demand constraints.
kpeter@687
   816
    /// If it is not used before calling \ref run(), the \ref GEQ supply
kpeter@656
   817
    /// type will be used.
kpeter@656
   818
    ///
kpeter@687
   819
    /// For more information see \ref SupplyType.
kpeter@656
   820
    ///
kpeter@656
   821
    /// \return <tt>(*this)</tt>
kpeter@687
   822
    NetworkSimplex& supplyType(SupplyType supply_type) {
kpeter@687
   823
      _stype = supply_type;
kpeter@656
   824
      return *this;
kpeter@656
   825
    }
kpeter@652
   826
kpeter@656
   827
    /// @}
kpeter@648
   828
kpeter@652
   829
    /// \name Execution Control
kpeter@652
   830
    /// The algorithm can be executed using \ref run().
kpeter@652
   831
kpeter@648
   832
    /// @{
kpeter@648
   833
kpeter@648
   834
    /// \brief Run the algorithm.
kpeter@648
   835
    ///
kpeter@648
   836
    /// This function runs the algorithm.
kpeter@656
   837
    /// The paramters can be specified using functions \ref lowerMap(),
kpeter@687
   838
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), 
kpeter@689
   839
    /// \ref supplyType().
kpeter@656
   840
    /// For example,
kpeter@652
   841
    /// \code
kpeter@652
   842
    ///   NetworkSimplex<ListDigraph> ns(graph);
kpeter@687
   843
    ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@652
   844
    ///     .supplyMap(sup).run();
kpeter@652
   845
    /// \endcode
kpeter@648
   846
    ///
kpeter@653
   847
    /// This function can be called more than once. All the parameters
kpeter@653
   848
    /// that have been given are kept for the next call, unless
kpeter@653
   849
    /// \ref reset() is called, thus only the modified parameters
kpeter@653
   850
    /// have to be set again. See \ref reset() for examples.
kpeter@689
   851
    /// However the underlying digraph must not be modified after this
kpeter@689
   852
    /// class have been constructed, since it copies and extends the graph.
kpeter@653
   853
    ///
kpeter@652
   854
    /// \param pivot_rule The pivot rule that will be used during the
kpeter@652
   855
    /// algorithm. For more information see \ref PivotRule.
kpeter@648
   856
    ///
kpeter@687
   857
    /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@687
   858
    /// \n \c OPTIMAL if the problem has optimal solution
kpeter@687
   859
    /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@687
   860
    /// optimal flow and node potentials (primal and dual solutions),
kpeter@687
   861
    /// \n \c UNBOUNDED if the objective function of the problem is
kpeter@687
   862
    /// unbounded, i.e. there is a directed cycle having negative total
kpeter@687
   863
    /// cost and infinite upper bound.
kpeter@687
   864
    ///
kpeter@687
   865
    /// \see ProblemType, PivotRule
kpeter@687
   866
    ProblemType run(PivotRule pivot_rule = BLOCK_SEARCH) {
kpeter@687
   867
      if (!init()) return INFEASIBLE;
kpeter@687
   868
      return start(pivot_rule);
kpeter@648
   869
    }
kpeter@648
   870
kpeter@653
   871
    /// \brief Reset all the parameters that have been given before.
kpeter@653
   872
    ///
kpeter@653
   873
    /// This function resets all the paramaters that have been given
kpeter@656
   874
    /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@689
   875
    /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType().
kpeter@653
   876
    ///
kpeter@653
   877
    /// It is useful for multiple run() calls. If this function is not
kpeter@653
   878
    /// used, all the parameters given before are kept for the next
kpeter@653
   879
    /// \ref run() call.
kpeter@689
   880
    /// However the underlying digraph must not be modified after this
kpeter@689
   881
    /// class have been constructed, since it copies and extends the graph.
kpeter@653
   882
    ///
kpeter@653
   883
    /// For example,
kpeter@653
   884
    /// \code
kpeter@653
   885
    ///   NetworkSimplex<ListDigraph> ns(graph);
kpeter@653
   886
    ///
kpeter@653
   887
    ///   // First run
kpeter@687
   888
    ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@653
   889
    ///     .supplyMap(sup).run();
kpeter@653
   890
    ///
kpeter@653
   891
    ///   // Run again with modified cost map (reset() is not called,
kpeter@653
   892
    ///   // so only the cost map have to be set again)
kpeter@653
   893
    ///   cost[e] += 100;
kpeter@653
   894
    ///   ns.costMap(cost).run();
kpeter@653
   895
    ///
kpeter@653
   896
    ///   // Run again from scratch using reset()
kpeter@653
   897
    ///   // (the lower bounds will be set to zero on all arcs)
kpeter@653
   898
    ///   ns.reset();
kpeter@687
   899
    ///   ns.upperMap(capacity).costMap(cost)
kpeter@653
   900
    ///     .supplyMap(sup).run();
kpeter@653
   901
    /// \endcode
kpeter@653
   902
    ///
kpeter@653
   903
    /// \return <tt>(*this)</tt>
kpeter@653
   904
    NetworkSimplex& reset() {
kpeter@689
   905
      for (int i = 0; i != _node_num; ++i) {
kpeter@689
   906
        _supply[i] = 0;
kpeter@689
   907
      }
kpeter@689
   908
      for (int i = 0; i != _arc_num; ++i) {
kpeter@689
   909
        _lower[i] = 0;
kpeter@689
   910
        _upper[i] = INF;
kpeter@689
   911
        _cost[i] = 1;
kpeter@689
   912
      }
kpeter@689
   913
      _have_lower = false;
kpeter@687
   914
      _stype = GEQ;
kpeter@653
   915
      return *this;
kpeter@653
   916
    }
kpeter@653
   917
kpeter@648
   918
    /// @}
kpeter@648
   919
kpeter@648
   920
    /// \name Query Functions
kpeter@648
   921
    /// The results of the algorithm can be obtained using these
kpeter@648
   922
    /// functions.\n
kpeter@652
   923
    /// The \ref run() function must be called before using them.
kpeter@652
   924
kpeter@648
   925
    /// @{
kpeter@648
   926
kpeter@652
   927
    /// \brief Return the total cost of the found flow.
kpeter@652
   928
    ///
kpeter@652
   929
    /// This function returns the total cost of the found flow.
kpeter@687
   930
    /// Its complexity is O(e).
kpeter@652
   931
    ///
kpeter@652
   932
    /// \note The return type of the function can be specified as a
kpeter@652
   933
    /// template parameter. For example,
kpeter@652
   934
    /// \code
kpeter@652
   935
    ///   ns.totalCost<double>();
kpeter@652
   936
    /// \endcode
kpeter@654
   937
    /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@652
   938
    /// type of the algorithm, which is the default return type of the
kpeter@652
   939
    /// function.
kpeter@652
   940
    ///
kpeter@652
   941
    /// \pre \ref run() must be called before using this function.
kpeter@689
   942
    template <typename Number>
kpeter@689
   943
    Number totalCost() const {
kpeter@689
   944
      Number c = 0;
kpeter@689
   945
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@689
   946
        int i = _arc_id[a];
kpeter@689
   947
        c += Number(_flow[i]) * Number(_cost[i]);
kpeter@652
   948
      }
kpeter@652
   949
      return c;
kpeter@652
   950
    }
kpeter@652
   951
kpeter@652
   952
#ifndef DOXYGEN
kpeter@654
   953
    Cost totalCost() const {
kpeter@654
   954
      return totalCost<Cost>();
kpeter@652
   955
    }
kpeter@652
   956
#endif
kpeter@652
   957
kpeter@652
   958
    /// \brief Return the flow on the given arc.
kpeter@652
   959
    ///
kpeter@652
   960
    /// This function returns the flow on the given arc.
kpeter@652
   961
    ///
kpeter@652
   962
    /// \pre \ref run() must be called before using this function.
kpeter@688
   963
    Value flow(const Arc& a) const {
kpeter@689
   964
      return _flow[_arc_id[a]];
kpeter@652
   965
    }
kpeter@652
   966
kpeter@689
   967
    /// \brief Return the flow map (the primal solution).
kpeter@648
   968
    ///
kpeter@689
   969
    /// This function copies the flow value on each arc into the given
kpeter@689
   970
    /// map. The \c Value type of the algorithm must be convertible to
kpeter@689
   971
    /// the \c Value type of the map.
kpeter@648
   972
    ///
kpeter@648
   973
    /// \pre \ref run() must be called before using this function.
kpeter@689
   974
    template <typename FlowMap>
kpeter@689
   975
    void flowMap(FlowMap &map) const {
kpeter@689
   976
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@689
   977
        map.set(a, _flow[_arc_id[a]]);
kpeter@689
   978
      }
kpeter@648
   979
    }
kpeter@648
   980
kpeter@652
   981
    /// \brief Return the potential (dual value) of the given node.
kpeter@652
   982
    ///
kpeter@652
   983
    /// This function returns the potential (dual value) of the
kpeter@652
   984
    /// given node.
kpeter@652
   985
    ///
kpeter@652
   986
    /// \pre \ref run() must be called before using this function.
kpeter@654
   987
    Cost potential(const Node& n) const {
kpeter@689
   988
      return _pi[_node_id[n]];
kpeter@652
   989
    }
kpeter@652
   990
kpeter@689
   991
    /// \brief Return the potential map (the dual solution).
kpeter@648
   992
    ///
kpeter@689
   993
    /// This function copies the potential (dual value) of each node
kpeter@689
   994
    /// into the given map.
kpeter@689
   995
    /// The \c Cost type of the algorithm must be convertible to the
kpeter@689
   996
    /// \c Value type of the map.
kpeter@648
   997
    ///
kpeter@648
   998
    /// \pre \ref run() must be called before using this function.
kpeter@689
   999
    template <typename PotentialMap>
kpeter@689
  1000
    void potentialMap(PotentialMap &map) const {
kpeter@689
  1001
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@689
  1002
        map.set(n, _pi[_node_id[n]]);
kpeter@689
  1003
      }
kpeter@648
  1004
    }
kpeter@648
  1005
kpeter@648
  1006
    /// @}
kpeter@648
  1007
kpeter@648
  1008
  private:
kpeter@648
  1009
kpeter@648
  1010
    // Initialize internal data structures
kpeter@648
  1011
    bool init() {
kpeter@652
  1012
      if (_node_num == 0) return false;
kpeter@648
  1013
kpeter@689
  1014
      // Check the sum of supply values
kpeter@689
  1015
      _sum_supply = 0;
kpeter@689
  1016
      for (int i = 0; i != _node_num; ++i) {
kpeter@689
  1017
        _sum_supply += _supply[i];
kpeter@689
  1018
      }
alpar@690
  1019
      if ( !((_stype == GEQ && _sum_supply <= 0) ||
alpar@690
  1020
             (_stype == LEQ && _sum_supply >= 0)) ) return false;
kpeter@648
  1021
kpeter@689
  1022
      // Remove non-zero lower bounds
kpeter@689
  1023
      if (_have_lower) {
kpeter@689
  1024
        for (int i = 0; i != _arc_num; ++i) {
kpeter@689
  1025
          Value c = _lower[i];
kpeter@689
  1026
          if (c >= 0) {
kpeter@689
  1027
            _cap[i] = _upper[i] < INF ? _upper[i] - c : INF;
kpeter@689
  1028
          } else {
kpeter@689
  1029
            _cap[i] = _upper[i] < INF + c ? _upper[i] - c : INF;
kpeter@689
  1030
          }
kpeter@689
  1031
          _supply[_source[i]] -= c;
kpeter@689
  1032
          _supply[_target[i]] += c;
kpeter@689
  1033
        }
kpeter@689
  1034
      } else {
kpeter@689
  1035
        for (int i = 0; i != _arc_num; ++i) {
kpeter@689
  1036
          _cap[i] = _upper[i];
kpeter@689
  1037
        }
kpeter@652
  1038
      }
kpeter@648
  1039
kpeter@656
  1040
      // Initialize artifical cost
kpeter@687
  1041
      Cost ART_COST;
kpeter@656
  1042
      if (std::numeric_limits<Cost>::is_exact) {
kpeter@710
  1043
        ART_COST = std::numeric_limits<Cost>::max() / 2 + 1;
kpeter@656
  1044
      } else {
kpeter@687
  1045
        ART_COST = std::numeric_limits<Cost>::min();
kpeter@656
  1046
        for (int i = 0; i != _arc_num; ++i) {
kpeter@687
  1047
          if (_cost[i] > ART_COST) ART_COST = _cost[i];
kpeter@656
  1048
        }
kpeter@687
  1049
        ART_COST = (ART_COST + 1) * _node_num;
kpeter@656
  1050
      }
kpeter@656
  1051
kpeter@689
  1052
      // Initialize arc maps
kpeter@689
  1053
      for (int i = 0; i != _arc_num; ++i) {
kpeter@689
  1054
        _flow[i] = 0;
kpeter@689
  1055
        _state[i] = STATE_LOWER;
kpeter@689
  1056
      }
kpeter@689
  1057
      
kpeter@648
  1058
      // Set data for the artificial root node
kpeter@648
  1059
      _root = _node_num;
kpeter@648
  1060
      _parent[_root] = -1;
kpeter@648
  1061
      _pred[_root] = -1;
kpeter@648
  1062
      _thread[_root] = 0;
kpeter@651
  1063
      _rev_thread[0] = _root;
kpeter@689
  1064
      _succ_num[_root] = _node_num + 1;
kpeter@651
  1065
      _last_succ[_root] = _root - 1;
kpeter@687
  1066
      _supply[_root] = -_sum_supply;
kpeter@710
  1067
      _pi[_root] = 0;
kpeter@648
  1068
kpeter@648
  1069
      // Add artificial arcs and initialize the spanning tree data structure
kpeter@710
  1070
      if (_sum_supply == 0) {
kpeter@710
  1071
        // EQ supply constraints
kpeter@710
  1072
        _search_arc_num = _arc_num;
kpeter@710
  1073
        _all_arc_num = _arc_num + _node_num;
kpeter@710
  1074
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@710
  1075
          _parent[u] = _root;
kpeter@710
  1076
          _pred[u] = e;
kpeter@710
  1077
          _thread[u] = u + 1;
kpeter@710
  1078
          _rev_thread[u + 1] = u;
kpeter@710
  1079
          _succ_num[u] = 1;
kpeter@710
  1080
          _last_succ[u] = u;
kpeter@710
  1081
          _cap[e] = INF;
kpeter@710
  1082
          _state[e] = STATE_TREE;
kpeter@710
  1083
          if (_supply[u] >= 0) {
kpeter@710
  1084
            _forward[u] = true;
kpeter@710
  1085
            _pi[u] = 0;
kpeter@710
  1086
            _source[e] = u;
kpeter@710
  1087
            _target[e] = _root;
kpeter@710
  1088
            _flow[e] = _supply[u];
kpeter@710
  1089
            _cost[e] = 0;
kpeter@710
  1090
          } else {
kpeter@710
  1091
            _forward[u] = false;
kpeter@710
  1092
            _pi[u] = ART_COST;
kpeter@710
  1093
            _source[e] = _root;
kpeter@710
  1094
            _target[e] = u;
kpeter@710
  1095
            _flow[e] = -_supply[u];
kpeter@710
  1096
            _cost[e] = ART_COST;
kpeter@710
  1097
          }
kpeter@648
  1098
        }
kpeter@648
  1099
      }
kpeter@710
  1100
      else if (_sum_supply > 0) {
kpeter@710
  1101
        // LEQ supply constraints
kpeter@710
  1102
        _search_arc_num = _arc_num + _node_num;
kpeter@710
  1103
        int f = _arc_num + _node_num;
kpeter@710
  1104
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@710
  1105
          _parent[u] = _root;
kpeter@710
  1106
          _thread[u] = u + 1;
kpeter@710
  1107
          _rev_thread[u + 1] = u;
kpeter@710
  1108
          _succ_num[u] = 1;
kpeter@710
  1109
          _last_succ[u] = u;
kpeter@710
  1110
          if (_supply[u] >= 0) {
kpeter@710
  1111
            _forward[u] = true;
kpeter@710
  1112
            _pi[u] = 0;
kpeter@710
  1113
            _pred[u] = e;
kpeter@710
  1114
            _source[e] = u;
kpeter@710
  1115
            _target[e] = _root;
kpeter@710
  1116
            _cap[e] = INF;
kpeter@710
  1117
            _flow[e] = _supply[u];
kpeter@710
  1118
            _cost[e] = 0;
kpeter@710
  1119
            _state[e] = STATE_TREE;
kpeter@710
  1120
          } else {
kpeter@710
  1121
            _forward[u] = false;
kpeter@710
  1122
            _pi[u] = ART_COST;
kpeter@710
  1123
            _pred[u] = f;
kpeter@710
  1124
            _source[f] = _root;
kpeter@710
  1125
            _target[f] = u;
kpeter@710
  1126
            _cap[f] = INF;
kpeter@710
  1127
            _flow[f] = -_supply[u];
kpeter@710
  1128
            _cost[f] = ART_COST;
kpeter@710
  1129
            _state[f] = STATE_TREE;
kpeter@710
  1130
            _source[e] = u;
kpeter@710
  1131
            _target[e] = _root;
kpeter@710
  1132
            _cap[e] = INF;
kpeter@710
  1133
            _flow[e] = 0;
kpeter@710
  1134
            _cost[e] = 0;
kpeter@710
  1135
            _state[e] = STATE_LOWER;
kpeter@710
  1136
            ++f;
kpeter@710
  1137
          }
kpeter@710
  1138
        }
kpeter@710
  1139
        _all_arc_num = f;
kpeter@710
  1140
      }
kpeter@710
  1141
      else {
kpeter@710
  1142
        // GEQ supply constraints
kpeter@710
  1143
        _search_arc_num = _arc_num + _node_num;
kpeter@710
  1144
        int f = _arc_num + _node_num;
kpeter@710
  1145
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@710
  1146
          _parent[u] = _root;
kpeter@710
  1147
          _thread[u] = u + 1;
kpeter@710
  1148
          _rev_thread[u + 1] = u;
kpeter@710
  1149
          _succ_num[u] = 1;
kpeter@710
  1150
          _last_succ[u] = u;
kpeter@710
  1151
          if (_supply[u] <= 0) {
kpeter@710
  1152
            _forward[u] = false;
kpeter@710
  1153
            _pi[u] = 0;
kpeter@710
  1154
            _pred[u] = e;
kpeter@710
  1155
            _source[e] = _root;
kpeter@710
  1156
            _target[e] = u;
kpeter@710
  1157
            _cap[e] = INF;
kpeter@710
  1158
            _flow[e] = -_supply[u];
kpeter@710
  1159
            _cost[e] = 0;
kpeter@710
  1160
            _state[e] = STATE_TREE;
kpeter@710
  1161
          } else {
kpeter@710
  1162
            _forward[u] = true;
kpeter@710
  1163
            _pi[u] = -ART_COST;
kpeter@710
  1164
            _pred[u] = f;
kpeter@710
  1165
            _source[f] = u;
kpeter@710
  1166
            _target[f] = _root;
kpeter@710
  1167
            _cap[f] = INF;
kpeter@710
  1168
            _flow[f] = _supply[u];
kpeter@710
  1169
            _state[f] = STATE_TREE;
kpeter@710
  1170
            _cost[f] = ART_COST;
kpeter@710
  1171
            _source[e] = _root;
kpeter@710
  1172
            _target[e] = u;
kpeter@710
  1173
            _cap[e] = INF;
kpeter@710
  1174
            _flow[e] = 0;
kpeter@710
  1175
            _cost[e] = 0;
kpeter@710
  1176
            _state[e] = STATE_LOWER;
kpeter@710
  1177
            ++f;
kpeter@710
  1178
          }
kpeter@710
  1179
        }
kpeter@710
  1180
        _all_arc_num = f;
kpeter@710
  1181
      }
kpeter@648
  1182
kpeter@648
  1183
      return true;
kpeter@648
  1184
    }
kpeter@648
  1185
kpeter@648
  1186
    // Find the join node
kpeter@648
  1187
    void findJoinNode() {
kpeter@650
  1188
      int u = _source[in_arc];
kpeter@650
  1189
      int v = _target[in_arc];
kpeter@648
  1190
      while (u != v) {
kpeter@651
  1191
        if (_succ_num[u] < _succ_num[v]) {
kpeter@651
  1192
          u = _parent[u];
kpeter@651
  1193
        } else {
kpeter@651
  1194
          v = _parent[v];
kpeter@651
  1195
        }
kpeter@648
  1196
      }
kpeter@648
  1197
      join = u;
kpeter@648
  1198
    }
kpeter@648
  1199
kpeter@648
  1200
    // Find the leaving arc of the cycle and returns true if the
kpeter@648
  1201
    // leaving arc is not the same as the entering arc
kpeter@648
  1202
    bool findLeavingArc() {
kpeter@648
  1203
      // Initialize first and second nodes according to the direction
kpeter@648
  1204
      // of the cycle
kpeter@650
  1205
      if (_state[in_arc] == STATE_LOWER) {
kpeter@650
  1206
        first  = _source[in_arc];
kpeter@650
  1207
        second = _target[in_arc];
kpeter@648
  1208
      } else {
kpeter@650
  1209
        first  = _target[in_arc];
kpeter@650
  1210
        second = _source[in_arc];
kpeter@648
  1211
      }
kpeter@650
  1212
      delta = _cap[in_arc];
kpeter@648
  1213
      int result = 0;
kpeter@688
  1214
      Value d;
kpeter@648
  1215
      int e;
kpeter@648
  1216
kpeter@648
  1217
      // Search the cycle along the path form the first node to the root
kpeter@648
  1218
      for (int u = first; u != join; u = _parent[u]) {
kpeter@648
  1219
        e = _pred[u];
kpeter@687
  1220
        d = _forward[u] ?
kpeter@687
  1221
          _flow[e] : (_cap[e] == INF ? INF : _cap[e] - _flow[e]);
kpeter@648
  1222
        if (d < delta) {
kpeter@648
  1223
          delta = d;
kpeter@648
  1224
          u_out = u;
kpeter@648
  1225
          result = 1;
kpeter@648
  1226
        }
kpeter@648
  1227
      }
kpeter@648
  1228
      // Search the cycle along the path form the second node to the root
kpeter@648
  1229
      for (int u = second; u != join; u = _parent[u]) {
kpeter@648
  1230
        e = _pred[u];
kpeter@687
  1231
        d = _forward[u] ? 
kpeter@687
  1232
          (_cap[e] == INF ? INF : _cap[e] - _flow[e]) : _flow[e];
kpeter@648
  1233
        if (d <= delta) {
kpeter@648
  1234
          delta = d;
kpeter@648
  1235
          u_out = u;
kpeter@648
  1236
          result = 2;
kpeter@648
  1237
        }
kpeter@648
  1238
      }
kpeter@648
  1239
kpeter@648
  1240
      if (result == 1) {
kpeter@648
  1241
        u_in = first;
kpeter@648
  1242
        v_in = second;
kpeter@648
  1243
      } else {
kpeter@648
  1244
        u_in = second;
kpeter@648
  1245
        v_in = first;
kpeter@648
  1246
      }
kpeter@648
  1247
      return result != 0;
kpeter@648
  1248
    }
kpeter@648
  1249
kpeter@648
  1250
    // Change _flow and _state vectors
kpeter@648
  1251
    void changeFlow(bool change) {
kpeter@648
  1252
      // Augment along the cycle
kpeter@648
  1253
      if (delta > 0) {
kpeter@688
  1254
        Value val = _state[in_arc] * delta;
kpeter@650
  1255
        _flow[in_arc] += val;
kpeter@650
  1256
        for (int u = _source[in_arc]; u != join; u = _parent[u]) {
kpeter@648
  1257
          _flow[_pred[u]] += _forward[u] ? -val : val;
kpeter@648
  1258
        }
kpeter@650
  1259
        for (int u = _target[in_arc]; u != join; u = _parent[u]) {
kpeter@648
  1260
          _flow[_pred[u]] += _forward[u] ? val : -val;
kpeter@648
  1261
        }
kpeter@648
  1262
      }
kpeter@648
  1263
      // Update the state of the entering and leaving arcs
kpeter@648
  1264
      if (change) {
kpeter@650
  1265
        _state[in_arc] = STATE_TREE;
kpeter@648
  1266
        _state[_pred[u_out]] =
kpeter@648
  1267
          (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
kpeter@648
  1268
      } else {
kpeter@650
  1269
        _state[in_arc] = -_state[in_arc];
kpeter@648
  1270
      }
kpeter@648
  1271
    }
kpeter@648
  1272
kpeter@651
  1273
    // Update the tree structure
kpeter@651
  1274
    void updateTreeStructure() {
kpeter@651
  1275
      int u, w;
kpeter@651
  1276
      int old_rev_thread = _rev_thread[u_out];
kpeter@651
  1277
      int old_succ_num = _succ_num[u_out];
kpeter@651
  1278
      int old_last_succ = _last_succ[u_out];
kpeter@648
  1279
      v_out = _parent[u_out];
kpeter@648
  1280
kpeter@651
  1281
      u = _last_succ[u_in];  // the last successor of u_in
kpeter@651
  1282
      right = _thread[u];    // the node after it
kpeter@651
  1283
kpeter@651
  1284
      // Handle the case when old_rev_thread equals to v_in
kpeter@651
  1285
      // (it also means that join and v_out coincide)
kpeter@651
  1286
      if (old_rev_thread == v_in) {
kpeter@651
  1287
        last = _thread[_last_succ[u_out]];
kpeter@651
  1288
      } else {
kpeter@651
  1289
        last = _thread[v_in];
kpeter@648
  1290
      }
kpeter@648
  1291
kpeter@651
  1292
      // Update _thread and _parent along the stem nodes (i.e. the nodes
kpeter@651
  1293
      // between u_in and u_out, whose parent have to be changed)
kpeter@648
  1294
      _thread[v_in] = stem = u_in;
kpeter@651
  1295
      _dirty_revs.clear();
kpeter@651
  1296
      _dirty_revs.push_back(v_in);
kpeter@648
  1297
      par_stem = v_in;
kpeter@648
  1298
      while (stem != u_out) {
kpeter@651
  1299
        // Insert the next stem node into the thread list
kpeter@651
  1300
        new_stem = _parent[stem];
kpeter@651
  1301
        _thread[u] = new_stem;
kpeter@651
  1302
        _dirty_revs.push_back(u);
kpeter@648
  1303
kpeter@651
  1304
        // Remove the subtree of stem from the thread list
kpeter@651
  1305
        w = _rev_thread[stem];
kpeter@651
  1306
        _thread[w] = right;
kpeter@651
  1307
        _rev_thread[right] = w;
kpeter@648
  1308
kpeter@651
  1309
        // Change the parent node and shift stem nodes
kpeter@648
  1310
        _parent[stem] = par_stem;
kpeter@648
  1311
        par_stem = stem;
kpeter@648
  1312
        stem = new_stem;
kpeter@648
  1313
kpeter@651
  1314
        // Update u and right
kpeter@651
  1315
        u = _last_succ[stem] == _last_succ[par_stem] ?
kpeter@651
  1316
          _rev_thread[par_stem] : _last_succ[stem];
kpeter@648
  1317
        right = _thread[u];
kpeter@648
  1318
      }
kpeter@648
  1319
      _parent[u_out] = par_stem;
kpeter@648
  1320
      _thread[u] = last;
kpeter@651
  1321
      _rev_thread[last] = u;
kpeter@651
  1322
      _last_succ[u_out] = u;
kpeter@648
  1323
kpeter@651
  1324
      // Remove the subtree of u_out from the thread list except for
kpeter@651
  1325
      // the case when old_rev_thread equals to v_in
kpeter@651
  1326
      // (it also means that join and v_out coincide)
kpeter@651
  1327
      if (old_rev_thread != v_in) {
kpeter@651
  1328
        _thread[old_rev_thread] = right;
kpeter@651
  1329
        _rev_thread[right] = old_rev_thread;
kpeter@651
  1330
      }
kpeter@651
  1331
kpeter@651
  1332
      // Update _rev_thread using the new _thread values
kpeter@651
  1333
      for (int i = 0; i < int(_dirty_revs.size()); ++i) {
kpeter@651
  1334
        u = _dirty_revs[i];
kpeter@651
  1335
        _rev_thread[_thread[u]] = u;
kpeter@651
  1336
      }
kpeter@651
  1337
kpeter@651
  1338
      // Update _pred, _forward, _last_succ and _succ_num for the
kpeter@651
  1339
      // stem nodes from u_out to u_in
kpeter@651
  1340
      int tmp_sc = 0, tmp_ls = _last_succ[u_out];
kpeter@651
  1341
      u = u_out;
kpeter@651
  1342
      while (u != u_in) {
kpeter@651
  1343
        w = _parent[u];
kpeter@651
  1344
        _pred[u] = _pred[w];
kpeter@651
  1345
        _forward[u] = !_forward[w];
kpeter@651
  1346
        tmp_sc += _succ_num[u] - _succ_num[w];
kpeter@651
  1347
        _succ_num[u] = tmp_sc;
kpeter@651
  1348
        _last_succ[w] = tmp_ls;
kpeter@651
  1349
        u = w;
kpeter@651
  1350
      }
kpeter@651
  1351
      _pred[u_in] = in_arc;
kpeter@651
  1352
      _forward[u_in] = (u_in == _source[in_arc]);
kpeter@651
  1353
      _succ_num[u_in] = old_succ_num;
kpeter@651
  1354
kpeter@651
  1355
      // Set limits for updating _last_succ form v_in and v_out
kpeter@651
  1356
      // towards the root
kpeter@651
  1357
      int up_limit_in = -1;
kpeter@651
  1358
      int up_limit_out = -1;
kpeter@651
  1359
      if (_last_succ[join] == v_in) {
kpeter@651
  1360
        up_limit_out = join;
kpeter@648
  1361
      } else {
kpeter@651
  1362
        up_limit_in = join;
kpeter@651
  1363
      }
kpeter@651
  1364
kpeter@651
  1365
      // Update _last_succ from v_in towards the root
kpeter@651
  1366
      for (u = v_in; u != up_limit_in && _last_succ[u] == v_in;
kpeter@651
  1367
           u = _parent[u]) {
kpeter@651
  1368
        _last_succ[u] = _last_succ[u_out];
kpeter@651
  1369
      }
kpeter@651
  1370
      // Update _last_succ from v_out towards the root
kpeter@651
  1371
      if (join != old_rev_thread && v_in != old_rev_thread) {
kpeter@651
  1372
        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@651
  1373
             u = _parent[u]) {
kpeter@651
  1374
          _last_succ[u] = old_rev_thread;
kpeter@651
  1375
        }
kpeter@651
  1376
      } else {
kpeter@651
  1377
        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@651
  1378
             u = _parent[u]) {
kpeter@651
  1379
          _last_succ[u] = _last_succ[u_out];
kpeter@651
  1380
        }
kpeter@651
  1381
      }
kpeter@651
  1382
kpeter@651
  1383
      // Update _succ_num from v_in to join
kpeter@651
  1384
      for (u = v_in; u != join; u = _parent[u]) {
kpeter@651
  1385
        _succ_num[u] += old_succ_num;
kpeter@651
  1386
      }
kpeter@651
  1387
      // Update _succ_num from v_out to join
kpeter@651
  1388
      for (u = v_out; u != join; u = _parent[u]) {
kpeter@651
  1389
        _succ_num[u] -= old_succ_num;
kpeter@648
  1390
      }
kpeter@648
  1391
    }
kpeter@648
  1392
kpeter@651
  1393
    // Update potentials
kpeter@651
  1394
    void updatePotential() {
kpeter@654
  1395
      Cost sigma = _forward[u_in] ?
kpeter@648
  1396
        _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
kpeter@648
  1397
        _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
kpeter@655
  1398
      // Update potentials in the subtree, which has been moved
kpeter@655
  1399
      int end = _thread[_last_succ[u_in]];
kpeter@655
  1400
      for (int u = u_in; u != end; u = _thread[u]) {
kpeter@655
  1401
        _pi[u] += sigma;
kpeter@648
  1402
      }
kpeter@648
  1403
    }
kpeter@648
  1404
kpeter@648
  1405
    // Execute the algorithm
kpeter@687
  1406
    ProblemType start(PivotRule pivot_rule) {
kpeter@648
  1407
      // Select the pivot rule implementation
kpeter@648
  1408
      switch (pivot_rule) {
kpeter@652
  1409
        case FIRST_ELIGIBLE:
kpeter@648
  1410
          return start<FirstEligiblePivotRule>();
kpeter@652
  1411
        case BEST_ELIGIBLE:
kpeter@648
  1412
          return start<BestEligiblePivotRule>();
kpeter@652
  1413
        case BLOCK_SEARCH:
kpeter@648
  1414
          return start<BlockSearchPivotRule>();
kpeter@652
  1415
        case CANDIDATE_LIST:
kpeter@648
  1416
          return start<CandidateListPivotRule>();
kpeter@652
  1417
        case ALTERING_LIST:
kpeter@648
  1418
          return start<AlteringListPivotRule>();
kpeter@648
  1419
      }
kpeter@687
  1420
      return INFEASIBLE; // avoid warning
kpeter@648
  1421
    }
kpeter@648
  1422
kpeter@652
  1423
    template <typename PivotRuleImpl>
kpeter@687
  1424
    ProblemType start() {
kpeter@652
  1425
      PivotRuleImpl pivot(*this);
kpeter@648
  1426
kpeter@652
  1427
      // Execute the Network Simplex algorithm
kpeter@648
  1428
      while (pivot.findEnteringArc()) {
kpeter@648
  1429
        findJoinNode();
kpeter@648
  1430
        bool change = findLeavingArc();
kpeter@687
  1431
        if (delta >= INF) return UNBOUNDED;
kpeter@648
  1432
        changeFlow(change);
kpeter@648
  1433
        if (change) {
kpeter@651
  1434
          updateTreeStructure();
kpeter@651
  1435
          updatePotential();
kpeter@648
  1436
        }
kpeter@648
  1437
      }
kpeter@687
  1438
      
kpeter@687
  1439
      // Check feasibility
kpeter@710
  1440
      for (int e = _search_arc_num; e != _all_arc_num; ++e) {
kpeter@710
  1441
        if (_flow[e] != 0) return INFEASIBLE;
kpeter@687
  1442
      }
kpeter@648
  1443
kpeter@689
  1444
      // Transform the solution and the supply map to the original form
kpeter@689
  1445
      if (_have_lower) {
kpeter@648
  1446
        for (int i = 0; i != _arc_num; ++i) {
kpeter@689
  1447
          Value c = _lower[i];
kpeter@689
  1448
          if (c != 0) {
kpeter@689
  1449
            _flow[i] += c;
kpeter@689
  1450
            _supply[_source[i]] += c;
kpeter@689
  1451
            _supply[_target[i]] -= c;
kpeter@689
  1452
          }
kpeter@648
  1453
        }
kpeter@648
  1454
      }
kpeter@710
  1455
      
kpeter@710
  1456
      // Shift potentials to meet the requirements of the GEQ/LEQ type
kpeter@710
  1457
      // optimality conditions
kpeter@710
  1458
      if (_sum_supply == 0) {
kpeter@710
  1459
        if (_stype == GEQ) {
kpeter@710
  1460
          Cost max_pot = std::numeric_limits<Cost>::min();
kpeter@710
  1461
          for (int i = 0; i != _node_num; ++i) {
kpeter@710
  1462
            if (_pi[i] > max_pot) max_pot = _pi[i];
kpeter@710
  1463
          }
kpeter@710
  1464
          if (max_pot > 0) {
kpeter@710
  1465
            for (int i = 0; i != _node_num; ++i)
kpeter@710
  1466
              _pi[i] -= max_pot;
kpeter@710
  1467
          }
kpeter@710
  1468
        } else {
kpeter@710
  1469
          Cost min_pot = std::numeric_limits<Cost>::max();
kpeter@710
  1470
          for (int i = 0; i != _node_num; ++i) {
kpeter@710
  1471
            if (_pi[i] < min_pot) min_pot = _pi[i];
kpeter@710
  1472
          }
kpeter@710
  1473
          if (min_pot < 0) {
kpeter@710
  1474
            for (int i = 0; i != _node_num; ++i)
kpeter@710
  1475
              _pi[i] -= min_pot;
kpeter@710
  1476
          }
kpeter@710
  1477
        }
kpeter@710
  1478
      }
kpeter@648
  1479
kpeter@687
  1480
      return OPTIMAL;
kpeter@648
  1481
    }
kpeter@648
  1482
kpeter@648
  1483
  }; //class NetworkSimplex
kpeter@648
  1484
kpeter@648
  1485
  ///@}
kpeter@648
  1486
kpeter@648
  1487
} //namespace lemon
kpeter@648
  1488
kpeter@648
  1489
#endif //LEMON_NETWORK_SIMPLEX_H