lemon/network_simplex.h
author Peter Kovacs <kpeter@inf.elte.hu>
Wed, 06 May 2009 14:44:05 +0200
changeset 648 4ff8041e9c2e
parent 642 111698359429
child 663 8b0df68370a4
permissions -rw-r--r--
Doc improvements and fixes for connectivity tools (#285)
And add loopFree(), parallelFree(), simpleGraph() to the module doc.
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2009
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#ifndef LEMON_NETWORK_SIMPLEX_H
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#define LEMON_NETWORK_SIMPLEX_H
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/// \ingroup min_cost_flow
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///
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/// \file
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/// \brief Network Simplex algorithm for finding a minimum cost flow.
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#include <vector>
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#include <limits>
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#include <algorithm>
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#include <lemon/core.h>
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#include <lemon/math.h>
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namespace lemon {
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  /// \addtogroup min_cost_flow
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  /// @{
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  /// \brief Implementation of the primal Network Simplex algorithm
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  /// for finding a \ref min_cost_flow "minimum cost flow".
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  ///
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  /// \ref NetworkSimplex implements the primal Network Simplex algorithm
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  /// for finding a \ref min_cost_flow "minimum cost flow".
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  /// This algorithm is a specialized version of the linear programming
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  /// simplex method directly for the minimum cost flow problem.
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  /// It is one of the most efficient solution methods.
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  ///
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  /// In general this class is the fastest implementation available
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  /// in LEMON for the minimum cost flow problem.
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  /// 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, since this form is supported
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    /// by other minimum cost flow algorithms and the \ref Circulation
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    /// algorithm, as well.
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    /// The \c LEQ problem type can be selected using the \ref supplyType()
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    /// function.
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    ///
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    /// Note that 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, i.e. the exact
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      /// formulation of the problem is the following.
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      /**
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          \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]
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          \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq
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              sup(u) \quad \forall u\in V \f]
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          \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]
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      */
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      /// It means that the total demand must be greater or equal to the 
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      /// total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or
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      /// negative) and all the supplies have to be carried out from 
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      /// the supply nodes, but there could be demands that are not 
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      /// satisfied.
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      GEQ,
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      /// It is just an alias for the \c GEQ option.
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      CARRY_SUPPLIES = 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, i.e. the exact
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      /// formulation of the problem is the following.
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      /**
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          \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]
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          \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \leq
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              sup(u) \quad \forall u\in V \f]
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          \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]
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      */
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      /// It means that the total demand must be less or equal to the 
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      /// total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or
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      /// positive) and all the demands have to be satisfied, but there
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      /// could be supplies that are not carried out from the supply
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      /// nodes.
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      LEQ,
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      /// It is just an alias for the \c LEQ option.
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      SATISFY_DEMANDS = 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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    // 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 _arc_num;
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      // Pivot rule data
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      int _next_arc;
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    public:
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      // Constructor
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      FirstEligiblePivotRule(NetworkSimplex &ns) :
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        _source(ns._source), _target(ns._target),
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        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
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        _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0)
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      {}
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      // Find next entering arc
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      bool findEnteringArc() {
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        Cost c;
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        for (int e = _next_arc; e < _arc_num; ++e) {
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          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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          if (c < 0) {
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            _in_arc = e;
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            _next_arc = e + 1;
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            return true;
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          }
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        }
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        for (int e = 0; e < _next_arc; ++e) {
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          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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          if (c < 0) {
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            _in_arc = e;
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            _next_arc = e + 1;
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            return true;
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          }
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        }
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        return false;
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      }
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    }; //class FirstEligiblePivotRule
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    // Implementation of the Best Eligible pivot rule
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    class BestEligiblePivotRule
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    {
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    private:
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      // References to the NetworkSimplex class
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      const IntVector  &_source;
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      const IntVector  &_target;
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      const 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 _arc_num;
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    public:
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      // Constructor
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      BestEligiblePivotRule(NetworkSimplex &ns) :
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        _source(ns._source), _target(ns._target),
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        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
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        _in_arc(ns.in_arc), _arc_num(ns._arc_num)
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      {}
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      // Find next entering arc
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      bool findEnteringArc() {
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        Cost c, min = 0;
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        for (int e = 0; e < _arc_num; ++e) {
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          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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          if (c < min) {
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            min = c;
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            _in_arc = e;
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          }
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        }
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        return min < 0;
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      }
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    }; //class BestEligiblePivotRule
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    // Implementation of the Block Search pivot rule
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    class BlockSearchPivotRule
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    {
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    private:
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      // References to the NetworkSimplex class
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      const IntVector  &_source;
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      const IntVector  &_target;
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      const 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 _arc_num;
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      // Pivot rule data
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      int _block_size;
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      int _next_arc;
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    public:
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      // Constructor
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      BlockSearchPivotRule(NetworkSimplex &ns) :
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        _source(ns._source), _target(ns._target),
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        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
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        _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0)
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      {
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        // The main parameters of the pivot rule
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        const double BLOCK_SIZE_FACTOR = 2.0;
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        const int MIN_BLOCK_SIZE = 10;
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        _block_size = std::max( int(BLOCK_SIZE_FACTOR *
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                                    std::sqrt(double(_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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   398
        for (e = _next_arc; e < _arc_num; ++e) {
kpeter@601
   399
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   400
          if (c < min) {
kpeter@601
   401
            min = c;
kpeter@601
   402
            min_arc = e;
kpeter@601
   403
          }
kpeter@601
   404
          if (--cnt == 0) {
kpeter@601
   405
            if (min < 0) break;
kpeter@601
   406
            cnt = _block_size;
kpeter@601
   407
          }
kpeter@601
   408
        }
kpeter@601
   409
        if (min == 0 || cnt > 0) {
kpeter@601
   410
          for (e = 0; e < _next_arc; ++e) {
kpeter@601
   411
            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   412
            if (c < min) {
kpeter@601
   413
              min = c;
kpeter@601
   414
              min_arc = e;
kpeter@601
   415
            }
kpeter@601
   416
            if (--cnt == 0) {
kpeter@601
   417
              if (min < 0) break;
kpeter@601
   418
              cnt = _block_size;
kpeter@601
   419
            }
kpeter@601
   420
          }
kpeter@601
   421
        }
kpeter@601
   422
        if (min >= 0) return false;
kpeter@601
   423
        _in_arc = min_arc;
kpeter@601
   424
        _next_arc = e;
kpeter@601
   425
        return true;
kpeter@601
   426
      }
kpeter@601
   427
kpeter@601
   428
    }; //class BlockSearchPivotRule
kpeter@601
   429
kpeter@601
   430
kpeter@605
   431
    // Implementation of the Candidate List pivot rule
kpeter@601
   432
    class CandidateListPivotRule
kpeter@601
   433
    {
kpeter@601
   434
    private:
kpeter@601
   435
kpeter@601
   436
      // References to the NetworkSimplex class
kpeter@601
   437
      const IntVector  &_source;
kpeter@601
   438
      const IntVector  &_target;
kpeter@607
   439
      const CostVector &_cost;
kpeter@601
   440
      const IntVector  &_state;
kpeter@607
   441
      const CostVector &_pi;
kpeter@601
   442
      int &_in_arc;
kpeter@601
   443
      int _arc_num;
kpeter@601
   444
kpeter@601
   445
      // Pivot rule data
kpeter@601
   446
      IntVector _candidates;
kpeter@601
   447
      int _list_length, _minor_limit;
kpeter@601
   448
      int _curr_length, _minor_count;
kpeter@601
   449
      int _next_arc;
kpeter@601
   450
kpeter@601
   451
    public:
kpeter@601
   452
kpeter@601
   453
      /// Constructor
kpeter@601
   454
      CandidateListPivotRule(NetworkSimplex &ns) :
kpeter@603
   455
        _source(ns._source), _target(ns._target),
kpeter@601
   456
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@603
   457
        _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0)
kpeter@601
   458
      {
kpeter@601
   459
        // The main parameters of the pivot rule
kpeter@601
   460
        const double LIST_LENGTH_FACTOR = 1.0;
kpeter@601
   461
        const int MIN_LIST_LENGTH = 10;
kpeter@601
   462
        const double MINOR_LIMIT_FACTOR = 0.1;
kpeter@601
   463
        const int MIN_MINOR_LIMIT = 3;
kpeter@601
   464
alpar@612
   465
        _list_length = std::max( int(LIST_LENGTH_FACTOR *
alpar@612
   466
                                     std::sqrt(double(_arc_num))),
kpeter@601
   467
                                 MIN_LIST_LENGTH );
kpeter@601
   468
        _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
kpeter@601
   469
                                 MIN_MINOR_LIMIT );
kpeter@601
   470
        _curr_length = _minor_count = 0;
kpeter@601
   471
        _candidates.resize(_list_length);
kpeter@601
   472
      }
kpeter@601
   473
kpeter@601
   474
      /// Find next entering arc
kpeter@601
   475
      bool findEnteringArc() {
kpeter@607
   476
        Cost min, c;
kpeter@601
   477
        int e, min_arc = _next_arc;
kpeter@601
   478
        if (_curr_length > 0 && _minor_count < _minor_limit) {
kpeter@601
   479
          // Minor iteration: select the best eligible arc from the
kpeter@601
   480
          // current candidate list
kpeter@601
   481
          ++_minor_count;
kpeter@601
   482
          min = 0;
kpeter@601
   483
          for (int i = 0; i < _curr_length; ++i) {
kpeter@601
   484
            e = _candidates[i];
kpeter@601
   485
            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   486
            if (c < min) {
kpeter@601
   487
              min = c;
kpeter@601
   488
              min_arc = e;
kpeter@601
   489
            }
kpeter@601
   490
            if (c >= 0) {
kpeter@601
   491
              _candidates[i--] = _candidates[--_curr_length];
kpeter@601
   492
            }
kpeter@601
   493
          }
kpeter@601
   494
          if (min < 0) {
kpeter@601
   495
            _in_arc = min_arc;
kpeter@601
   496
            return true;
kpeter@601
   497
          }
kpeter@601
   498
        }
kpeter@601
   499
kpeter@601
   500
        // Major iteration: build a new candidate list
kpeter@601
   501
        min = 0;
kpeter@601
   502
        _curr_length = 0;
kpeter@601
   503
        for (e = _next_arc; e < _arc_num; ++e) {
kpeter@601
   504
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   505
          if (c < 0) {
kpeter@601
   506
            _candidates[_curr_length++] = e;
kpeter@601
   507
            if (c < min) {
kpeter@601
   508
              min = c;
kpeter@601
   509
              min_arc = e;
kpeter@601
   510
            }
kpeter@601
   511
            if (_curr_length == _list_length) break;
kpeter@601
   512
          }
kpeter@601
   513
        }
kpeter@601
   514
        if (_curr_length < _list_length) {
kpeter@601
   515
          for (e = 0; e < _next_arc; ++e) {
kpeter@601
   516
            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   517
            if (c < 0) {
kpeter@601
   518
              _candidates[_curr_length++] = e;
kpeter@601
   519
              if (c < min) {
kpeter@601
   520
                min = c;
kpeter@601
   521
                min_arc = e;
kpeter@601
   522
              }
kpeter@601
   523
              if (_curr_length == _list_length) break;
kpeter@601
   524
            }
kpeter@601
   525
          }
kpeter@601
   526
        }
kpeter@601
   527
        if (_curr_length == 0) return false;
kpeter@601
   528
        _minor_count = 1;
kpeter@601
   529
        _in_arc = min_arc;
kpeter@601
   530
        _next_arc = e;
kpeter@601
   531
        return true;
kpeter@601
   532
      }
kpeter@601
   533
kpeter@601
   534
    }; //class CandidateListPivotRule
kpeter@601
   535
kpeter@601
   536
kpeter@605
   537
    // Implementation of the Altering Candidate List pivot rule
kpeter@601
   538
    class AlteringListPivotRule
kpeter@601
   539
    {
kpeter@601
   540
    private:
kpeter@601
   541
kpeter@601
   542
      // References to the NetworkSimplex class
kpeter@601
   543
      const IntVector  &_source;
kpeter@601
   544
      const IntVector  &_target;
kpeter@607
   545
      const CostVector &_cost;
kpeter@601
   546
      const IntVector  &_state;
kpeter@607
   547
      const CostVector &_pi;
kpeter@601
   548
      int &_in_arc;
kpeter@601
   549
      int _arc_num;
kpeter@601
   550
kpeter@601
   551
      // Pivot rule data
kpeter@601
   552
      int _block_size, _head_length, _curr_length;
kpeter@601
   553
      int _next_arc;
kpeter@601
   554
      IntVector _candidates;
kpeter@607
   555
      CostVector _cand_cost;
kpeter@601
   556
kpeter@601
   557
      // Functor class to compare arcs during sort of the candidate list
kpeter@601
   558
      class SortFunc
kpeter@601
   559
      {
kpeter@601
   560
      private:
kpeter@607
   561
        const CostVector &_map;
kpeter@601
   562
      public:
kpeter@607
   563
        SortFunc(const CostVector &map) : _map(map) {}
kpeter@601
   564
        bool operator()(int left, int right) {
kpeter@601
   565
          return _map[left] > _map[right];
kpeter@601
   566
        }
kpeter@601
   567
      };
kpeter@601
   568
kpeter@601
   569
      SortFunc _sort_func;
kpeter@601
   570
kpeter@601
   571
    public:
kpeter@601
   572
kpeter@605
   573
      // Constructor
kpeter@601
   574
      AlteringListPivotRule(NetworkSimplex &ns) :
kpeter@603
   575
        _source(ns._source), _target(ns._target),
kpeter@601
   576
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@603
   577
        _in_arc(ns.in_arc), _arc_num(ns._arc_num),
kpeter@601
   578
        _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost)
kpeter@601
   579
      {
kpeter@601
   580
        // The main parameters of the pivot rule
kpeter@601
   581
        const double BLOCK_SIZE_FACTOR = 1.5;
kpeter@601
   582
        const int MIN_BLOCK_SIZE = 10;
kpeter@601
   583
        const double HEAD_LENGTH_FACTOR = 0.1;
kpeter@601
   584
        const int MIN_HEAD_LENGTH = 3;
kpeter@601
   585
alpar@612
   586
        _block_size = std::max( int(BLOCK_SIZE_FACTOR *
alpar@612
   587
                                    std::sqrt(double(_arc_num))),
kpeter@601
   588
                                MIN_BLOCK_SIZE );
kpeter@601
   589
        _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),
kpeter@601
   590
                                 MIN_HEAD_LENGTH );
kpeter@601
   591
        _candidates.resize(_head_length + _block_size);
kpeter@601
   592
        _curr_length = 0;
kpeter@601
   593
      }
kpeter@601
   594
kpeter@605
   595
      // Find next entering arc
kpeter@601
   596
      bool findEnteringArc() {
kpeter@601
   597
        // Check the current candidate list
kpeter@601
   598
        int e;
kpeter@601
   599
        for (int i = 0; i < _curr_length; ++i) {
kpeter@601
   600
          e = _candidates[i];
kpeter@601
   601
          _cand_cost[e] = _state[e] *
kpeter@601
   602
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   603
          if (_cand_cost[e] >= 0) {
kpeter@601
   604
            _candidates[i--] = _candidates[--_curr_length];
kpeter@601
   605
          }
kpeter@601
   606
        }
kpeter@601
   607
kpeter@601
   608
        // Extend the list
kpeter@601
   609
        int cnt = _block_size;
kpeter@603
   610
        int last_arc = 0;
kpeter@601
   611
        int limit = _head_length;
kpeter@601
   612
kpeter@601
   613
        for (int e = _next_arc; e < _arc_num; ++e) {
kpeter@601
   614
          _cand_cost[e] = _state[e] *
kpeter@601
   615
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   616
          if (_cand_cost[e] < 0) {
kpeter@601
   617
            _candidates[_curr_length++] = e;
kpeter@603
   618
            last_arc = e;
kpeter@601
   619
          }
kpeter@601
   620
          if (--cnt == 0) {
kpeter@601
   621
            if (_curr_length > limit) break;
kpeter@601
   622
            limit = 0;
kpeter@601
   623
            cnt = _block_size;
kpeter@601
   624
          }
kpeter@601
   625
        }
kpeter@601
   626
        if (_curr_length <= limit) {
kpeter@601
   627
          for (int e = 0; e < _next_arc; ++e) {
kpeter@601
   628
            _cand_cost[e] = _state[e] *
kpeter@601
   629
              (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@601
   630
            if (_cand_cost[e] < 0) {
kpeter@601
   631
              _candidates[_curr_length++] = e;
kpeter@603
   632
              last_arc = e;
kpeter@601
   633
            }
kpeter@601
   634
            if (--cnt == 0) {
kpeter@601
   635
              if (_curr_length > limit) break;
kpeter@601
   636
              limit = 0;
kpeter@601
   637
              cnt = _block_size;
kpeter@601
   638
            }
kpeter@601
   639
          }
kpeter@601
   640
        }
kpeter@601
   641
        if (_curr_length == 0) return false;
kpeter@603
   642
        _next_arc = last_arc + 1;
kpeter@601
   643
kpeter@601
   644
        // Make heap of the candidate list (approximating a partial sort)
kpeter@601
   645
        make_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@601
   646
                   _sort_func );
kpeter@601
   647
kpeter@601
   648
        // Pop the first element of the heap
kpeter@601
   649
        _in_arc = _candidates[0];
kpeter@601
   650
        pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@601
   651
                  _sort_func );
kpeter@601
   652
        _curr_length = std::min(_head_length, _curr_length - 1);
kpeter@601
   653
        return true;
kpeter@601
   654
      }
kpeter@601
   655
kpeter@601
   656
    }; //class AlteringListPivotRule
kpeter@601
   657
kpeter@601
   658
  public:
kpeter@601
   659
kpeter@605
   660
    /// \brief Constructor.
kpeter@601
   661
    ///
kpeter@609
   662
    /// The constructor of the class.
kpeter@601
   663
    ///
kpeter@603
   664
    /// \param graph The digraph the algorithm runs on.
kpeter@605
   665
    NetworkSimplex(const GR& graph) :
kpeter@642
   666
      _graph(graph), _node_id(graph), _arc_id(graph),
kpeter@641
   667
      INF(std::numeric_limits<Value>::has_infinity ?
kpeter@641
   668
          std::numeric_limits<Value>::infinity() :
kpeter@641
   669
          std::numeric_limits<Value>::max())
kpeter@605
   670
    {
kpeter@640
   671
      // Check the value types
kpeter@641
   672
      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
kpeter@640
   673
        "The flow type of NetworkSimplex must be signed");
kpeter@640
   674
      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
kpeter@640
   675
        "The cost type of NetworkSimplex must be signed");
kpeter@642
   676
        
kpeter@642
   677
      // Resize vectors
kpeter@642
   678
      _node_num = countNodes(_graph);
kpeter@642
   679
      _arc_num = countArcs(_graph);
kpeter@642
   680
      int all_node_num = _node_num + 1;
kpeter@642
   681
      int all_arc_num = _arc_num + _node_num;
kpeter@601
   682
kpeter@642
   683
      _source.resize(all_arc_num);
kpeter@642
   684
      _target.resize(all_arc_num);
kpeter@642
   685
kpeter@642
   686
      _lower.resize(all_arc_num);
kpeter@642
   687
      _upper.resize(all_arc_num);
kpeter@642
   688
      _cap.resize(all_arc_num);
kpeter@642
   689
      _cost.resize(all_arc_num);
kpeter@642
   690
      _supply.resize(all_node_num);
kpeter@642
   691
      _flow.resize(all_arc_num);
kpeter@642
   692
      _pi.resize(all_node_num);
kpeter@642
   693
kpeter@642
   694
      _parent.resize(all_node_num);
kpeter@642
   695
      _pred.resize(all_node_num);
kpeter@642
   696
      _forward.resize(all_node_num);
kpeter@642
   697
      _thread.resize(all_node_num);
kpeter@642
   698
      _rev_thread.resize(all_node_num);
kpeter@642
   699
      _succ_num.resize(all_node_num);
kpeter@642
   700
      _last_succ.resize(all_node_num);
kpeter@642
   701
      _state.resize(all_arc_num);
kpeter@642
   702
kpeter@642
   703
      // Copy the graph (store the arcs in a mixed order)
kpeter@642
   704
      int i = 0;
kpeter@642
   705
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@642
   706
        _node_id[n] = i;
kpeter@642
   707
      }
kpeter@642
   708
      int k = std::max(int(std::sqrt(double(_arc_num))), 10);
kpeter@642
   709
      i = 0;
kpeter@642
   710
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   711
        _arc_id[a] = i;
kpeter@642
   712
        _source[i] = _node_id[_graph.source(a)];
kpeter@642
   713
        _target[i] = _node_id[_graph.target(a)];
kpeter@642
   714
        if ((i += k) >= _arc_num) i = (i % k) + 1;
kpeter@642
   715
      }
kpeter@642
   716
      
kpeter@642
   717
      // Initialize maps
kpeter@642
   718
      for (int i = 0; i != _node_num; ++i) {
kpeter@642
   719
        _supply[i] = 0;
kpeter@642
   720
      }
kpeter@642
   721
      for (int i = 0; i != _arc_num; ++i) {
kpeter@642
   722
        _lower[i] = 0;
kpeter@642
   723
        _upper[i] = INF;
kpeter@642
   724
        _cost[i] = 1;
kpeter@642
   725
      }
kpeter@642
   726
      _have_lower = false;
kpeter@642
   727
      _stype = GEQ;
kpeter@601
   728
    }
kpeter@601
   729
kpeter@609
   730
    /// \name Parameters
kpeter@609
   731
    /// The parameters of the algorithm can be specified using these
kpeter@609
   732
    /// functions.
kpeter@609
   733
kpeter@609
   734
    /// @{
kpeter@609
   735
kpeter@605
   736
    /// \brief Set the lower bounds on the arcs.
kpeter@605
   737
    ///
kpeter@605
   738
    /// This function sets the lower bounds on the arcs.
kpeter@640
   739
    /// If it is not used before calling \ref run(), the lower bounds
kpeter@640
   740
    /// will be set to zero on all arcs.
kpeter@605
   741
    ///
kpeter@605
   742
    /// \param map An arc map storing the lower bounds.
kpeter@641
   743
    /// Its \c Value type must be convertible to the \c Value type
kpeter@605
   744
    /// of the algorithm.
kpeter@605
   745
    ///
kpeter@605
   746
    /// \return <tt>(*this)</tt>
kpeter@640
   747
    template <typename LowerMap>
kpeter@640
   748
    NetworkSimplex& lowerMap(const LowerMap& map) {
kpeter@642
   749
      _have_lower = true;
kpeter@605
   750
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   751
        _lower[_arc_id[a]] = map[a];
kpeter@605
   752
      }
kpeter@605
   753
      return *this;
kpeter@605
   754
    }
kpeter@605
   755
kpeter@605
   756
    /// \brief Set the upper bounds (capacities) on the arcs.
kpeter@605
   757
    ///
kpeter@605
   758
    /// This function sets the upper bounds (capacities) on the arcs.
kpeter@640
   759
    /// If it is not used before calling \ref run(), the upper bounds
kpeter@640
   760
    /// will be set to \ref INF on all arcs (i.e. the flow value will be
kpeter@640
   761
    /// unbounded from above on each arc).
kpeter@605
   762
    ///
kpeter@605
   763
    /// \param map An arc map storing the upper bounds.
kpeter@641
   764
    /// Its \c Value type must be convertible to the \c Value type
kpeter@605
   765
    /// of the algorithm.
kpeter@605
   766
    ///
kpeter@605
   767
    /// \return <tt>(*this)</tt>
kpeter@640
   768
    template<typename UpperMap>
kpeter@640
   769
    NetworkSimplex& upperMap(const UpperMap& map) {
kpeter@605
   770
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   771
        _upper[_arc_id[a]] = map[a];
kpeter@605
   772
      }
kpeter@605
   773
      return *this;
kpeter@605
   774
    }
kpeter@605
   775
kpeter@605
   776
    /// \brief Set the costs of the arcs.
kpeter@605
   777
    ///
kpeter@605
   778
    /// This function sets the costs of the arcs.
kpeter@605
   779
    /// If it is not used before calling \ref run(), the costs
kpeter@605
   780
    /// will be set to \c 1 on all arcs.
kpeter@605
   781
    ///
kpeter@605
   782
    /// \param map An arc map storing the costs.
kpeter@607
   783
    /// Its \c Value type must be convertible to the \c Cost type
kpeter@605
   784
    /// of the algorithm.
kpeter@605
   785
    ///
kpeter@605
   786
    /// \return <tt>(*this)</tt>
kpeter@640
   787
    template<typename CostMap>
kpeter@640
   788
    NetworkSimplex& costMap(const CostMap& map) {
kpeter@605
   789
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   790
        _cost[_arc_id[a]] = map[a];
kpeter@605
   791
      }
kpeter@605
   792
      return *this;
kpeter@605
   793
    }
kpeter@605
   794
kpeter@605
   795
    /// \brief Set the supply values of the nodes.
kpeter@605
   796
    ///
kpeter@605
   797
    /// This function sets the supply values of the nodes.
kpeter@605
   798
    /// If neither this function nor \ref stSupply() is used before
kpeter@605
   799
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@605
   800
    /// (It makes sense only if non-zero lower bounds are given.)
kpeter@605
   801
    ///
kpeter@605
   802
    /// \param map A node map storing the supply values.
kpeter@641
   803
    /// Its \c Value type must be convertible to the \c Value type
kpeter@605
   804
    /// of the algorithm.
kpeter@605
   805
    ///
kpeter@605
   806
    /// \return <tt>(*this)</tt>
kpeter@640
   807
    template<typename SupplyMap>
kpeter@640
   808
    NetworkSimplex& supplyMap(const SupplyMap& map) {
kpeter@605
   809
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@642
   810
        _supply[_node_id[n]] = map[n];
kpeter@605
   811
      }
kpeter@605
   812
      return *this;
kpeter@605
   813
    }
kpeter@605
   814
kpeter@605
   815
    /// \brief Set single source and target nodes and a supply value.
kpeter@605
   816
    ///
kpeter@605
   817
    /// This function sets a single source node and a single target node
kpeter@605
   818
    /// and the required flow value.
kpeter@605
   819
    /// If neither this function nor \ref supplyMap() is used before
kpeter@605
   820
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@605
   821
    /// (It makes sense only if non-zero lower bounds are given.)
kpeter@605
   822
    ///
kpeter@640
   823
    /// Using this function has the same effect as using \ref supplyMap()
kpeter@640
   824
    /// with such a map in which \c k is assigned to \c s, \c -k is
kpeter@640
   825
    /// assigned to \c t and all other nodes have zero supply value.
kpeter@640
   826
    ///
kpeter@605
   827
    /// \param s The source node.
kpeter@605
   828
    /// \param t The target node.
kpeter@605
   829
    /// \param k The required amount of flow from node \c s to node \c t
kpeter@605
   830
    /// (i.e. the supply of \c s and the demand of \c t).
kpeter@605
   831
    ///
kpeter@605
   832
    /// \return <tt>(*this)</tt>
kpeter@641
   833
    NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) {
kpeter@642
   834
      for (int i = 0; i != _node_num; ++i) {
kpeter@642
   835
        _supply[i] = 0;
kpeter@642
   836
      }
kpeter@642
   837
      _supply[_node_id[s]] =  k;
kpeter@642
   838
      _supply[_node_id[t]] = -k;
kpeter@605
   839
      return *this;
kpeter@605
   840
    }
kpeter@609
   841
    
kpeter@640
   842
    /// \brief Set the type of the supply constraints.
kpeter@609
   843
    ///
kpeter@640
   844
    /// This function sets the type of the supply/demand constraints.
kpeter@640
   845
    /// If it is not used before calling \ref run(), the \ref GEQ supply
kpeter@609
   846
    /// type will be used.
kpeter@609
   847
    ///
kpeter@640
   848
    /// For more information see \ref SupplyType.
kpeter@609
   849
    ///
kpeter@609
   850
    /// \return <tt>(*this)</tt>
kpeter@640
   851
    NetworkSimplex& supplyType(SupplyType supply_type) {
kpeter@640
   852
      _stype = supply_type;
kpeter@609
   853
      return *this;
kpeter@609
   854
    }
kpeter@605
   855
kpeter@609
   856
    /// @}
kpeter@601
   857
kpeter@605
   858
    /// \name Execution Control
kpeter@605
   859
    /// The algorithm can be executed using \ref run().
kpeter@605
   860
kpeter@601
   861
    /// @{
kpeter@601
   862
kpeter@601
   863
    /// \brief Run the algorithm.
kpeter@601
   864
    ///
kpeter@601
   865
    /// This function runs the algorithm.
kpeter@609
   866
    /// The paramters can be specified using functions \ref lowerMap(),
kpeter@640
   867
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), 
kpeter@642
   868
    /// \ref supplyType().
kpeter@609
   869
    /// For example,
kpeter@605
   870
    /// \code
kpeter@605
   871
    ///   NetworkSimplex<ListDigraph> ns(graph);
kpeter@640
   872
    ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@605
   873
    ///     .supplyMap(sup).run();
kpeter@605
   874
    /// \endcode
kpeter@601
   875
    ///
kpeter@606
   876
    /// This function can be called more than once. All the parameters
kpeter@606
   877
    /// that have been given are kept for the next call, unless
kpeter@606
   878
    /// \ref reset() is called, thus only the modified parameters
kpeter@606
   879
    /// have to be set again. See \ref reset() for examples.
kpeter@642
   880
    /// However the underlying digraph must not be modified after this
kpeter@642
   881
    /// class have been constructed, since it copies and extends the graph.
kpeter@606
   882
    ///
kpeter@605
   883
    /// \param pivot_rule The pivot rule that will be used during the
kpeter@605
   884
    /// algorithm. For more information see \ref PivotRule.
kpeter@601
   885
    ///
kpeter@640
   886
    /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@640
   887
    /// \n \c OPTIMAL if the problem has optimal solution
kpeter@640
   888
    /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@640
   889
    /// optimal flow and node potentials (primal and dual solutions),
kpeter@640
   890
    /// \n \c UNBOUNDED if the objective function of the problem is
kpeter@640
   891
    /// unbounded, i.e. there is a directed cycle having negative total
kpeter@640
   892
    /// cost and infinite upper bound.
kpeter@640
   893
    ///
kpeter@640
   894
    /// \see ProblemType, PivotRule
kpeter@640
   895
    ProblemType run(PivotRule pivot_rule = BLOCK_SEARCH) {
kpeter@640
   896
      if (!init()) return INFEASIBLE;
kpeter@640
   897
      return start(pivot_rule);
kpeter@601
   898
    }
kpeter@601
   899
kpeter@606
   900
    /// \brief Reset all the parameters that have been given before.
kpeter@606
   901
    ///
kpeter@606
   902
    /// This function resets all the paramaters that have been given
kpeter@609
   903
    /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@642
   904
    /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType().
kpeter@606
   905
    ///
kpeter@606
   906
    /// It is useful for multiple run() calls. If this function is not
kpeter@606
   907
    /// used, all the parameters given before are kept for the next
kpeter@606
   908
    /// \ref run() call.
kpeter@642
   909
    /// However the underlying digraph must not be modified after this
kpeter@642
   910
    /// class have been constructed, since it copies and extends the graph.
kpeter@606
   911
    ///
kpeter@606
   912
    /// For example,
kpeter@606
   913
    /// \code
kpeter@606
   914
    ///   NetworkSimplex<ListDigraph> ns(graph);
kpeter@606
   915
    ///
kpeter@606
   916
    ///   // First run
kpeter@640
   917
    ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@606
   918
    ///     .supplyMap(sup).run();
kpeter@606
   919
    ///
kpeter@606
   920
    ///   // Run again with modified cost map (reset() is not called,
kpeter@606
   921
    ///   // so only the cost map have to be set again)
kpeter@606
   922
    ///   cost[e] += 100;
kpeter@606
   923
    ///   ns.costMap(cost).run();
kpeter@606
   924
    ///
kpeter@606
   925
    ///   // Run again from scratch using reset()
kpeter@606
   926
    ///   // (the lower bounds will be set to zero on all arcs)
kpeter@606
   927
    ///   ns.reset();
kpeter@640
   928
    ///   ns.upperMap(capacity).costMap(cost)
kpeter@606
   929
    ///     .supplyMap(sup).run();
kpeter@606
   930
    /// \endcode
kpeter@606
   931
    ///
kpeter@606
   932
    /// \return <tt>(*this)</tt>
kpeter@606
   933
    NetworkSimplex& reset() {
kpeter@642
   934
      for (int i = 0; i != _node_num; ++i) {
kpeter@642
   935
        _supply[i] = 0;
kpeter@642
   936
      }
kpeter@642
   937
      for (int i = 0; i != _arc_num; ++i) {
kpeter@642
   938
        _lower[i] = 0;
kpeter@642
   939
        _upper[i] = INF;
kpeter@642
   940
        _cost[i] = 1;
kpeter@642
   941
      }
kpeter@642
   942
      _have_lower = false;
kpeter@640
   943
      _stype = GEQ;
kpeter@606
   944
      return *this;
kpeter@606
   945
    }
kpeter@606
   946
kpeter@601
   947
    /// @}
kpeter@601
   948
kpeter@601
   949
    /// \name Query Functions
kpeter@601
   950
    /// The results of the algorithm can be obtained using these
kpeter@601
   951
    /// functions.\n
kpeter@605
   952
    /// The \ref run() function must be called before using them.
kpeter@605
   953
kpeter@601
   954
    /// @{
kpeter@601
   955
kpeter@605
   956
    /// \brief Return the total cost of the found flow.
kpeter@605
   957
    ///
kpeter@605
   958
    /// This function returns the total cost of the found flow.
kpeter@640
   959
    /// Its complexity is O(e).
kpeter@605
   960
    ///
kpeter@605
   961
    /// \note The return type of the function can be specified as a
kpeter@605
   962
    /// template parameter. For example,
kpeter@605
   963
    /// \code
kpeter@605
   964
    ///   ns.totalCost<double>();
kpeter@605
   965
    /// \endcode
kpeter@607
   966
    /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@605
   967
    /// type of the algorithm, which is the default return type of the
kpeter@605
   968
    /// function.
kpeter@605
   969
    ///
kpeter@605
   970
    /// \pre \ref run() must be called before using this function.
kpeter@642
   971
    template <typename Number>
kpeter@642
   972
    Number totalCost() const {
kpeter@642
   973
      Number c = 0;
kpeter@642
   974
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
   975
        int i = _arc_id[a];
kpeter@642
   976
        c += Number(_flow[i]) * Number(_cost[i]);
kpeter@605
   977
      }
kpeter@605
   978
      return c;
kpeter@605
   979
    }
kpeter@605
   980
kpeter@605
   981
#ifndef DOXYGEN
kpeter@607
   982
    Cost totalCost() const {
kpeter@607
   983
      return totalCost<Cost>();
kpeter@605
   984
    }
kpeter@605
   985
#endif
kpeter@605
   986
kpeter@605
   987
    /// \brief Return the flow on the given arc.
kpeter@605
   988
    ///
kpeter@605
   989
    /// This function returns the flow on the given arc.
kpeter@605
   990
    ///
kpeter@605
   991
    /// \pre \ref run() must be called before using this function.
kpeter@641
   992
    Value flow(const Arc& a) const {
kpeter@642
   993
      return _flow[_arc_id[a]];
kpeter@605
   994
    }
kpeter@605
   995
kpeter@642
   996
    /// \brief Return the flow map (the primal solution).
kpeter@601
   997
    ///
kpeter@642
   998
    /// This function copies the flow value on each arc into the given
kpeter@642
   999
    /// map. The \c Value type of the algorithm must be convertible to
kpeter@642
  1000
    /// the \c Value type of the map.
kpeter@601
  1001
    ///
kpeter@601
  1002
    /// \pre \ref run() must be called before using this function.
kpeter@642
  1003
    template <typename FlowMap>
kpeter@642
  1004
    void flowMap(FlowMap &map) const {
kpeter@642
  1005
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@642
  1006
        map.set(a, _flow[_arc_id[a]]);
kpeter@642
  1007
      }
kpeter@601
  1008
    }
kpeter@601
  1009
kpeter@605
  1010
    /// \brief Return the potential (dual value) of the given node.
kpeter@605
  1011
    ///
kpeter@605
  1012
    /// This function returns the potential (dual value) of the
kpeter@605
  1013
    /// given node.
kpeter@605
  1014
    ///
kpeter@605
  1015
    /// \pre \ref run() must be called before using this function.
kpeter@607
  1016
    Cost potential(const Node& n) const {
kpeter@642
  1017
      return _pi[_node_id[n]];
kpeter@605
  1018
    }
kpeter@605
  1019
kpeter@642
  1020
    /// \brief Return the potential map (the dual solution).
kpeter@601
  1021
    ///
kpeter@642
  1022
    /// This function copies the potential (dual value) of each node
kpeter@642
  1023
    /// into the given map.
kpeter@642
  1024
    /// The \c Cost type of the algorithm must be convertible to the
kpeter@642
  1025
    /// \c Value type of the map.
kpeter@601
  1026
    ///
kpeter@601
  1027
    /// \pre \ref run() must be called before using this function.
kpeter@642
  1028
    template <typename PotentialMap>
kpeter@642
  1029
    void potentialMap(PotentialMap &map) const {
kpeter@642
  1030
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@642
  1031
        map.set(n, _pi[_node_id[n]]);
kpeter@642
  1032
      }
kpeter@601
  1033
    }
kpeter@601
  1034
kpeter@601
  1035
    /// @}
kpeter@601
  1036
kpeter@601
  1037
  private:
kpeter@601
  1038
kpeter@601
  1039
    // Initialize internal data structures
kpeter@601
  1040
    bool init() {
kpeter@605
  1041
      if (_node_num == 0) return false;
kpeter@601
  1042
kpeter@642
  1043
      // Check the sum of supply values
kpeter@642
  1044
      _sum_supply = 0;
kpeter@642
  1045
      for (int i = 0; i != _node_num; ++i) {
kpeter@642
  1046
        _sum_supply += _supply[i];
kpeter@642
  1047
      }
alpar@643
  1048
      if ( !((_stype == GEQ && _sum_supply <= 0) ||
alpar@643
  1049
             (_stype == LEQ && _sum_supply >= 0)) ) return false;
kpeter@601
  1050
kpeter@642
  1051
      // Remove non-zero lower bounds
kpeter@642
  1052
      if (_have_lower) {
kpeter@642
  1053
        for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1054
          Value c = _lower[i];
kpeter@642
  1055
          if (c >= 0) {
kpeter@642
  1056
            _cap[i] = _upper[i] < INF ? _upper[i] - c : INF;
kpeter@642
  1057
          } else {
kpeter@642
  1058
            _cap[i] = _upper[i] < INF + c ? _upper[i] - c : INF;
kpeter@642
  1059
          }
kpeter@642
  1060
          _supply[_source[i]] -= c;
kpeter@642
  1061
          _supply[_target[i]] += c;
kpeter@642
  1062
        }
kpeter@642
  1063
      } else {
kpeter@642
  1064
        for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1065
          _cap[i] = _upper[i];
kpeter@642
  1066
        }
kpeter@605
  1067
      }
kpeter@601
  1068
kpeter@609
  1069
      // Initialize artifical cost
kpeter@640
  1070
      Cost ART_COST;
kpeter@609
  1071
      if (std::numeric_limits<Cost>::is_exact) {
kpeter@640
  1072
        ART_COST = std::numeric_limits<Cost>::max() / 4 + 1;
kpeter@609
  1073
      } else {
kpeter@640
  1074
        ART_COST = std::numeric_limits<Cost>::min();
kpeter@609
  1075
        for (int i = 0; i != _arc_num; ++i) {
kpeter@640
  1076
          if (_cost[i] > ART_COST) ART_COST = _cost[i];
kpeter@609
  1077
        }
kpeter@640
  1078
        ART_COST = (ART_COST + 1) * _node_num;
kpeter@609
  1079
      }
kpeter@609
  1080
kpeter@642
  1081
      // Initialize arc maps
kpeter@642
  1082
      for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1083
        _flow[i] = 0;
kpeter@642
  1084
        _state[i] = STATE_LOWER;
kpeter@642
  1085
      }
kpeter@642
  1086
      
kpeter@601
  1087
      // Set data for the artificial root node
kpeter@601
  1088
      _root = _node_num;
kpeter@601
  1089
      _parent[_root] = -1;
kpeter@601
  1090
      _pred[_root] = -1;
kpeter@601
  1091
      _thread[_root] = 0;
kpeter@604
  1092
      _rev_thread[0] = _root;
kpeter@642
  1093
      _succ_num[_root] = _node_num + 1;
kpeter@604
  1094
      _last_succ[_root] = _root - 1;
kpeter@640
  1095
      _supply[_root] = -_sum_supply;
kpeter@642
  1096
      _pi[_root] = _sum_supply < 0 ? -ART_COST : ART_COST;
kpeter@601
  1097
kpeter@601
  1098
      // Add artificial arcs and initialize the spanning tree data structure
kpeter@601
  1099
      for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@642
  1100
        _parent[u] = _root;
kpeter@642
  1101
        _pred[u] = e;
kpeter@601
  1102
        _thread[u] = u + 1;
kpeter@604
  1103
        _rev_thread[u + 1] = u;
kpeter@604
  1104
        _succ_num[u] = 1;
kpeter@604
  1105
        _last_succ[u] = u;
kpeter@640
  1106
        _cost[e] = ART_COST;
kpeter@640
  1107
        _cap[e] = INF;
kpeter@606
  1108
        _state[e] = STATE_TREE;
kpeter@640
  1109
        if (_supply[u] > 0 || (_supply[u] == 0 && _sum_supply <= 0)) {
kpeter@601
  1110
          _flow[e] = _supply[u];
kpeter@601
  1111
          _forward[u] = true;
kpeter@640
  1112
          _pi[u] = -ART_COST + _pi[_root];
kpeter@601
  1113
        } else {
kpeter@601
  1114
          _flow[e] = -_supply[u];
kpeter@601
  1115
          _forward[u] = false;
kpeter@640
  1116
          _pi[u] = ART_COST + _pi[_root];
kpeter@601
  1117
        }
kpeter@601
  1118
      }
kpeter@601
  1119
kpeter@601
  1120
      return true;
kpeter@601
  1121
    }
kpeter@601
  1122
kpeter@601
  1123
    // Find the join node
kpeter@601
  1124
    void findJoinNode() {
kpeter@603
  1125
      int u = _source[in_arc];
kpeter@603
  1126
      int v = _target[in_arc];
kpeter@601
  1127
      while (u != v) {
kpeter@604
  1128
        if (_succ_num[u] < _succ_num[v]) {
kpeter@604
  1129
          u = _parent[u];
kpeter@604
  1130
        } else {
kpeter@604
  1131
          v = _parent[v];
kpeter@604
  1132
        }
kpeter@601
  1133
      }
kpeter@601
  1134
      join = u;
kpeter@601
  1135
    }
kpeter@601
  1136
kpeter@601
  1137
    // Find the leaving arc of the cycle and returns true if the
kpeter@601
  1138
    // leaving arc is not the same as the entering arc
kpeter@601
  1139
    bool findLeavingArc() {
kpeter@601
  1140
      // Initialize first and second nodes according to the direction
kpeter@601
  1141
      // of the cycle
kpeter@603
  1142
      if (_state[in_arc] == STATE_LOWER) {
kpeter@603
  1143
        first  = _source[in_arc];
kpeter@603
  1144
        second = _target[in_arc];
kpeter@601
  1145
      } else {
kpeter@603
  1146
        first  = _target[in_arc];
kpeter@603
  1147
        second = _source[in_arc];
kpeter@601
  1148
      }
kpeter@603
  1149
      delta = _cap[in_arc];
kpeter@601
  1150
      int result = 0;
kpeter@641
  1151
      Value d;
kpeter@601
  1152
      int e;
kpeter@601
  1153
kpeter@601
  1154
      // Search the cycle along the path form the first node to the root
kpeter@601
  1155
      for (int u = first; u != join; u = _parent[u]) {
kpeter@601
  1156
        e = _pred[u];
kpeter@640
  1157
        d = _forward[u] ?
kpeter@640
  1158
          _flow[e] : (_cap[e] == INF ? INF : _cap[e] - _flow[e]);
kpeter@601
  1159
        if (d < delta) {
kpeter@601
  1160
          delta = d;
kpeter@601
  1161
          u_out = u;
kpeter@601
  1162
          result = 1;
kpeter@601
  1163
        }
kpeter@601
  1164
      }
kpeter@601
  1165
      // Search the cycle along the path form the second node to the root
kpeter@601
  1166
      for (int u = second; u != join; u = _parent[u]) {
kpeter@601
  1167
        e = _pred[u];
kpeter@640
  1168
        d = _forward[u] ? 
kpeter@640
  1169
          (_cap[e] == INF ? INF : _cap[e] - _flow[e]) : _flow[e];
kpeter@601
  1170
        if (d <= delta) {
kpeter@601
  1171
          delta = d;
kpeter@601
  1172
          u_out = u;
kpeter@601
  1173
          result = 2;
kpeter@601
  1174
        }
kpeter@601
  1175
      }
kpeter@601
  1176
kpeter@601
  1177
      if (result == 1) {
kpeter@601
  1178
        u_in = first;
kpeter@601
  1179
        v_in = second;
kpeter@601
  1180
      } else {
kpeter@601
  1181
        u_in = second;
kpeter@601
  1182
        v_in = first;
kpeter@601
  1183
      }
kpeter@601
  1184
      return result != 0;
kpeter@601
  1185
    }
kpeter@601
  1186
kpeter@601
  1187
    // Change _flow and _state vectors
kpeter@601
  1188
    void changeFlow(bool change) {
kpeter@601
  1189
      // Augment along the cycle
kpeter@601
  1190
      if (delta > 0) {
kpeter@641
  1191
        Value val = _state[in_arc] * delta;
kpeter@603
  1192
        _flow[in_arc] += val;
kpeter@603
  1193
        for (int u = _source[in_arc]; u != join; u = _parent[u]) {
kpeter@601
  1194
          _flow[_pred[u]] += _forward[u] ? -val : val;
kpeter@601
  1195
        }
kpeter@603
  1196
        for (int u = _target[in_arc]; u != join; u = _parent[u]) {
kpeter@601
  1197
          _flow[_pred[u]] += _forward[u] ? val : -val;
kpeter@601
  1198
        }
kpeter@601
  1199
      }
kpeter@601
  1200
      // Update the state of the entering and leaving arcs
kpeter@601
  1201
      if (change) {
kpeter@603
  1202
        _state[in_arc] = STATE_TREE;
kpeter@601
  1203
        _state[_pred[u_out]] =
kpeter@601
  1204
          (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
kpeter@601
  1205
      } else {
kpeter@603
  1206
        _state[in_arc] = -_state[in_arc];
kpeter@601
  1207
      }
kpeter@601
  1208
    }
kpeter@601
  1209
kpeter@604
  1210
    // Update the tree structure
kpeter@604
  1211
    void updateTreeStructure() {
kpeter@604
  1212
      int u, w;
kpeter@604
  1213
      int old_rev_thread = _rev_thread[u_out];
kpeter@604
  1214
      int old_succ_num = _succ_num[u_out];
kpeter@604
  1215
      int old_last_succ = _last_succ[u_out];
kpeter@601
  1216
      v_out = _parent[u_out];
kpeter@601
  1217
kpeter@604
  1218
      u = _last_succ[u_in];  // the last successor of u_in
kpeter@604
  1219
      right = _thread[u];    // the node after it
kpeter@604
  1220
kpeter@604
  1221
      // Handle the case when old_rev_thread equals to v_in
kpeter@604
  1222
      // (it also means that join and v_out coincide)
kpeter@604
  1223
      if (old_rev_thread == v_in) {
kpeter@604
  1224
        last = _thread[_last_succ[u_out]];
kpeter@604
  1225
      } else {
kpeter@604
  1226
        last = _thread[v_in];
kpeter@601
  1227
      }
kpeter@601
  1228
kpeter@604
  1229
      // Update _thread and _parent along the stem nodes (i.e. the nodes
kpeter@604
  1230
      // between u_in and u_out, whose parent have to be changed)
kpeter@601
  1231
      _thread[v_in] = stem = u_in;
kpeter@604
  1232
      _dirty_revs.clear();
kpeter@604
  1233
      _dirty_revs.push_back(v_in);
kpeter@601
  1234
      par_stem = v_in;
kpeter@601
  1235
      while (stem != u_out) {
kpeter@604
  1236
        // Insert the next stem node into the thread list
kpeter@604
  1237
        new_stem = _parent[stem];
kpeter@604
  1238
        _thread[u] = new_stem;
kpeter@604
  1239
        _dirty_revs.push_back(u);
kpeter@601
  1240
kpeter@604
  1241
        // Remove the subtree of stem from the thread list
kpeter@604
  1242
        w = _rev_thread[stem];
kpeter@604
  1243
        _thread[w] = right;
kpeter@604
  1244
        _rev_thread[right] = w;
kpeter@601
  1245
kpeter@604
  1246
        // Change the parent node and shift stem nodes
kpeter@601
  1247
        _parent[stem] = par_stem;
kpeter@601
  1248
        par_stem = stem;
kpeter@601
  1249
        stem = new_stem;
kpeter@601
  1250
kpeter@604
  1251
        // Update u and right
kpeter@604
  1252
        u = _last_succ[stem] == _last_succ[par_stem] ?
kpeter@604
  1253
          _rev_thread[par_stem] : _last_succ[stem];
kpeter@601
  1254
        right = _thread[u];
kpeter@601
  1255
      }
kpeter@601
  1256
      _parent[u_out] = par_stem;
kpeter@601
  1257
      _thread[u] = last;
kpeter@604
  1258
      _rev_thread[last] = u;
kpeter@604
  1259
      _last_succ[u_out] = u;
kpeter@601
  1260
kpeter@604
  1261
      // Remove the subtree of u_out from the thread list except for
kpeter@604
  1262
      // the case when old_rev_thread equals to v_in
kpeter@604
  1263
      // (it also means that join and v_out coincide)
kpeter@604
  1264
      if (old_rev_thread != v_in) {
kpeter@604
  1265
        _thread[old_rev_thread] = right;
kpeter@604
  1266
        _rev_thread[right] = old_rev_thread;
kpeter@604
  1267
      }
kpeter@604
  1268
kpeter@604
  1269
      // Update _rev_thread using the new _thread values
kpeter@604
  1270
      for (int i = 0; i < int(_dirty_revs.size()); ++i) {
kpeter@604
  1271
        u = _dirty_revs[i];
kpeter@604
  1272
        _rev_thread[_thread[u]] = u;
kpeter@604
  1273
      }
kpeter@604
  1274
kpeter@604
  1275
      // Update _pred, _forward, _last_succ and _succ_num for the
kpeter@604
  1276
      // stem nodes from u_out to u_in
kpeter@604
  1277
      int tmp_sc = 0, tmp_ls = _last_succ[u_out];
kpeter@604
  1278
      u = u_out;
kpeter@604
  1279
      while (u != u_in) {
kpeter@604
  1280
        w = _parent[u];
kpeter@604
  1281
        _pred[u] = _pred[w];
kpeter@604
  1282
        _forward[u] = !_forward[w];
kpeter@604
  1283
        tmp_sc += _succ_num[u] - _succ_num[w];
kpeter@604
  1284
        _succ_num[u] = tmp_sc;
kpeter@604
  1285
        _last_succ[w] = tmp_ls;
kpeter@604
  1286
        u = w;
kpeter@604
  1287
      }
kpeter@604
  1288
      _pred[u_in] = in_arc;
kpeter@604
  1289
      _forward[u_in] = (u_in == _source[in_arc]);
kpeter@604
  1290
      _succ_num[u_in] = old_succ_num;
kpeter@604
  1291
kpeter@604
  1292
      // Set limits for updating _last_succ form v_in and v_out
kpeter@604
  1293
      // towards the root
kpeter@604
  1294
      int up_limit_in = -1;
kpeter@604
  1295
      int up_limit_out = -1;
kpeter@604
  1296
      if (_last_succ[join] == v_in) {
kpeter@604
  1297
        up_limit_out = join;
kpeter@601
  1298
      } else {
kpeter@604
  1299
        up_limit_in = join;
kpeter@604
  1300
      }
kpeter@604
  1301
kpeter@604
  1302
      // Update _last_succ from v_in towards the root
kpeter@604
  1303
      for (u = v_in; u != up_limit_in && _last_succ[u] == v_in;
kpeter@604
  1304
           u = _parent[u]) {
kpeter@604
  1305
        _last_succ[u] = _last_succ[u_out];
kpeter@604
  1306
      }
kpeter@604
  1307
      // Update _last_succ from v_out towards the root
kpeter@604
  1308
      if (join != old_rev_thread && v_in != old_rev_thread) {
kpeter@604
  1309
        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@604
  1310
             u = _parent[u]) {
kpeter@604
  1311
          _last_succ[u] = old_rev_thread;
kpeter@604
  1312
        }
kpeter@604
  1313
      } else {
kpeter@604
  1314
        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@604
  1315
             u = _parent[u]) {
kpeter@604
  1316
          _last_succ[u] = _last_succ[u_out];
kpeter@604
  1317
        }
kpeter@604
  1318
      }
kpeter@604
  1319
kpeter@604
  1320
      // Update _succ_num from v_in to join
kpeter@604
  1321
      for (u = v_in; u != join; u = _parent[u]) {
kpeter@604
  1322
        _succ_num[u] += old_succ_num;
kpeter@604
  1323
      }
kpeter@604
  1324
      // Update _succ_num from v_out to join
kpeter@604
  1325
      for (u = v_out; u != join; u = _parent[u]) {
kpeter@604
  1326
        _succ_num[u] -= old_succ_num;
kpeter@601
  1327
      }
kpeter@601
  1328
    }
kpeter@601
  1329
kpeter@604
  1330
    // Update potentials
kpeter@604
  1331
    void updatePotential() {
kpeter@607
  1332
      Cost sigma = _forward[u_in] ?
kpeter@601
  1333
        _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
kpeter@601
  1334
        _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
kpeter@608
  1335
      // Update potentials in the subtree, which has been moved
kpeter@608
  1336
      int end = _thread[_last_succ[u_in]];
kpeter@608
  1337
      for (int u = u_in; u != end; u = _thread[u]) {
kpeter@608
  1338
        _pi[u] += sigma;
kpeter@601
  1339
      }
kpeter@601
  1340
    }
kpeter@601
  1341
kpeter@601
  1342
    // Execute the algorithm
kpeter@640
  1343
    ProblemType start(PivotRule pivot_rule) {
kpeter@601
  1344
      // Select the pivot rule implementation
kpeter@601
  1345
      switch (pivot_rule) {
kpeter@605
  1346
        case FIRST_ELIGIBLE:
kpeter@601
  1347
          return start<FirstEligiblePivotRule>();
kpeter@605
  1348
        case BEST_ELIGIBLE:
kpeter@601
  1349
          return start<BestEligiblePivotRule>();
kpeter@605
  1350
        case BLOCK_SEARCH:
kpeter@601
  1351
          return start<BlockSearchPivotRule>();
kpeter@605
  1352
        case CANDIDATE_LIST:
kpeter@601
  1353
          return start<CandidateListPivotRule>();
kpeter@605
  1354
        case ALTERING_LIST:
kpeter@601
  1355
          return start<AlteringListPivotRule>();
kpeter@601
  1356
      }
kpeter@640
  1357
      return INFEASIBLE; // avoid warning
kpeter@601
  1358
    }
kpeter@601
  1359
kpeter@605
  1360
    template <typename PivotRuleImpl>
kpeter@640
  1361
    ProblemType start() {
kpeter@605
  1362
      PivotRuleImpl pivot(*this);
kpeter@601
  1363
kpeter@605
  1364
      // Execute the Network Simplex algorithm
kpeter@601
  1365
      while (pivot.findEnteringArc()) {
kpeter@601
  1366
        findJoinNode();
kpeter@601
  1367
        bool change = findLeavingArc();
kpeter@640
  1368
        if (delta >= INF) return UNBOUNDED;
kpeter@601
  1369
        changeFlow(change);
kpeter@601
  1370
        if (change) {
kpeter@604
  1371
          updateTreeStructure();
kpeter@604
  1372
          updatePotential();
kpeter@601
  1373
        }
kpeter@601
  1374
      }
kpeter@640
  1375
      
kpeter@640
  1376
      // Check feasibility
kpeter@640
  1377
      if (_sum_supply < 0) {
kpeter@640
  1378
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@640
  1379
          if (_supply[u] >= 0 && _flow[e] != 0) return INFEASIBLE;
kpeter@640
  1380
        }
kpeter@640
  1381
      }
kpeter@640
  1382
      else if (_sum_supply > 0) {
kpeter@640
  1383
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@640
  1384
          if (_supply[u] <= 0 && _flow[e] != 0) return INFEASIBLE;
kpeter@640
  1385
        }
kpeter@640
  1386
      }
kpeter@640
  1387
      else {
kpeter@640
  1388
        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@640
  1389
          if (_flow[e] != 0) return INFEASIBLE;
kpeter@640
  1390
        }
kpeter@640
  1391
      }
kpeter@601
  1392
kpeter@642
  1393
      // Transform the solution and the supply map to the original form
kpeter@642
  1394
      if (_have_lower) {
kpeter@601
  1395
        for (int i = 0; i != _arc_num; ++i) {
kpeter@642
  1396
          Value c = _lower[i];
kpeter@642
  1397
          if (c != 0) {
kpeter@642
  1398
            _flow[i] += c;
kpeter@642
  1399
            _supply[_source[i]] += c;
kpeter@642
  1400
            _supply[_target[i]] -= c;
kpeter@642
  1401
          }
kpeter@601
  1402
        }
kpeter@601
  1403
      }
kpeter@601
  1404
kpeter@640
  1405
      return OPTIMAL;
kpeter@601
  1406
    }
kpeter@601
  1407
kpeter@601
  1408
  }; //class NetworkSimplex
kpeter@601
  1409
kpeter@601
  1410
  ///@}
kpeter@601
  1411
kpeter@601
  1412
} //namespace lemon
kpeter@601
  1413
kpeter@601
  1414
#endif //LEMON_NETWORK_SIMPLEX_H