[2375] | 1 | /* -*- C++ -*- |
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| 2 | * |
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[2391] | 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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[2553] | 5 | * Copyright (C) 2003-2008 |
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[2391] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[2375] | 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/graph_utils.h> |
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| 23 | #include <iostream> |
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| 24 | #include <queue> |
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| 25 | #include <lemon/tolerance.h> |
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| 26 | #include <lemon/elevator.h> |
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| 27 | |
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[2376] | 28 | ///\ingroup max_flow |
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[2375] | 29 | ///\file |
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| 30 | ///\brief Push-prelabel algorithm for finding a feasible circulation. |
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| 31 | /// |
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| 32 | namespace lemon { |
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| 33 | |
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[2526] | 34 | /// \brief Default traits class of Circulation class. |
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| 35 | /// |
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| 36 | /// Default traits class of Circulation class. |
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| 37 | /// \param _Graph Graph type. |
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| 38 | /// \param _CapacityMap Type of capacity map. |
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| 39 | template <typename _Graph, typename _LCapMap, |
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| 40 | typename _UCapMap, typename _DeltaMap> |
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| 41 | struct CirculationDefaultTraits { |
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| 42 | |
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| 43 | /// \brief The graph type the algorithm runs on. |
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| 44 | typedef _Graph Graph; |
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| 45 | |
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| 46 | /// \brief The type of the map that stores the circulation lower |
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| 47 | /// bound. |
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| 48 | /// |
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| 49 | /// The type of the map that stores the circulation lower bound. |
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| 50 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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| 51 | typedef _LCapMap LCapMap; |
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| 52 | |
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| 53 | /// \brief The type of the map that stores the circulation upper |
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| 54 | /// bound. |
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| 55 | /// |
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| 56 | /// The type of the map that stores the circulation upper bound. |
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| 57 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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| 58 | typedef _UCapMap UCapMap; |
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| 59 | |
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| 60 | /// \brief The type of the map that stores the upper bound of |
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| 61 | /// node excess. |
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| 62 | /// |
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| 63 | /// The type of the map that stores the lower bound of node |
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| 64 | /// excess. It must meet the \ref concepts::ReadMap "ReadMap" |
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| 65 | /// concept. |
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| 66 | typedef _DeltaMap DeltaMap; |
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| 67 | |
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| 68 | /// \brief The type of the length of the edges. |
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| 69 | typedef typename DeltaMap::Value Value; |
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| 70 | |
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| 71 | /// \brief The map type that stores the flow values. |
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| 72 | /// |
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| 73 | /// The map type that stores the flow values. |
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| 74 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
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| 75 | typedef typename Graph::template EdgeMap<Value> FlowMap; |
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| 76 | |
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| 77 | /// \brief Instantiates a FlowMap. |
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| 78 | /// |
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| 79 | /// This function instantiates a \ref FlowMap. |
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| 80 | /// \param graph The graph, to which we would like to define the flow map. |
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| 81 | static FlowMap* createFlowMap(const Graph& graph) { |
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| 82 | return new FlowMap(graph); |
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| 83 | } |
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| 84 | |
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| 85 | /// \brief The eleavator type used by Circulation algorithm. |
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| 86 | /// |
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| 87 | /// The elevator type used by Circulation algorithm. |
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| 88 | /// |
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| 89 | /// \sa Elevator |
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| 90 | /// \sa LinkedElevator |
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[2618] | 91 | typedef lemon::Elevator<Graph, typename Graph::Node> Elevator; |
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[2526] | 92 | |
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| 93 | /// \brief Instantiates an Elevator. |
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| 94 | /// |
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| 95 | /// This function instantiates a \ref Elevator. |
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| 96 | /// \param graph The graph, to which we would like to define the elevator. |
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| 97 | /// \param max_level The maximum level of the elevator. |
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| 98 | static Elevator* createElevator(const Graph& graph, int max_level) { |
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| 99 | return new Elevator(graph, max_level); |
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| 100 | } |
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| 101 | |
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| 102 | /// \brief The tolerance used by the algorithm |
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| 103 | /// |
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| 104 | /// The tolerance used by the algorithm to handle inexact computation. |
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[2618] | 105 | typedef lemon::Tolerance<Value> Tolerance; |
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[2526] | 106 | |
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| 107 | }; |
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| 108 | |
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| 109 | ///Push-relabel algorithm for the Network Circulation Problem. |
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[2375] | 110 | |
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[2378] | 111 | ///\ingroup max_flow |
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[2526] | 112 | ///This class implements a push-relabel algorithm |
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[2375] | 113 | ///for the Network Circulation Problem. |
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| 114 | ///The exact formulation of this problem is the following. |
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[2450] | 115 | /// \f[\sum_{e\in\rho(v)}x(e)-\sum_{e\in\delta(v)}x(e)\leq -delta(v)\quad \forall v\in V \f] |
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[2375] | 116 | /// \f[ lo(e)\leq x(e) \leq up(e) \quad \forall e\in E \f] |
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| 117 | /// |
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[2526] | 118 | template<class _Graph, |
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| 119 | class _LCapMap=typename _Graph::template EdgeMap<int>, |
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| 120 | class _UCapMap=_LCapMap, |
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| 121 | class _DeltaMap=typename _Graph::template NodeMap< |
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| 122 | typename _UCapMap::Value>, |
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| 123 | class _Traits=CirculationDefaultTraits<_Graph, _LCapMap, |
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| 124 | _UCapMap, _DeltaMap> > |
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[2375] | 125 | class Circulation { |
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[2526] | 126 | |
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| 127 | typedef _Traits Traits; |
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| 128 | typedef typename Traits::Graph Graph; |
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| 129 | GRAPH_TYPEDEFS(typename Graph); |
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| 130 | |
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| 131 | typedef typename Traits::Value Value; |
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| 132 | |
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| 133 | typedef typename Traits::LCapMap LCapMap; |
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| 134 | typedef typename Traits::UCapMap UCapMap; |
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| 135 | typedef typename Traits::DeltaMap DeltaMap; |
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| 136 | typedef typename Traits::FlowMap FlowMap; |
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| 137 | typedef typename Traits::Elevator Elevator; |
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| 138 | typedef typename Traits::Tolerance Tolerance; |
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| 139 | |
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| 140 | typedef typename Graph::template NodeMap<Value> ExcessMap; |
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[2375] | 141 | |
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| 142 | const Graph &_g; |
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| 143 | int _node_num; |
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| 144 | |
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[2526] | 145 | const LCapMap *_lo; |
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| 146 | const UCapMap *_up; |
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| 147 | const DeltaMap *_delta; |
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| 148 | |
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| 149 | FlowMap *_flow; |
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| 150 | bool _local_flow; |
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| 151 | |
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| 152 | Elevator* _level; |
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| 153 | bool _local_level; |
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| 154 | |
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| 155 | ExcessMap* _excess; |
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| 156 | |
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| 157 | Tolerance _tol; |
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| 158 | int _el; |
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[2375] | 159 | |
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| 160 | public: |
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[2526] | 161 | |
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| 162 | typedef Circulation Create; |
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| 163 | |
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| 164 | ///\name Named template parameters |
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| 165 | |
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| 166 | ///@{ |
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| 167 | |
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| 168 | template <typename _FlowMap> |
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| 169 | struct DefFlowMapTraits : public Traits { |
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| 170 | typedef _FlowMap FlowMap; |
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| 171 | static FlowMap *createFlowMap(const Graph&) { |
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| 172 | throw UninitializedParameter(); |
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| 173 | } |
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| 174 | }; |
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| 175 | |
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| 176 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 177 | /// FlowMap type |
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| 178 | /// |
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| 179 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
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| 180 | /// type |
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| 181 | template <typename _FlowMap> |
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| 182 | struct DefFlowMap |
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| 183 | : public Circulation<Graph, LCapMap, UCapMap, DeltaMap, |
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| 184 | DefFlowMapTraits<_FlowMap> > { |
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| 185 | typedef Circulation<Graph, LCapMap, UCapMap, DeltaMap, |
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| 186 | DefFlowMapTraits<_FlowMap> > Create; |
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| 187 | }; |
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| 188 | |
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| 189 | template <typename _Elevator> |
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| 190 | struct DefElevatorTraits : public Traits { |
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| 191 | typedef _Elevator Elevator; |
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| 192 | static Elevator *createElevator(const Graph&, int) { |
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| 193 | throw UninitializedParameter(); |
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| 194 | } |
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| 195 | }; |
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| 196 | |
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| 197 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 198 | /// Elevator type |
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| 199 | /// |
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| 200 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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| 201 | /// type |
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| 202 | template <typename _Elevator> |
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| 203 | struct DefElevator |
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| 204 | : public Circulation<Graph, LCapMap, UCapMap, DeltaMap, |
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| 205 | DefElevatorTraits<_Elevator> > { |
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| 206 | typedef Circulation<Graph, LCapMap, UCapMap, DeltaMap, |
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| 207 | DefElevatorTraits<_Elevator> > Create; |
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| 208 | }; |
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| 209 | |
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| 210 | template <typename _Elevator> |
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| 211 | struct DefStandardElevatorTraits : public Traits { |
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| 212 | typedef _Elevator Elevator; |
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| 213 | static Elevator *createElevator(const Graph& graph, int max_level) { |
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| 214 | return new Elevator(graph, max_level); |
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| 215 | } |
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| 216 | }; |
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| 217 | |
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| 218 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 219 | /// Elevator type |
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| 220 | /// |
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| 221 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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| 222 | /// type. The Elevator should be standard constructor interface, ie. |
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| 223 | /// the graph and the maximum level should be passed to it. |
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| 224 | template <typename _Elevator> |
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| 225 | struct DefStandardElevator |
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| 226 | : public Circulation<Graph, LCapMap, UCapMap, DeltaMap, |
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| 227 | DefStandardElevatorTraits<_Elevator> > { |
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| 228 | typedef Circulation<Graph, LCapMap, UCapMap, DeltaMap, |
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| 229 | DefStandardElevatorTraits<_Elevator> > Create; |
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| 230 | }; |
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| 231 | |
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| 232 | /// @} |
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| 233 | |
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[2527] | 234 | protected: |
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| 235 | |
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| 236 | Circulation() {} |
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| 237 | |
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| 238 | public: |
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| 239 | |
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[2526] | 240 | /// The constructor of the class. |
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| 241 | |
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| 242 | /// The constructor of the class. |
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| 243 | /// \param g The directed graph the algorithm runs on. |
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| 244 | /// \param lo The lower bound capacity of the edges. |
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| 245 | /// \param up The upper bound capacity of the edges. |
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| 246 | /// \param delta The lower bound on node excess. |
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| 247 | Circulation(const Graph &g,const LCapMap &lo, |
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| 248 | const UCapMap &up,const DeltaMap &delta) |
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| 249 | : _g(g), _node_num(), |
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| 250 | _lo(&lo),_up(&up),_delta(&delta),_flow(0),_local_flow(false), |
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| 251 | _level(0), _local_level(false), _excess(0), _el() {} |
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| 252 | |
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| 253 | /// Destrcutor. |
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| 254 | ~Circulation() { |
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| 255 | destroyStructures(); |
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[2375] | 256 | } |
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[2526] | 257 | |
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[2375] | 258 | private: |
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| 259 | |
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[2526] | 260 | void createStructures() { |
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| 261 | _node_num = _el = countNodes(_g); |
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| 262 | |
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| 263 | if (!_flow) { |
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| 264 | _flow = Traits::createFlowMap(_g); |
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| 265 | _local_flow = true; |
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| 266 | } |
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| 267 | if (!_level) { |
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| 268 | _level = Traits::createElevator(_g, _node_num); |
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| 269 | _local_level = true; |
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| 270 | } |
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| 271 | if (!_excess) { |
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| 272 | _excess = new ExcessMap(_g); |
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| 273 | } |
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[2375] | 274 | } |
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| 275 | |
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[2526] | 276 | void destroyStructures() { |
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| 277 | if (_local_flow) { |
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| 278 | delete _flow; |
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| 279 | } |
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| 280 | if (_local_level) { |
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| 281 | delete _level; |
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| 282 | } |
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| 283 | if (_excess) { |
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| 284 | delete _excess; |
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| 285 | } |
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[2375] | 286 | } |
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| 287 | |
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| 288 | public: |
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[2526] | 289 | |
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| 290 | /// Sets the lower bound capacity map. |
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| 291 | |
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| 292 | /// Sets the lower bound capacity map. |
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| 293 | /// \return \c (*this) |
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| 294 | Circulation& lowerCapMap(const LCapMap& map) { |
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| 295 | _lo = ↦ |
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| 296 | return *this; |
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| 297 | } |
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| 298 | |
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| 299 | /// Sets the upper bound capacity map. |
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| 300 | |
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| 301 | /// Sets the upper bound capacity map. |
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| 302 | /// \return \c (*this) |
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| 303 | Circulation& upperCapMap(const LCapMap& map) { |
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| 304 | _up = ↦ |
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| 305 | return *this; |
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| 306 | } |
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| 307 | |
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| 308 | /// Sets the lower bound map on excess. |
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| 309 | |
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| 310 | /// Sets the lower bound map on excess. |
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| 311 | /// \return \c (*this) |
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| 312 | Circulation& deltaMap(const DeltaMap& map) { |
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| 313 | _delta = ↦ |
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| 314 | return *this; |
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| 315 | } |
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| 316 | |
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| 317 | /// Sets the flow map. |
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| 318 | |
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| 319 | /// Sets the flow map. |
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| 320 | /// \return \c (*this) |
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| 321 | Circulation& flowMap(FlowMap& map) { |
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| 322 | if (_local_flow) { |
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| 323 | delete _flow; |
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| 324 | _local_flow = false; |
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| 325 | } |
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| 326 | _flow = ↦ |
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| 327 | return *this; |
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| 328 | } |
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| 329 | |
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| 330 | /// Returns the flow map. |
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| 331 | |
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| 332 | /// \return The flow map. |
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| 333 | /// |
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| 334 | const FlowMap& flowMap() { |
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| 335 | return *_flow; |
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| 336 | } |
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| 337 | |
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| 338 | /// Sets the elevator. |
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| 339 | |
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| 340 | /// Sets the elevator. |
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| 341 | /// \return \c (*this) |
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| 342 | Circulation& elevator(Elevator& elevator) { |
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| 343 | if (_local_level) { |
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| 344 | delete _level; |
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| 345 | _local_level = false; |
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| 346 | } |
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| 347 | _level = &elevator; |
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| 348 | return *this; |
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| 349 | } |
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| 350 | |
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| 351 | /// Returns the elevator. |
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| 352 | |
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| 353 | /// \return The elevator. |
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| 354 | /// |
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| 355 | const Elevator& elevator() { |
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| 356 | return *_level; |
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| 357 | } |
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| 358 | |
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| 359 | /// Sets the tolerance used by algorithm. |
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| 360 | |
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| 361 | /// Sets the tolerance used by algorithm. |
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| 362 | /// |
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| 363 | Circulation& tolerance(const Tolerance& tolerance) const { |
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| 364 | _tol = tolerance; |
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| 365 | return *this; |
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| 366 | } |
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| 367 | |
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| 368 | /// Returns the tolerance used by algorithm. |
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| 369 | |
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| 370 | /// Returns the tolerance used by algorithm. |
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| 371 | /// |
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| 372 | const Tolerance& tolerance() const { |
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| 373 | return tolerance; |
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| 374 | } |
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| 375 | |
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[2533] | 376 | /// \name Execution control |
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| 377 | /// The simplest way to execute the algorithm is to use one of the |
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| 378 | /// member functions called \c run(). |
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[2526] | 379 | /// \n |
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| 380 | /// If you need more control on initial solution or execution then |
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| 381 | /// you have to call one \ref init() function and then the start() |
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| 382 | /// function. |
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| 383 | |
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| 384 | ///@{ |
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| 385 | |
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| 386 | /// Initializes the internal data structures. |
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| 387 | |
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| 388 | /// Initializes the internal data structures. This function sets |
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| 389 | /// all flow values to the lower bound. |
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| 390 | /// \return This function returns false if the initialization |
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| 391 | /// process found a barrier. |
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| 392 | void init() |
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| 393 | { |
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| 394 | createStructures(); |
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| 395 | |
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| 396 | for(NodeIt n(_g);n!=INVALID;++n) { |
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| 397 | _excess->set(n, (*_delta)[n]); |
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| 398 | } |
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| 399 | |
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| 400 | for (EdgeIt e(_g);e!=INVALID;++e) { |
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| 401 | _flow->set(e, (*_lo)[e]); |
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| 402 | _excess->set(_g.target(e), (*_excess)[_g.target(e)] + (*_flow)[e]); |
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| 403 | _excess->set(_g.source(e), (*_excess)[_g.source(e)] - (*_flow)[e]); |
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| 404 | } |
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| 405 | |
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| 406 | // global relabeling tested, but in general case it provides |
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| 407 | // worse performance for random graphs |
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| 408 | _level->initStart(); |
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| 409 | for(NodeIt n(_g);n!=INVALID;++n) |
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| 410 | _level->initAddItem(n); |
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| 411 | _level->initFinish(); |
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| 412 | for(NodeIt n(_g);n!=INVALID;++n) |
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| 413 | if(_tol.positive((*_excess)[n])) |
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| 414 | _level->activate(n); |
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| 415 | } |
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| 416 | |
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| 417 | /// Initializes the internal data structures. |
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| 418 | |
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| 419 | /// Initializes the internal data structures. This functions uses |
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| 420 | /// greedy approach to construct the initial solution. |
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| 421 | void greedyInit() |
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| 422 | { |
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| 423 | createStructures(); |
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| 424 | |
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| 425 | for(NodeIt n(_g);n!=INVALID;++n) { |
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| 426 | _excess->set(n, (*_delta)[n]); |
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| 427 | } |
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| 428 | |
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| 429 | for (EdgeIt e(_g);e!=INVALID;++e) { |
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| 430 | if (!_tol.positive((*_excess)[_g.target(e)] + (*_up)[e])) { |
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| 431 | _flow->set(e, (*_up)[e]); |
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| 432 | _excess->set(_g.target(e), (*_excess)[_g.target(e)] + (*_up)[e]); |
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| 433 | _excess->set(_g.source(e), (*_excess)[_g.source(e)] - (*_up)[e]); |
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| 434 | } else if (_tol.positive((*_excess)[_g.target(e)] + (*_lo)[e])) { |
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| 435 | _flow->set(e, (*_lo)[e]); |
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[2541] | 436 | _excess->set(_g.target(e), (*_excess)[_g.target(e)] + (*_lo)[e]); |
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| 437 | _excess->set(_g.source(e), (*_excess)[_g.source(e)] - (*_lo)[e]); |
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[2526] | 438 | } else { |
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| 439 | Value fc = -(*_excess)[_g.target(e)]; |
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| 440 | _flow->set(e, fc); |
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| 441 | _excess->set(_g.target(e), 0); |
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| 442 | _excess->set(_g.source(e), (*_excess)[_g.source(e)] - fc); |
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| 443 | } |
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| 444 | } |
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| 445 | |
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| 446 | _level->initStart(); |
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| 447 | for(NodeIt n(_g);n!=INVALID;++n) |
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| 448 | _level->initAddItem(n); |
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| 449 | _level->initFinish(); |
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| 450 | for(NodeIt n(_g);n!=INVALID;++n) |
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| 451 | if(_tol.positive((*_excess)[n])) |
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| 452 | _level->activate(n); |
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| 453 | } |
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| 454 | |
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| 455 | ///Starts the algorithm |
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| 456 | |
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| 457 | ///This function starts the algorithm. |
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| 458 | ///\return This function returns true if it found a feasible circulation. |
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| 459 | /// |
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| 460 | ///\sa barrier() |
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| 461 | bool start() |
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| 462 | { |
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| 463 | |
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| 464 | Node act; |
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| 465 | Node bact=INVALID; |
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| 466 | Node last_activated=INVALID; |
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| 467 | while((act=_level->highestActive())!=INVALID) { |
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| 468 | int actlevel=(*_level)[act]; |
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| 469 | int mlevel=_node_num; |
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| 470 | Value exc=(*_excess)[act]; |
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[2541] | 471 | |
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[2526] | 472 | for(OutEdgeIt e(_g,act);e!=INVALID; ++e) { |
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| 473 | Node v = _g.target(e); |
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| 474 | Value fc=(*_up)[e]-(*_flow)[e]; |
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| 475 | if(!_tol.positive(fc)) continue; |
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| 476 | if((*_level)[v]<actlevel) { |
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| 477 | if(!_tol.less(fc, exc)) { |
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| 478 | _flow->set(e, (*_flow)[e] + exc); |
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| 479 | _excess->set(v, (*_excess)[v] + exc); |
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| 480 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
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| 481 | _level->activate(v); |
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| 482 | _excess->set(act,0); |
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| 483 | _level->deactivate(act); |
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| 484 | goto next_l; |
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| 485 | } |
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| 486 | else { |
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| 487 | _flow->set(e, (*_up)[e]); |
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[2541] | 488 | _excess->set(v, (*_excess)[v] + fc); |
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[2526] | 489 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
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| 490 | _level->activate(v); |
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| 491 | exc-=fc; |
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| 492 | } |
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| 493 | } |
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| 494 | else if((*_level)[v]<mlevel) mlevel=(*_level)[v]; |
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| 495 | } |
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| 496 | for(InEdgeIt e(_g,act);e!=INVALID; ++e) { |
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| 497 | Node v = _g.source(e); |
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| 498 | Value fc=(*_flow)[e]-(*_lo)[e]; |
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| 499 | if(!_tol.positive(fc)) continue; |
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| 500 | if((*_level)[v]<actlevel) { |
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| 501 | if(!_tol.less(fc, exc)) { |
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| 502 | _flow->set(e, (*_flow)[e] - exc); |
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| 503 | _excess->set(v, (*_excess)[v] + exc); |
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| 504 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
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| 505 | _level->activate(v); |
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| 506 | _excess->set(act,0); |
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| 507 | _level->deactivate(act); |
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| 508 | goto next_l; |
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| 509 | } |
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| 510 | else { |
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| 511 | _flow->set(e, (*_lo)[e]); |
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| 512 | _excess->set(v, (*_excess)[v] + fc); |
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| 513 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
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| 514 | _level->activate(v); |
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| 515 | exc-=fc; |
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| 516 | } |
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| 517 | } |
---|
| 518 | else if((*_level)[v]<mlevel) mlevel=(*_level)[v]; |
---|
| 519 | } |
---|
| 520 | |
---|
| 521 | _excess->set(act, exc); |
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| 522 | if(!_tol.positive(exc)) _level->deactivate(act); |
---|
| 523 | else if(mlevel==_node_num) { |
---|
| 524 | _level->liftHighestActiveToTop(); |
---|
| 525 | _el = _node_num; |
---|
| 526 | return false; |
---|
| 527 | } |
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| 528 | else { |
---|
| 529 | _level->liftHighestActive(mlevel+1); |
---|
| 530 | if(_level->onLevel(actlevel)==0) { |
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| 531 | _el = actlevel; |
---|
| 532 | return false; |
---|
| 533 | } |
---|
| 534 | } |
---|
| 535 | next_l: |
---|
| 536 | ; |
---|
| 537 | } |
---|
| 538 | return true; |
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| 539 | } |
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| 540 | |
---|
| 541 | /// Runs the circulation algorithm. |
---|
| 542 | |
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| 543 | /// Runs the circulation algorithm. |
---|
| 544 | /// \note fc.run() is just a shortcut of the following code. |
---|
| 545 | /// \code |
---|
| 546 | /// fc.greedyInit(); |
---|
| 547 | /// return fc.start(); |
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| 548 | /// \endcode |
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| 549 | bool run() { |
---|
| 550 | greedyInit(); |
---|
| 551 | return start(); |
---|
| 552 | } |
---|
| 553 | |
---|
| 554 | /// @} |
---|
| 555 | |
---|
| 556 | /// \name Query Functions |
---|
| 557 | /// The result of the %Circulation algorithm can be obtained using |
---|
| 558 | /// these functions. |
---|
| 559 | /// \n |
---|
| 560 | /// Before the use of these functions, |
---|
| 561 | /// either run() or start() must be called. |
---|
| 562 | |
---|
| 563 | ///@{ |
---|
| 564 | |
---|
| 565 | ///Returns a barrier |
---|
| 566 | |
---|
| 567 | ///Barrier is a set \e B of nodes for which |
---|
| 568 | /// \f[ \sum_{v\in B}-delta(v)<\sum_{e\in\rho(B)}lo(e)-\sum_{e\in\delta(B)}up(e) \f] |
---|
| 569 | ///holds. The existence of a set with this property prooves that a feasible |
---|
| 570 | ///flow cannot exists. |
---|
| 571 | ///\sa checkBarrier() |
---|
| 572 | ///\sa run() |
---|
| 573 | template<class GT> |
---|
| 574 | void barrierMap(GT &bar) |
---|
| 575 | { |
---|
| 576 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
| 577 | bar.set(n, (*_level)[n] >= _el); |
---|
| 578 | } |
---|
| 579 | |
---|
| 580 | ///Returns true if the node is in the barrier |
---|
| 581 | |
---|
| 582 | ///Returns true if the node is in the barrier |
---|
| 583 | ///\sa barrierMap() |
---|
| 584 | bool barrier(const Node& node) |
---|
| 585 | { |
---|
| 586 | return (*_level)[node] >= _el; |
---|
| 587 | } |
---|
| 588 | |
---|
| 589 | /// \brief Returns the flow on the edge. |
---|
| 590 | /// |
---|
| 591 | /// Sets the \c flowMap to the flow on the edges. This method can |
---|
| 592 | /// be called after the second phase of algorithm. |
---|
| 593 | Value flow(const Edge& edge) const { |
---|
| 594 | return (*_flow)[edge]; |
---|
| 595 | } |
---|
| 596 | |
---|
| 597 | /// @} |
---|
| 598 | |
---|
| 599 | /// \name Checker Functions |
---|
| 600 | /// The feasibility of the results can be checked using |
---|
| 601 | /// these functions. |
---|
| 602 | /// \n |
---|
| 603 | /// Before the use of these functions, |
---|
| 604 | /// either run() or start() must be called. |
---|
| 605 | |
---|
| 606 | ///@{ |
---|
| 607 | |
---|
| 608 | ///Check if the \c flow is a feasible circulation |
---|
| 609 | bool checkFlow() { |
---|
[2375] | 610 | for(EdgeIt e(_g);e!=INVALID;++e) |
---|
[2526] | 611 | if((*_flow)[e]<(*_lo)[e]||(*_flow)[e]>(*_up)[e]) return false; |
---|
[2375] | 612 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
| 613 | { |
---|
[2526] | 614 | Value dif=-(*_delta)[n]; |
---|
| 615 | for(InEdgeIt e(_g,n);e!=INVALID;++e) dif-=(*_flow)[e]; |
---|
| 616 | for(OutEdgeIt e(_g,n);e!=INVALID;++e) dif+=(*_flow)[e]; |
---|
[2375] | 617 | if(_tol.negative(dif)) return false; |
---|
| 618 | } |
---|
| 619 | return true; |
---|
[2526] | 620 | } |
---|
[2375] | 621 | |
---|
[2408] | 622 | ///Check whether or not the last execution provides a barrier |
---|
[2375] | 623 | |
---|
[2408] | 624 | ///Check whether or not the last execution provides a barrier |
---|
[2375] | 625 | ///\sa barrier() |
---|
| 626 | bool checkBarrier() |
---|
| 627 | { |
---|
[2526] | 628 | Value delta=0; |
---|
| 629 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
| 630 | if(barrier(n)) |
---|
| 631 | delta-=(*_delta)[n]; |
---|
| 632 | for(EdgeIt e(_g);e!=INVALID;++e) |
---|
| 633 | { |
---|
| 634 | Node s=_g.source(e); |
---|
| 635 | Node t=_g.target(e); |
---|
| 636 | if(barrier(s)&&!barrier(t)) delta+=(*_up)[e]; |
---|
| 637 | else if(barrier(t)&&!barrier(s)) delta-=(*_lo)[e]; |
---|
| 638 | } |
---|
| 639 | return _tol.negative(delta); |
---|
[2375] | 640 | } |
---|
| 641 | |
---|
[2526] | 642 | /// @} |
---|
[2375] | 643 | |
---|
| 644 | }; |
---|
| 645 | |
---|
| 646 | } |
---|
| 647 | |
---|
| 648 | #endif |
---|