[399] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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| 4 | * |
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[440] | 5 | * Copyright (C) 2003-2009 |
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[399] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_CIRCULATION_H |
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| 20 | #define LEMON_CIRCULATION_H |
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| 21 | |
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| 22 | #include <lemon/tolerance.h> |
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| 23 | #include <lemon/elevator.h> |
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| 24 | |
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| 25 | ///\ingroup max_flow |
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| 26 | ///\file |
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[402] | 27 | ///\brief Push-relabel algorithm for finding a feasible circulation. |
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[399] | 28 | /// |
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| 29 | namespace lemon { |
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| 30 | |
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| 31 | /// \brief Default traits class of Circulation class. |
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| 32 | /// |
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| 33 | /// Default traits class of Circulation class. |
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[492] | 34 | /// \tparam GR Digraph type. |
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| 35 | /// \tparam LM Lower bound capacity map type. |
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| 36 | /// \tparam UM Upper bound capacity map type. |
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| 37 | /// \tparam DM Delta map type. |
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| 38 | template <typename GR, typename LM, |
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| 39 | typename UM, typename DM> |
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[399] | 40 | struct CirculationDefaultTraits { |
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| 41 | |
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[402] | 42 | /// \brief The type of the digraph the algorithm runs on. |
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[492] | 43 | typedef GR Digraph; |
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[399] | 44 | |
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| 45 | /// \brief The type of the map that stores the circulation lower |
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| 46 | /// bound. |
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| 47 | /// |
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| 48 | /// The type of the map that stores the circulation lower bound. |
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| 49 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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[492] | 50 | typedef LM LCapMap; |
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[399] | 51 | |
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| 52 | /// \brief The type of the map that stores the circulation upper |
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| 53 | /// bound. |
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| 54 | /// |
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| 55 | /// The type of the map that stores the circulation upper bound. |
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| 56 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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[492] | 57 | typedef UM UCapMap; |
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[399] | 58 | |
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[402] | 59 | /// \brief The type of the map that stores the lower bound for |
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| 60 | /// the supply of the nodes. |
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[399] | 61 | /// |
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[402] | 62 | /// The type of the map that stores the lower bound for the supply |
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| 63 | /// of the nodes. It must meet the \ref concepts::ReadMap "ReadMap" |
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[399] | 64 | /// concept. |
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[492] | 65 | typedef DM DeltaMap; |
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[399] | 66 | |
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[402] | 67 | /// \brief The type of the flow values. |
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[399] | 68 | typedef typename DeltaMap::Value Value; |
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| 69 | |
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[402] | 70 | /// \brief The type of the map that stores the flow values. |
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[399] | 71 | /// |
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[402] | 72 | /// The type of the map that stores the flow values. |
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[399] | 73 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
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| 74 | typedef typename Digraph::template ArcMap<Value> FlowMap; |
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| 75 | |
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| 76 | /// \brief Instantiates a FlowMap. |
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| 77 | /// |
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| 78 | /// This function instantiates a \ref FlowMap. |
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| 79 | /// \param digraph The digraph, to which we would like to define |
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| 80 | /// the flow map. |
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| 81 | static FlowMap* createFlowMap(const Digraph& digraph) { |
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| 82 | return new FlowMap(digraph); |
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| 83 | } |
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| 84 | |
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[402] | 85 | /// \brief The elevator type used by the algorithm. |
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[399] | 86 | /// |
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[402] | 87 | /// The elevator type used by the algorithm. |
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[399] | 88 | /// |
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| 89 | /// \sa Elevator |
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| 90 | /// \sa LinkedElevator |
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| 91 | typedef lemon::Elevator<Digraph, typename Digraph::Node> Elevator; |
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| 92 | |
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| 93 | /// \brief Instantiates an Elevator. |
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| 94 | /// |
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[402] | 95 | /// This function instantiates an \ref Elevator. |
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[399] | 96 | /// \param digraph The digraph, to which we would like to define |
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| 97 | /// the elevator. |
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| 98 | /// \param max_level The maximum level of the elevator. |
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| 99 | static Elevator* createElevator(const Digraph& digraph, int max_level) { |
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| 100 | return new Elevator(digraph, max_level); |
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| 101 | } |
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| 102 | |
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| 103 | /// \brief The tolerance used by the algorithm |
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| 104 | /// |
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| 105 | /// The tolerance used by the algorithm to handle inexact computation. |
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| 106 | typedef lemon::Tolerance<Value> Tolerance; |
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| 107 | |
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| 108 | }; |
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| 109 | |
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[402] | 110 | /** |
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| 111 | \brief Push-relabel algorithm for the network circulation problem. |
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[399] | 112 | |
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| 113 | \ingroup max_flow |
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[402] | 114 | This class implements a push-relabel algorithm for the network |
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| 115 | circulation problem. |
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| 116 | It is to find a feasible circulation when lower and upper bounds |
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| 117 | are given for the flow values on the arcs and lower bounds |
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| 118 | are given for the supply values of the nodes. |
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| 119 | |
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[399] | 120 | The exact formulation of this problem is the following. |
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[402] | 121 | Let \f$G=(V,A)\f$ be a digraph, |
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| 122 | \f$lower, upper: A\rightarrow\mathbf{R}^+_0\f$, |
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| 123 | \f$delta: V\rightarrow\mathbf{R}\f$. Find a feasible circulation |
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| 124 | \f$f: A\rightarrow\mathbf{R}^+_0\f$ so that |
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| 125 | \f[ \sum_{a\in\delta_{out}(v)} f(a) - \sum_{a\in\delta_{in}(v)} f(a) |
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| 126 | \geq delta(v) \quad \forall v\in V, \f] |
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| 127 | \f[ lower(a)\leq f(a) \leq upper(a) \quad \forall a\in A. \f] |
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| 128 | \note \f$delta(v)\f$ specifies a lower bound for the supply of node |
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| 129 | \f$v\f$. It can be either positive or negative, however note that |
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| 130 | \f$\sum_{v\in V}delta(v)\f$ should be zero or negative in order to |
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| 131 | have a feasible solution. |
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| 132 | |
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| 133 | \note A special case of this problem is when |
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| 134 | \f$\sum_{v\in V}delta(v) = 0\f$. Then the supply of each node \f$v\f$ |
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| 135 | will be \e equal \e to \f$delta(v)\f$, if a circulation can be found. |
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| 136 | Thus a feasible solution for the |
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| 137 | \ref min_cost_flow "minimum cost flow" problem can be calculated |
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| 138 | in this way. |
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| 139 | |
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[492] | 140 | \tparam GR The type of the digraph the algorithm runs on. |
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| 141 | \tparam LM The type of the lower bound capacity map. The default |
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| 142 | map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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| 143 | \tparam UM The type of the upper bound capacity map. The default |
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| 144 | map type is \c LM. |
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| 145 | \tparam DM The type of the map that stores the lower bound |
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[402] | 146 | for the supply of the nodes. The default map type is |
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[492] | 147 | \ref concepts::Digraph::NodeMap "GR::NodeMap<UM::Value>". |
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[399] | 148 | */ |
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[402] | 149 | #ifdef DOXYGEN |
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[492] | 150 | template< typename GR, |
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| 151 | typename LM, |
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| 152 | typename UM, |
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| 153 | typename DM, |
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| 154 | typename TR > |
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[402] | 155 | #else |
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[492] | 156 | template< typename GR, |
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| 157 | typename LM = typename GR::template ArcMap<int>, |
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| 158 | typename UM = LM, |
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| 159 | typename DM = typename GR::template NodeMap<typename UM::Value>, |
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| 160 | typename TR = CirculationDefaultTraits<GR, LM, UM, DM> > |
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[402] | 161 | #endif |
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[399] | 162 | class Circulation { |
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[402] | 163 | public: |
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[399] | 164 | |
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[402] | 165 | ///The \ref CirculationDefaultTraits "traits class" of the algorithm. |
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[492] | 166 | typedef TR Traits; |
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[402] | 167 | ///The type of the digraph the algorithm runs on. |
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[399] | 168 | typedef typename Traits::Digraph Digraph; |
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[402] | 169 | ///The type of the flow values. |
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[399] | 170 | typedef typename Traits::Value Value; |
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| 171 | |
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[402] | 172 | /// The type of the lower bound capacity map. |
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[399] | 173 | typedef typename Traits::LCapMap LCapMap; |
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[402] | 174 | /// The type of the upper bound capacity map. |
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[399] | 175 | typedef typename Traits::UCapMap UCapMap; |
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[402] | 176 | /// \brief The type of the map that stores the lower bound for |
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| 177 | /// the supply of the nodes. |
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[399] | 178 | typedef typename Traits::DeltaMap DeltaMap; |
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[402] | 179 | ///The type of the flow map. |
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[399] | 180 | typedef typename Traits::FlowMap FlowMap; |
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[402] | 181 | |
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| 182 | ///The type of the elevator. |
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[399] | 183 | typedef typename Traits::Elevator Elevator; |
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[402] | 184 | ///The type of the tolerance. |
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[399] | 185 | typedef typename Traits::Tolerance Tolerance; |
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| 186 | |
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[402] | 187 | private: |
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| 188 | |
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| 189 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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[399] | 190 | |
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| 191 | const Digraph &_g; |
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| 192 | int _node_num; |
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| 193 | |
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| 194 | const LCapMap *_lo; |
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| 195 | const UCapMap *_up; |
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| 196 | const DeltaMap *_delta; |
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| 197 | |
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| 198 | FlowMap *_flow; |
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| 199 | bool _local_flow; |
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| 200 | |
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| 201 | Elevator* _level; |
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| 202 | bool _local_level; |
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| 203 | |
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[402] | 204 | typedef typename Digraph::template NodeMap<Value> ExcessMap; |
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[399] | 205 | ExcessMap* _excess; |
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| 206 | |
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| 207 | Tolerance _tol; |
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| 208 | int _el; |
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| 209 | |
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| 210 | public: |
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| 211 | |
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| 212 | typedef Circulation Create; |
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| 213 | |
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[402] | 214 | ///\name Named Template Parameters |
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[399] | 215 | |
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| 216 | ///@{ |
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| 217 | |
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| 218 | template <typename _FlowMap> |
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[401] | 219 | struct SetFlowMapTraits : public Traits { |
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[399] | 220 | typedef _FlowMap FlowMap; |
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| 221 | static FlowMap *createFlowMap(const Digraph&) { |
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| 222 | LEMON_ASSERT(false, "FlowMap is not initialized"); |
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| 223 | return 0; // ignore warnings |
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| 224 | } |
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| 225 | }; |
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| 226 | |
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| 227 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 228 | /// FlowMap type |
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| 229 | /// |
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| 230 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
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[402] | 231 | /// type. |
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[399] | 232 | template <typename _FlowMap> |
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[401] | 233 | struct SetFlowMap |
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[399] | 234 | : public Circulation<Digraph, LCapMap, UCapMap, DeltaMap, |
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[401] | 235 | SetFlowMapTraits<_FlowMap> > { |
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[399] | 236 | typedef Circulation<Digraph, LCapMap, UCapMap, DeltaMap, |
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[401] | 237 | SetFlowMapTraits<_FlowMap> > Create; |
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[399] | 238 | }; |
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| 239 | |
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| 240 | template <typename _Elevator> |
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[401] | 241 | struct SetElevatorTraits : public Traits { |
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[399] | 242 | typedef _Elevator Elevator; |
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| 243 | static Elevator *createElevator(const Digraph&, int) { |
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| 244 | LEMON_ASSERT(false, "Elevator is not initialized"); |
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| 245 | return 0; // ignore warnings |
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| 246 | } |
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| 247 | }; |
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| 248 | |
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| 249 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 250 | /// Elevator type |
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| 251 | /// |
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| 252 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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[402] | 253 | /// type. If this named parameter is used, then an external |
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| 254 | /// elevator object must be passed to the algorithm using the |
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| 255 | /// \ref elevator(Elevator&) "elevator()" function before calling |
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| 256 | /// \ref run() or \ref init(). |
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| 257 | /// \sa SetStandardElevator |
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[399] | 258 | template <typename _Elevator> |
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[401] | 259 | struct SetElevator |
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[399] | 260 | : public Circulation<Digraph, LCapMap, UCapMap, DeltaMap, |
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[401] | 261 | SetElevatorTraits<_Elevator> > { |
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[399] | 262 | typedef Circulation<Digraph, LCapMap, UCapMap, DeltaMap, |
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[401] | 263 | SetElevatorTraits<_Elevator> > Create; |
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[399] | 264 | }; |
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| 265 | |
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| 266 | template <typename _Elevator> |
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[401] | 267 | struct SetStandardElevatorTraits : public Traits { |
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[399] | 268 | typedef _Elevator Elevator; |
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| 269 | static Elevator *createElevator(const Digraph& digraph, int max_level) { |
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| 270 | return new Elevator(digraph, max_level); |
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| 271 | } |
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| 272 | }; |
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| 273 | |
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| 274 | /// \brief \ref named-templ-param "Named parameter" for setting |
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[402] | 275 | /// Elevator type with automatic allocation |
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[399] | 276 | /// |
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| 277 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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[402] | 278 | /// type with automatic allocation. |
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| 279 | /// The Elevator should have standard constructor interface to be |
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| 280 | /// able to automatically created by the algorithm (i.e. the |
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| 281 | /// digraph and the maximum level should be passed to it). |
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| 282 | /// However an external elevator object could also be passed to the |
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| 283 | /// algorithm with the \ref elevator(Elevator&) "elevator()" function |
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| 284 | /// before calling \ref run() or \ref init(). |
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| 285 | /// \sa SetElevator |
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[399] | 286 | template <typename _Elevator> |
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[401] | 287 | struct SetStandardElevator |
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[399] | 288 | : public Circulation<Digraph, LCapMap, UCapMap, DeltaMap, |
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[401] | 289 | SetStandardElevatorTraits<_Elevator> > { |
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[399] | 290 | typedef Circulation<Digraph, LCapMap, UCapMap, DeltaMap, |
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[401] | 291 | SetStandardElevatorTraits<_Elevator> > Create; |
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[399] | 292 | }; |
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| 293 | |
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| 294 | /// @} |
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| 295 | |
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| 296 | protected: |
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| 297 | |
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| 298 | Circulation() {} |
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| 299 | |
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| 300 | public: |
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| 301 | |
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| 302 | /// The constructor of the class. |
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| 303 | |
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| 304 | /// The constructor of the class. |
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| 305 | /// \param g The digraph the algorithm runs on. |
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| 306 | /// \param lo The lower bound capacity of the arcs. |
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| 307 | /// \param up The upper bound capacity of the arcs. |
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[402] | 308 | /// \param delta The lower bound for the supply of the nodes. |
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[399] | 309 | Circulation(const Digraph &g,const LCapMap &lo, |
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| 310 | const UCapMap &up,const DeltaMap &delta) |
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| 311 | : _g(g), _node_num(), |
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| 312 | _lo(&lo),_up(&up),_delta(&delta),_flow(0),_local_flow(false), |
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| 313 | _level(0), _local_level(false), _excess(0), _el() {} |
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| 314 | |
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[402] | 315 | /// Destructor. |
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[399] | 316 | ~Circulation() { |
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| 317 | destroyStructures(); |
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| 318 | } |
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| 319 | |
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[402] | 320 | |
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[399] | 321 | private: |
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| 322 | |
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| 323 | void createStructures() { |
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| 324 | _node_num = _el = countNodes(_g); |
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| 325 | |
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| 326 | if (!_flow) { |
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| 327 | _flow = Traits::createFlowMap(_g); |
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| 328 | _local_flow = true; |
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| 329 | } |
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| 330 | if (!_level) { |
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| 331 | _level = Traits::createElevator(_g, _node_num); |
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| 332 | _local_level = true; |
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| 333 | } |
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| 334 | if (!_excess) { |
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| 335 | _excess = new ExcessMap(_g); |
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| 336 | } |
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| 337 | } |
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| 338 | |
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| 339 | void destroyStructures() { |
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| 340 | if (_local_flow) { |
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| 341 | delete _flow; |
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| 342 | } |
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| 343 | if (_local_level) { |
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| 344 | delete _level; |
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| 345 | } |
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| 346 | if (_excess) { |
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| 347 | delete _excess; |
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| 348 | } |
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| 349 | } |
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| 350 | |
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| 351 | public: |
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| 352 | |
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| 353 | /// Sets the lower bound capacity map. |
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| 354 | |
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| 355 | /// Sets the lower bound capacity map. |
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[402] | 356 | /// \return <tt>(*this)</tt> |
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[399] | 357 | Circulation& lowerCapMap(const LCapMap& map) { |
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| 358 | _lo = ↦ |
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| 359 | return *this; |
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| 360 | } |
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| 361 | |
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| 362 | /// Sets the upper bound capacity map. |
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| 363 | |
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| 364 | /// Sets the upper bound capacity map. |
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[402] | 365 | /// \return <tt>(*this)</tt> |
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[399] | 366 | Circulation& upperCapMap(const LCapMap& map) { |
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| 367 | _up = ↦ |
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| 368 | return *this; |
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| 369 | } |
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| 370 | |
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[402] | 371 | /// Sets the lower bound map for the supply of the nodes. |
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[399] | 372 | |
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[402] | 373 | /// Sets the lower bound map for the supply of the nodes. |
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| 374 | /// \return <tt>(*this)</tt> |
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[399] | 375 | Circulation& deltaMap(const DeltaMap& map) { |
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| 376 | _delta = ↦ |
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| 377 | return *this; |
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| 378 | } |
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| 379 | |
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[402] | 380 | /// \brief Sets the flow map. |
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| 381 | /// |
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[399] | 382 | /// Sets the flow map. |
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[402] | 383 | /// If you don't use this function before calling \ref run() or |
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| 384 | /// \ref init(), an instance will be allocated automatically. |
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| 385 | /// The destructor deallocates this automatically allocated map, |
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| 386 | /// of course. |
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| 387 | /// \return <tt>(*this)</tt> |
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[399] | 388 | Circulation& flowMap(FlowMap& map) { |
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| 389 | if (_local_flow) { |
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| 390 | delete _flow; |
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| 391 | _local_flow = false; |
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| 392 | } |
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| 393 | _flow = ↦ |
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| 394 | return *this; |
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| 395 | } |
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| 396 | |
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[402] | 397 | /// \brief Sets the elevator used by algorithm. |
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[399] | 398 | /// |
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[402] | 399 | /// Sets the elevator used by algorithm. |
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| 400 | /// If you don't use this function before calling \ref run() or |
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| 401 | /// \ref init(), an instance will be allocated automatically. |
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| 402 | /// The destructor deallocates this automatically allocated elevator, |
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| 403 | /// of course. |
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| 404 | /// \return <tt>(*this)</tt> |
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[399] | 405 | Circulation& elevator(Elevator& elevator) { |
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| 406 | if (_local_level) { |
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| 407 | delete _level; |
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| 408 | _local_level = false; |
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| 409 | } |
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| 410 | _level = &elevator; |
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| 411 | return *this; |
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| 412 | } |
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| 413 | |
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[402] | 414 | /// \brief Returns a const reference to the elevator. |
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[399] | 415 | /// |
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[402] | 416 | /// Returns a const reference to the elevator. |
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| 417 | /// |
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| 418 | /// \pre Either \ref run() or \ref init() must be called before |
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| 419 | /// using this function. |
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[420] | 420 | const Elevator& elevator() const { |
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[399] | 421 | return *_level; |
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| 422 | } |
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| 423 | |
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[402] | 424 | /// \brief Sets the tolerance used by algorithm. |
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| 425 | /// |
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[399] | 426 | /// Sets the tolerance used by algorithm. |
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| 427 | Circulation& tolerance(const Tolerance& tolerance) const { |
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| 428 | _tol = tolerance; |
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| 429 | return *this; |
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| 430 | } |
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| 431 | |
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[402] | 432 | /// \brief Returns a const reference to the tolerance. |
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[399] | 433 | /// |
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[402] | 434 | /// Returns a const reference to the tolerance. |
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[399] | 435 | const Tolerance& tolerance() const { |
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| 436 | return tolerance; |
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| 437 | } |
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| 438 | |
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[402] | 439 | /// \name Execution Control |
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| 440 | /// The simplest way to execute the algorithm is to call \ref run().\n |
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| 441 | /// If you need more control on the initial solution or the execution, |
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| 442 | /// first you have to call one of the \ref init() functions, then |
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| 443 | /// the \ref start() function. |
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[399] | 444 | |
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| 445 | ///@{ |
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| 446 | |
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| 447 | /// Initializes the internal data structures. |
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| 448 | |
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[402] | 449 | /// Initializes the internal data structures and sets all flow values |
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| 450 | /// to the lower bound. |
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[399] | 451 | void init() |
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| 452 | { |
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| 453 | createStructures(); |
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| 454 | |
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| 455 | for(NodeIt n(_g);n!=INVALID;++n) { |
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| 456 | _excess->set(n, (*_delta)[n]); |
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| 457 | } |
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| 458 | |
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| 459 | for (ArcIt e(_g);e!=INVALID;++e) { |
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| 460 | _flow->set(e, (*_lo)[e]); |
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| 461 | _excess->set(_g.target(e), (*_excess)[_g.target(e)] + (*_flow)[e]); |
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| 462 | _excess->set(_g.source(e), (*_excess)[_g.source(e)] - (*_flow)[e]); |
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| 463 | } |
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| 464 | |
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| 465 | // global relabeling tested, but in general case it provides |
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| 466 | // worse performance for random digraphs |
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| 467 | _level->initStart(); |
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| 468 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
| 469 | _level->initAddItem(n); |
---|
| 470 | _level->initFinish(); |
---|
| 471 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
| 472 | if(_tol.positive((*_excess)[n])) |
---|
| 473 | _level->activate(n); |
---|
| 474 | } |
---|
| 475 | |
---|
[402] | 476 | /// Initializes the internal data structures using a greedy approach. |
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[399] | 477 | |
---|
[402] | 478 | /// Initializes the internal data structures using a greedy approach |
---|
| 479 | /// to construct the initial solution. |
---|
[399] | 480 | void greedyInit() |
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| 481 | { |
---|
| 482 | createStructures(); |
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| 483 | |
---|
| 484 | for(NodeIt n(_g);n!=INVALID;++n) { |
---|
| 485 | _excess->set(n, (*_delta)[n]); |
---|
| 486 | } |
---|
| 487 | |
---|
| 488 | for (ArcIt e(_g);e!=INVALID;++e) { |
---|
| 489 | if (!_tol.positive((*_excess)[_g.target(e)] + (*_up)[e])) { |
---|
| 490 | _flow->set(e, (*_up)[e]); |
---|
| 491 | _excess->set(_g.target(e), (*_excess)[_g.target(e)] + (*_up)[e]); |
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| 492 | _excess->set(_g.source(e), (*_excess)[_g.source(e)] - (*_up)[e]); |
---|
| 493 | } else if (_tol.positive((*_excess)[_g.target(e)] + (*_lo)[e])) { |
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| 494 | _flow->set(e, (*_lo)[e]); |
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| 495 | _excess->set(_g.target(e), (*_excess)[_g.target(e)] + (*_lo)[e]); |
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| 496 | _excess->set(_g.source(e), (*_excess)[_g.source(e)] - (*_lo)[e]); |
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| 497 | } else { |
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| 498 | Value fc = -(*_excess)[_g.target(e)]; |
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| 499 | _flow->set(e, fc); |
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| 500 | _excess->set(_g.target(e), 0); |
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| 501 | _excess->set(_g.source(e), (*_excess)[_g.source(e)] - fc); |
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| 502 | } |
---|
| 503 | } |
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| 504 | |
---|
| 505 | _level->initStart(); |
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| 506 | for(NodeIt n(_g);n!=INVALID;++n) |
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| 507 | _level->initAddItem(n); |
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| 508 | _level->initFinish(); |
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| 509 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
| 510 | if(_tol.positive((*_excess)[n])) |
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| 511 | _level->activate(n); |
---|
| 512 | } |
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| 513 | |
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[402] | 514 | ///Executes the algorithm |
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[399] | 515 | |
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[402] | 516 | ///This function executes the algorithm. |
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| 517 | /// |
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| 518 | ///\return \c true if a feasible circulation is found. |
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[399] | 519 | /// |
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| 520 | ///\sa barrier() |
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[402] | 521 | ///\sa barrierMap() |
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[399] | 522 | bool start() |
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| 523 | { |
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| 524 | |
---|
| 525 | Node act; |
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| 526 | Node bact=INVALID; |
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| 527 | Node last_activated=INVALID; |
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| 528 | while((act=_level->highestActive())!=INVALID) { |
---|
| 529 | int actlevel=(*_level)[act]; |
---|
| 530 | int mlevel=_node_num; |
---|
| 531 | Value exc=(*_excess)[act]; |
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| 532 | |
---|
| 533 | for(OutArcIt e(_g,act);e!=INVALID; ++e) { |
---|
| 534 | Node v = _g.target(e); |
---|
| 535 | Value fc=(*_up)[e]-(*_flow)[e]; |
---|
| 536 | if(!_tol.positive(fc)) continue; |
---|
| 537 | if((*_level)[v]<actlevel) { |
---|
| 538 | if(!_tol.less(fc, exc)) { |
---|
| 539 | _flow->set(e, (*_flow)[e] + exc); |
---|
| 540 | _excess->set(v, (*_excess)[v] + exc); |
---|
| 541 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
---|
| 542 | _level->activate(v); |
---|
| 543 | _excess->set(act,0); |
---|
| 544 | _level->deactivate(act); |
---|
| 545 | goto next_l; |
---|
| 546 | } |
---|
| 547 | else { |
---|
| 548 | _flow->set(e, (*_up)[e]); |
---|
| 549 | _excess->set(v, (*_excess)[v] + fc); |
---|
| 550 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
---|
| 551 | _level->activate(v); |
---|
| 552 | exc-=fc; |
---|
| 553 | } |
---|
| 554 | } |
---|
| 555 | else if((*_level)[v]<mlevel) mlevel=(*_level)[v]; |
---|
| 556 | } |
---|
| 557 | for(InArcIt e(_g,act);e!=INVALID; ++e) { |
---|
| 558 | Node v = _g.source(e); |
---|
| 559 | Value fc=(*_flow)[e]-(*_lo)[e]; |
---|
| 560 | if(!_tol.positive(fc)) continue; |
---|
| 561 | if((*_level)[v]<actlevel) { |
---|
| 562 | if(!_tol.less(fc, exc)) { |
---|
| 563 | _flow->set(e, (*_flow)[e] - exc); |
---|
| 564 | _excess->set(v, (*_excess)[v] + exc); |
---|
| 565 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
---|
| 566 | _level->activate(v); |
---|
| 567 | _excess->set(act,0); |
---|
| 568 | _level->deactivate(act); |
---|
| 569 | goto next_l; |
---|
| 570 | } |
---|
| 571 | else { |
---|
| 572 | _flow->set(e, (*_lo)[e]); |
---|
| 573 | _excess->set(v, (*_excess)[v] + fc); |
---|
| 574 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
---|
| 575 | _level->activate(v); |
---|
| 576 | exc-=fc; |
---|
| 577 | } |
---|
| 578 | } |
---|
| 579 | else if((*_level)[v]<mlevel) mlevel=(*_level)[v]; |
---|
| 580 | } |
---|
| 581 | |
---|
| 582 | _excess->set(act, exc); |
---|
| 583 | if(!_tol.positive(exc)) _level->deactivate(act); |
---|
| 584 | else if(mlevel==_node_num) { |
---|
| 585 | _level->liftHighestActiveToTop(); |
---|
| 586 | _el = _node_num; |
---|
| 587 | return false; |
---|
| 588 | } |
---|
| 589 | else { |
---|
| 590 | _level->liftHighestActive(mlevel+1); |
---|
| 591 | if(_level->onLevel(actlevel)==0) { |
---|
| 592 | _el = actlevel; |
---|
| 593 | return false; |
---|
| 594 | } |
---|
| 595 | } |
---|
| 596 | next_l: |
---|
| 597 | ; |
---|
| 598 | } |
---|
| 599 | return true; |
---|
| 600 | } |
---|
| 601 | |
---|
[402] | 602 | /// Runs the algorithm. |
---|
[399] | 603 | |
---|
[402] | 604 | /// This function runs the algorithm. |
---|
| 605 | /// |
---|
| 606 | /// \return \c true if a feasible circulation is found. |
---|
| 607 | /// |
---|
| 608 | /// \note Apart from the return value, c.run() is just a shortcut of |
---|
| 609 | /// the following code. |
---|
[399] | 610 | /// \code |
---|
[402] | 611 | /// c.greedyInit(); |
---|
| 612 | /// c.start(); |
---|
[399] | 613 | /// \endcode |
---|
| 614 | bool run() { |
---|
| 615 | greedyInit(); |
---|
| 616 | return start(); |
---|
| 617 | } |
---|
| 618 | |
---|
| 619 | /// @} |
---|
| 620 | |
---|
| 621 | /// \name Query Functions |
---|
[402] | 622 | /// The results of the circulation algorithm can be obtained using |
---|
| 623 | /// these functions.\n |
---|
| 624 | /// Either \ref run() or \ref start() should be called before |
---|
| 625 | /// using them. |
---|
[399] | 626 | |
---|
| 627 | ///@{ |
---|
| 628 | |
---|
[402] | 629 | /// \brief Returns the flow on the given arc. |
---|
| 630 | /// |
---|
| 631 | /// Returns the flow on the given arc. |
---|
| 632 | /// |
---|
| 633 | /// \pre Either \ref run() or \ref init() must be called before |
---|
| 634 | /// using this function. |
---|
| 635 | Value flow(const Arc& arc) const { |
---|
| 636 | return (*_flow)[arc]; |
---|
| 637 | } |
---|
| 638 | |
---|
| 639 | /// \brief Returns a const reference to the flow map. |
---|
| 640 | /// |
---|
| 641 | /// Returns a const reference to the arc map storing the found flow. |
---|
| 642 | /// |
---|
| 643 | /// \pre Either \ref run() or \ref init() must be called before |
---|
| 644 | /// using this function. |
---|
[420] | 645 | const FlowMap& flowMap() const { |
---|
[402] | 646 | return *_flow; |
---|
| 647 | } |
---|
| 648 | |
---|
[399] | 649 | /** |
---|
[402] | 650 | \brief Returns \c true if the given node is in a barrier. |
---|
| 651 | |
---|
[399] | 652 | Barrier is a set \e B of nodes for which |
---|
[402] | 653 | |
---|
| 654 | \f[ \sum_{a\in\delta_{out}(B)} upper(a) - |
---|
| 655 | \sum_{a\in\delta_{in}(B)} lower(a) < \sum_{v\in B}delta(v) \f] |
---|
| 656 | |
---|
| 657 | holds. The existence of a set with this property prooves that a |
---|
| 658 | feasible circualtion cannot exist. |
---|
| 659 | |
---|
| 660 | This function returns \c true if the given node is in the found |
---|
| 661 | barrier. If a feasible circulation is found, the function |
---|
| 662 | gives back \c false for every node. |
---|
| 663 | |
---|
| 664 | \pre Either \ref run() or \ref init() must be called before |
---|
| 665 | using this function. |
---|
| 666 | |
---|
| 667 | \sa barrierMap() |
---|
[399] | 668 | \sa checkBarrier() |
---|
| 669 | */ |
---|
[420] | 670 | bool barrier(const Node& node) const |
---|
[402] | 671 | { |
---|
| 672 | return (*_level)[node] >= _el; |
---|
| 673 | } |
---|
| 674 | |
---|
| 675 | /// \brief Gives back a barrier. |
---|
| 676 | /// |
---|
| 677 | /// This function sets \c bar to the characteristic vector of the |
---|
| 678 | /// found barrier. \c bar should be a \ref concepts::WriteMap "writable" |
---|
| 679 | /// node map with \c bool (or convertible) value type. |
---|
| 680 | /// |
---|
| 681 | /// If a feasible circulation is found, the function gives back an |
---|
| 682 | /// empty set, so \c bar[v] will be \c false for all nodes \c v. |
---|
| 683 | /// |
---|
| 684 | /// \note This function calls \ref barrier() for each node, |
---|
| 685 | /// so it runs in \f$O(n)\f$ time. |
---|
| 686 | /// |
---|
| 687 | /// \pre Either \ref run() or \ref init() must be called before |
---|
| 688 | /// using this function. |
---|
| 689 | /// |
---|
| 690 | /// \sa barrier() |
---|
| 691 | /// \sa checkBarrier() |
---|
| 692 | template<class BarrierMap> |
---|
[420] | 693 | void barrierMap(BarrierMap &bar) const |
---|
[399] | 694 | { |
---|
| 695 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
| 696 | bar.set(n, (*_level)[n] >= _el); |
---|
| 697 | } |
---|
| 698 | |
---|
| 699 | /// @} |
---|
| 700 | |
---|
| 701 | /// \name Checker Functions |
---|
[402] | 702 | /// The feasibility of the results can be checked using |
---|
| 703 | /// these functions.\n |
---|
| 704 | /// Either \ref run() or \ref start() should be called before |
---|
| 705 | /// using them. |
---|
[399] | 706 | |
---|
| 707 | ///@{ |
---|
| 708 | |
---|
[402] | 709 | ///Check if the found flow is a feasible circulation |
---|
| 710 | |
---|
| 711 | ///Check if the found flow is a feasible circulation, |
---|
| 712 | /// |
---|
[420] | 713 | bool checkFlow() const { |
---|
[399] | 714 | for(ArcIt e(_g);e!=INVALID;++e) |
---|
| 715 | if((*_flow)[e]<(*_lo)[e]||(*_flow)[e]>(*_up)[e]) return false; |
---|
| 716 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
| 717 | { |
---|
| 718 | Value dif=-(*_delta)[n]; |
---|
| 719 | for(InArcIt e(_g,n);e!=INVALID;++e) dif-=(*_flow)[e]; |
---|
| 720 | for(OutArcIt e(_g,n);e!=INVALID;++e) dif+=(*_flow)[e]; |
---|
| 721 | if(_tol.negative(dif)) return false; |
---|
| 722 | } |
---|
| 723 | return true; |
---|
| 724 | } |
---|
| 725 | |
---|
| 726 | ///Check whether or not the last execution provides a barrier |
---|
| 727 | |
---|
[402] | 728 | ///Check whether or not the last execution provides a barrier. |
---|
[399] | 729 | ///\sa barrier() |
---|
[402] | 730 | ///\sa barrierMap() |
---|
[420] | 731 | bool checkBarrier() const |
---|
[399] | 732 | { |
---|
| 733 | Value delta=0; |
---|
| 734 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
| 735 | if(barrier(n)) |
---|
| 736 | delta-=(*_delta)[n]; |
---|
| 737 | for(ArcIt e(_g);e!=INVALID;++e) |
---|
| 738 | { |
---|
| 739 | Node s=_g.source(e); |
---|
| 740 | Node t=_g.target(e); |
---|
| 741 | if(barrier(s)&&!barrier(t)) delta+=(*_up)[e]; |
---|
| 742 | else if(barrier(t)&&!barrier(s)) delta-=(*_lo)[e]; |
---|
| 743 | } |
---|
| 744 | return _tol.negative(delta); |
---|
| 745 | } |
---|
| 746 | |
---|
| 747 | /// @} |
---|
| 748 | |
---|
| 749 | }; |
---|
| 750 | |
---|
| 751 | } |
---|
| 752 | |
---|
| 753 | #endif |
---|