[2514] | 1 | /* -*- C++ -*- |
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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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| 5 | * Copyright (C) 2003-2007 |
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| 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_DINITZ_SLEATOR_TARJAN_H |
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| 20 | #define LEMON_DINITZ_SLEATOR_TARJAN_H |
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| 21 | |
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| 22 | /// \file |
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| 23 | /// \ingroup max_flow |
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| 24 | /// \brief Implementation the dynamic tree data structure of Sleator |
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| 25 | /// and Tarjan. |
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| 26 | |
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| 27 | #include <lemon/graph_utils.h> |
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| 28 | #include <lemon/tolerance.h> |
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| 29 | #include <lemon/dynamic_tree.h> |
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| 30 | |
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| 31 | #include <vector> |
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| 32 | #include <limits> |
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| 33 | #include <fstream> |
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| 34 | |
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| 35 | |
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| 36 | namespace lemon { |
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| 37 | |
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| 38 | /// \brief Default traits class of DinitzSleatorTarjan class. |
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| 39 | /// |
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| 40 | /// Default traits class of DinitzSleatorTarjan class. |
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| 41 | /// \param _Graph Graph type. |
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| 42 | /// \param _CapacityMap Type of capacity map. |
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| 43 | template <typename _Graph, typename _CapacityMap> |
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| 44 | struct DinitzSleatorTarjanDefaultTraits { |
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| 45 | |
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| 46 | /// \brief The graph type the algorithm runs on. |
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| 47 | typedef _Graph Graph; |
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| 48 | |
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| 49 | /// \brief The type of the map that stores the edge capacities. |
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| 50 | /// |
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| 51 | /// The type of the map that stores the edge capacities. |
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| 52 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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| 53 | typedef _CapacityMap CapacityMap; |
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| 54 | |
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| 55 | /// \brief The type of the length of the edges. |
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| 56 | typedef typename CapacityMap::Value Value; |
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| 57 | |
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| 58 | /// \brief The map type that stores the flow values. |
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| 59 | /// |
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| 60 | /// The map type that stores the flow values. |
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| 61 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
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| 62 | typedef typename Graph::template EdgeMap<Value> FlowMap; |
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| 63 | |
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| 64 | /// \brief Instantiates a FlowMap. |
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| 65 | /// |
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| 66 | /// This function instantiates a \ref FlowMap. |
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| 67 | /// \param graph The graph, to which we would like to define the flow map. |
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| 68 | static FlowMap* createFlowMap(const Graph& graph) { |
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| 69 | return new FlowMap(graph); |
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| 70 | } |
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| 71 | |
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| 72 | /// \brief The tolerance used by the algorithm |
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| 73 | /// |
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| 74 | /// The tolerance used by the algorithm to handle inexact computation. |
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| 75 | typedef Tolerance<Value> Tolerance; |
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| 76 | |
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| 77 | }; |
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| 78 | |
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| 79 | /// \ingroup max_flow |
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| 80 | /// |
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| 81 | /// \brief Dinitz-Sleator-Tarjan algorithms class. |
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| 82 | /// |
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| 83 | /// This class provides an implementation of the \e |
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| 84 | /// Dinitz-Sleator-Tarjan \e algorithm producing a flow of maximum |
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| 85 | /// value in a directed graph. The DinitzSleatorTarjan algorithm is |
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| 86 | /// the fastest known max flow algorithms wich using blocking |
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| 87 | /// flow. It is an improvement of the Dinitz algorithm by using the |
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| 88 | /// \ref DynamicTree "dynamic tree" data structure of Sleator and |
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| 89 | /// Tarjan. |
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| 90 | /// |
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| 91 | /// This blocking flow algorithms builds a layered graph according |
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| 92 | /// to \ref Bfs "breadth-first search" distance from the target node |
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| 93 | /// in the reversed residual graph. The layered graph contains each |
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| 94 | /// residual edge which steps one level down. After that the |
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| 95 | /// algorithm constructs a blocking flow on the layered graph and |
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| 96 | /// augments the overall flow with it. The number of the levels in |
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| 97 | /// the layered graph is strictly increasing in each augmenting |
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| 98 | /// phase therefore the number of the augmentings is at most |
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| 99 | /// \f$n-1\f$. The length of each phase is at most |
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| 100 | /// \f$O(m\log(n))\f$, that the overall time complexity is |
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| 101 | /// \f$O(nm\log(n))\f$. |
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| 102 | /// |
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| 103 | /// \param _Graph The directed graph type the algorithm runs on. |
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| 104 | /// \param _CapacityMap The capacity map type. |
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| 105 | /// \param _Traits Traits class to set various data types used by |
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| 106 | /// the algorithm. The default traits class is \ref |
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| 107 | /// DinitzSleatorTarjanDefaultTraits. See \ref |
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| 108 | /// DinitzSleatorTarjanDefaultTraits for the documentation of a |
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| 109 | /// Dinitz-Sleator-Tarjan traits class. |
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| 110 | /// |
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| 111 | /// \author Tamas Hamori and Balazs Dezso |
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| 112 | #ifdef DOXYGEN |
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| 113 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
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| 114 | #else |
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| 115 | template <typename _Graph, |
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| 116 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
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| 117 | typename _Traits = |
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| 118 | DinitzSleatorTarjanDefaultTraits<_Graph, _CapacityMap> > |
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| 119 | #endif |
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| 120 | class DinitzSleatorTarjan { |
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| 121 | public: |
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| 122 | |
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| 123 | typedef _Traits Traits; |
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| 124 | typedef typename Traits::Graph Graph; |
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| 125 | typedef typename Traits::CapacityMap CapacityMap; |
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| 126 | typedef typename Traits::Value Value; |
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| 127 | |
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| 128 | typedef typename Traits::FlowMap FlowMap; |
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| 129 | typedef typename Traits::Tolerance Tolerance; |
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| 130 | |
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| 131 | |
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| 132 | private: |
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| 133 | |
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| 134 | GRAPH_TYPEDEFS(typename Graph); |
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| 135 | |
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| 136 | |
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| 137 | typedef typename Graph::template NodeMap<int> LevelMap; |
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| 138 | typedef typename Graph::template NodeMap<int> IntNodeMap; |
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| 139 | typedef typename Graph::template NodeMap<Edge> EdgeNodeMap; |
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| 140 | typedef DynamicTree<Value, IntNodeMap, Tolerance, false> DynTree; |
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| 141 | |
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| 142 | private: |
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| 143 | |
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| 144 | const Graph& _graph; |
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| 145 | const CapacityMap* _capacity; |
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| 146 | |
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| 147 | Node _source, _target; |
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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 | IntNodeMap* _level; |
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| 153 | EdgeNodeMap* _dt_edges; |
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| 154 | |
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| 155 | IntNodeMap* _dt_index; |
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| 156 | DynTree* _dt; |
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| 157 | |
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[2519] | 158 | std::vector<Node> _queue; |
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| 159 | |
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[2514] | 160 | Tolerance _tolerance; |
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| 161 | |
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| 162 | Value _flow_value; |
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| 163 | Value _max_value; |
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| 164 | |
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| 165 | |
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| 166 | public: |
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| 167 | |
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| 168 | typedef DinitzSleatorTarjan Create; |
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| 169 | |
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| 170 | ///\name Named template parameters |
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| 171 | |
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| 172 | ///@{ |
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| 173 | |
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| 174 | template <typename _FlowMap> |
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| 175 | struct DefFlowMapTraits : public Traits { |
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| 176 | typedef _FlowMap FlowMap; |
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| 177 | static FlowMap *createFlowMap(const Graph&) { |
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| 178 | throw UninitializedParameter(); |
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| 179 | } |
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| 180 | }; |
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| 181 | |
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| 182 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 183 | /// FlowMap type |
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| 184 | /// |
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| 185 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
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| 186 | /// type |
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| 187 | template <typename _FlowMap> |
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| 188 | struct DefFlowMap |
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| 189 | : public DinitzSleatorTarjan<Graph, CapacityMap, |
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| 190 | DefFlowMapTraits<_FlowMap> > { |
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| 191 | typedef DinitzSleatorTarjan<Graph, CapacityMap, |
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| 192 | DefFlowMapTraits<_FlowMap> > Create; |
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| 193 | }; |
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| 194 | |
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| 195 | template <typename _Elevator> |
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| 196 | struct DefElevatorTraits : public Traits { |
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| 197 | typedef _Elevator Elevator; |
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| 198 | static Elevator *createElevator(const Graph&, int) { |
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| 199 | throw UninitializedParameter(); |
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| 200 | } |
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| 201 | }; |
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| 202 | |
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| 203 | /// @} |
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| 204 | |
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| 205 | /// \brief \ref Exception for the case when the source equals the target. |
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| 206 | /// |
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| 207 | /// \ref Exception for the case when the source equals the target. |
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| 208 | /// |
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| 209 | class InvalidArgument : public lemon::LogicError { |
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| 210 | public: |
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| 211 | virtual const char* what() const throw() { |
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| 212 | return "lemon::DinitzSleatorTarjan::InvalidArgument"; |
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| 213 | } |
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| 214 | }; |
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| 215 | |
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[2527] | 216 | protected: |
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| 217 | |
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| 218 | DinitzSleatorTarjan() {} |
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| 219 | |
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| 220 | public: |
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| 221 | |
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[2514] | 222 | /// \brief The constructor of the class. |
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| 223 | /// |
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| 224 | /// The constructor of the class. |
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| 225 | /// \param graph The directed graph the algorithm runs on. |
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| 226 | /// \param capacity The capacity of the edges. |
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| 227 | /// \param source The source node. |
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| 228 | /// \param target The target node. |
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| 229 | DinitzSleatorTarjan(const Graph& graph, const CapacityMap& capacity, |
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| 230 | Node source, Node target) |
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| 231 | : _graph(graph), _capacity(&capacity), |
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| 232 | _source(source), _target(target), |
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| 233 | _flow(0), _local_flow(false), |
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| 234 | _level(0), _dt_edges(0), |
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[2519] | 235 | _dt_index(0), _dt(0), _queue(), |
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[2514] | 236 | _tolerance(), _flow_value(), _max_value() |
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| 237 | { |
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| 238 | if (_source == _target) { |
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| 239 | throw InvalidArgument(); |
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| 240 | } |
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| 241 | } |
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| 242 | |
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| 243 | /// \brief Destrcutor. |
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| 244 | /// |
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| 245 | /// Destructor. |
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| 246 | ~DinitzSleatorTarjan() { |
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| 247 | destroyStructures(); |
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| 248 | } |
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| 249 | |
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| 250 | /// \brief Sets the capacity map. |
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| 251 | /// |
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| 252 | /// Sets the capacity map. |
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| 253 | /// \return \c (*this) |
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| 254 | DinitzSleatorTarjan& capacityMap(const CapacityMap& map) { |
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| 255 | _capacity = ↦ |
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| 256 | return *this; |
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| 257 | } |
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| 258 | |
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| 259 | /// \brief Sets the flow map. |
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| 260 | /// |
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| 261 | /// Sets the flow map. |
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| 262 | /// \return \c (*this) |
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| 263 | DinitzSleatorTarjan& flowMap(FlowMap& map) { |
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| 264 | if (_local_flow) { |
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| 265 | delete _flow; |
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| 266 | _local_flow = false; |
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| 267 | } |
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| 268 | _flow = ↦ |
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| 269 | return *this; |
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| 270 | } |
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| 271 | |
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| 272 | /// \brief Returns the flow map. |
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| 273 | /// |
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| 274 | /// \return The flow map. |
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| 275 | const FlowMap& flowMap() { |
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| 276 | return *_flow; |
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| 277 | } |
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| 278 | |
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| 279 | /// \brief Sets the source node. |
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| 280 | /// |
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| 281 | /// Sets the source node. |
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| 282 | /// \return \c (*this) |
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| 283 | DinitzSleatorTarjan& source(const Node& node) { |
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| 284 | _source = node; |
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| 285 | return *this; |
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| 286 | } |
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| 287 | |
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| 288 | /// \brief Sets the target node. |
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| 289 | /// |
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| 290 | /// Sets the target node. |
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| 291 | /// \return \c (*this) |
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| 292 | DinitzSleatorTarjan& target(const Node& node) { |
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| 293 | _target = node; |
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| 294 | return *this; |
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| 295 | } |
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| 296 | |
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| 297 | /// \brief Sets the tolerance used by algorithm. |
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| 298 | /// |
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| 299 | /// Sets the tolerance used by algorithm. |
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| 300 | DinitzSleatorTarjan& tolerance(const Tolerance& tolerance) const { |
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| 301 | _tolerance = tolerance; |
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| 302 | if (_dt) { |
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| 303 | _dt.tolerance(_tolerance); |
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| 304 | } |
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| 305 | return *this; |
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| 306 | } |
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| 307 | |
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| 308 | /// \brief Returns the tolerance used by algorithm. |
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| 309 | /// |
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| 310 | /// Returns the tolerance used by algorithm. |
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| 311 | const Tolerance& tolerance() const { |
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| 312 | return tolerance; |
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| 313 | } |
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| 314 | |
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| 315 | private: |
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| 316 | |
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| 317 | void createStructures() { |
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| 318 | if (!_flow) { |
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| 319 | _flow = Traits::createFlowMap(_graph); |
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| 320 | _local_flow = true; |
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| 321 | } |
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| 322 | if (!_level) { |
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| 323 | _level = new LevelMap(_graph); |
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| 324 | } |
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| 325 | if (!_dt_index && !_dt) { |
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| 326 | _dt_index = new IntNodeMap(_graph); |
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| 327 | _dt = new DynTree(*_dt_index, _tolerance); |
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| 328 | } |
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| 329 | if (!_dt_edges) { |
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| 330 | _dt_edges = new EdgeNodeMap(_graph); |
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| 331 | } |
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[2519] | 332 | _queue.resize(countNodes(_graph)); |
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[2514] | 333 | _max_value = _dt->maxValue(); |
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| 334 | } |
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| 335 | |
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| 336 | void destroyStructures() { |
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| 337 | if (_local_flow) { |
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| 338 | delete _flow; |
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| 339 | } |
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| 340 | if (_level) { |
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| 341 | delete _level; |
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| 342 | } |
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| 343 | if (_dt) { |
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| 344 | delete _dt; |
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| 345 | } |
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| 346 | if (_dt_index) { |
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| 347 | delete _dt_index; |
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| 348 | } |
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| 349 | if (_dt_edges) { |
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| 350 | delete _dt_edges; |
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| 351 | } |
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| 352 | } |
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| 353 | |
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| 354 | bool createLayeredGraph() { |
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| 355 | |
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| 356 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 357 | _level->set(n, -2); |
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| 358 | } |
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| 359 | |
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| 360 | int level = 0; |
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| 361 | |
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[2519] | 362 | _queue[0] = _target; |
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[2514] | 363 | _level->set(_target, level); |
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[2519] | 364 | |
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| 365 | int first = 0, last = 1, limit = 0; |
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[2514] | 366 | |
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[2519] | 367 | while (first != last && (*_level)[_source] == -2) { |
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| 368 | if (first == limit) { |
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| 369 | limit = last; |
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| 370 | ++level; |
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| 371 | } |
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[2514] | 372 | |
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[2519] | 373 | Node n = _queue[first++]; |
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[2514] | 374 | |
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[2519] | 375 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
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| 376 | Node v = _graph.target(e); |
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| 377 | if ((*_level)[v] != -2) continue; |
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| 378 | Value rem = (*_flow)[e]; |
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| 379 | if (!_tolerance.positive(rem)) continue; |
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| 380 | _level->set(v, level); |
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| 381 | _queue[last++] = v; |
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[2514] | 382 | } |
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[2519] | 383 | |
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| 384 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
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| 385 | Node v = _graph.source(e); |
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| 386 | if ((*_level)[v] != -2) continue; |
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| 387 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
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| 388 | if (!_tolerance.positive(rem)) continue; |
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| 389 | _level->set(v, level); |
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| 390 | _queue[last++] = v; |
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| 391 | } |
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[2514] | 392 | } |
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| 393 | return (*_level)[_source] != -2; |
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| 394 | } |
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| 395 | |
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| 396 | void initEdges() { |
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| 397 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 398 | _graph.firstOut((*_dt_edges)[n], n); |
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| 399 | } |
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| 400 | } |
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| 401 | |
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| 402 | |
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| 403 | void augmentPath() { |
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| 404 | Value rem; |
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| 405 | Node n = _dt->findCost(_source, rem); |
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| 406 | _flow_value += rem; |
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| 407 | _dt->addCost(_source, - rem); |
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| 408 | |
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| 409 | _dt->cut(n); |
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| 410 | _dt->addCost(n, _max_value); |
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| 411 | |
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| 412 | Edge e = (*_dt_edges)[n]; |
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| 413 | if (_graph.source(e) == n) { |
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| 414 | _flow->set(e, (*_capacity)[e]); |
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| 415 | |
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| 416 | _graph.nextOut(e); |
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| 417 | if (e == INVALID) { |
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| 418 | _graph.firstIn(e, n); |
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| 419 | } |
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| 420 | } else { |
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| 421 | _flow->set(e, 0); |
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| 422 | _graph.nextIn(e); |
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| 423 | } |
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| 424 | _dt_edges->set(n, e); |
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| 425 | |
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| 426 | } |
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| 427 | |
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| 428 | bool advance(Node n) { |
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| 429 | Edge e = (*_dt_edges)[n]; |
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| 430 | if (e == INVALID) return false; |
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| 431 | |
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| 432 | Node u; |
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| 433 | Value rem; |
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| 434 | if (_graph.source(e) == n) { |
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| 435 | u = _graph.target(e); |
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| 436 | while ((*_level)[n] != (*_level)[u] + 1 || |
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| 437 | !_tolerance.positive((*_capacity)[e] - (*_flow)[e])) { |
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| 438 | _graph.nextOut(e); |
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| 439 | if (e == INVALID) break; |
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| 440 | u = _graph.target(e); |
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| 441 | } |
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| 442 | if (e != INVALID) { |
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| 443 | rem = (*_capacity)[e] - (*_flow)[e]; |
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| 444 | } else { |
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| 445 | _graph.firstIn(e, n); |
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| 446 | if (e == INVALID) { |
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| 447 | _dt_edges->set(n, INVALID); |
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| 448 | return false; |
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| 449 | } |
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| 450 | u = _graph.source(e); |
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| 451 | while ((*_level)[n] != (*_level)[u] + 1 || |
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| 452 | !_tolerance.positive((*_flow)[e])) { |
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| 453 | _graph.nextIn(e); |
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| 454 | if (e == INVALID) { |
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| 455 | _dt_edges->set(n, INVALID); |
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| 456 | return false; |
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| 457 | } |
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| 458 | u = _graph.source(e); |
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| 459 | } |
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| 460 | rem = (*_flow)[e]; |
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| 461 | } |
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| 462 | } else { |
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| 463 | u = _graph.source(e); |
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| 464 | while ((*_level)[n] != (*_level)[u] + 1 || |
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| 465 | !_tolerance.positive((*_flow)[e])) { |
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| 466 | _graph.nextIn(e); |
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| 467 | if (e == INVALID) { |
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| 468 | _dt_edges->set(n, INVALID); |
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| 469 | return false; |
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| 470 | } |
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| 471 | u = _graph.source(e); |
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| 472 | } |
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| 473 | rem = (*_flow)[e]; |
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| 474 | } |
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| 475 | |
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| 476 | _dt->addCost(n, - std::numeric_limits<Value>::max()); |
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| 477 | _dt->addCost(n, rem); |
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| 478 | _dt->link(n, u); |
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| 479 | _dt_edges->set(n, e); |
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| 480 | return true; |
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| 481 | } |
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| 482 | |
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| 483 | void retreat(Node n) { |
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| 484 | _level->set(n, -1); |
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| 485 | |
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| 486 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
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| 487 | Node u = _graph.target(e); |
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| 488 | if ((*_dt_edges)[u] == e && _dt->findRoot(u) == n) { |
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| 489 | Value rem; |
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| 490 | _dt->findCost(u, rem); |
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| 491 | _flow->set(e, rem); |
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| 492 | _dt->cut(u); |
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| 493 | _dt->addCost(u, - rem); |
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| 494 | _dt->addCost(u, _max_value); |
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| 495 | } |
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| 496 | } |
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| 497 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
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| 498 | Node u = _graph.source(e); |
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| 499 | if ((*_dt_edges)[u] == e && _dt->findRoot(u) == n) { |
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| 500 | Value rem; |
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| 501 | _dt->findCost(u, rem); |
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| 502 | _flow->set(e, (*_capacity)[e] - rem); |
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| 503 | _dt->cut(u); |
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| 504 | _dt->addCost(u, - rem); |
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| 505 | _dt->addCost(u, _max_value); |
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| 506 | } |
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| 507 | } |
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| 508 | } |
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| 509 | |
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| 510 | void extractTrees() { |
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| 511 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 512 | |
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| 513 | Node w = _dt->findRoot(n); |
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| 514 | |
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| 515 | while (w != n) { |
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| 516 | |
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| 517 | Value rem; |
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| 518 | Node u = _dt->findCost(n, rem); |
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| 519 | |
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| 520 | _dt->cut(u); |
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| 521 | _dt->addCost(u, - rem); |
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| 522 | _dt->addCost(u, _max_value); |
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| 523 | |
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| 524 | Edge e = (*_dt_edges)[u]; |
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| 525 | _dt_edges->set(u, INVALID); |
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| 526 | |
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| 527 | if (u == _graph.source(e)) { |
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| 528 | _flow->set(e, (*_capacity)[e] - rem); |
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| 529 | } else { |
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| 530 | _flow->set(e, rem); |
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| 531 | } |
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| 532 | |
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| 533 | w = _dt->findRoot(n); |
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| 534 | } |
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| 535 | } |
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| 536 | } |
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| 537 | |
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| 538 | |
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| 539 | public: |
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| 540 | |
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| 541 | /// \name Execution control The simplest way to execute the |
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| 542 | /// algorithm is to use the \c run() member functions. |
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| 543 | /// \n |
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| 544 | /// If you need more control on initial solution or |
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| 545 | /// execution then you have to call one \ref init() function and then |
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| 546 | /// the start() or multiple times the \c augment() member function. |
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| 547 | |
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| 548 | ///@{ |
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| 549 | |
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| 550 | /// \brief Initializes the algorithm |
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| 551 | /// |
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| 552 | /// It sets the flow to empty flow. |
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| 553 | void init() { |
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| 554 | createStructures(); |
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| 555 | |
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| 556 | _dt->clear(); |
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| 557 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 558 | _dt->makeTree(n); |
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| 559 | _dt->addCost(n, _max_value); |
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| 560 | } |
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| 561 | |
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| 562 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
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| 563 | _flow->set(it, 0); |
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| 564 | } |
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| 565 | _flow_value = 0; |
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| 566 | } |
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| 567 | |
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| 568 | /// \brief Initializes the algorithm |
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| 569 | /// |
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| 570 | /// Initializes the flow to the \c flowMap. The \c flowMap should |
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| 571 | /// contain a feasible flow, ie. in each node excluding the source |
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| 572 | /// and the target the incoming flow should be equal to the |
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| 573 | /// outgoing flow. |
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| 574 | template <typename FlowMap> |
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| 575 | void flowInit(const FlowMap& flowMap) { |
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| 576 | createStructures(); |
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| 577 | |
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| 578 | _dt->clear(); |
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| 579 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 580 | _dt->makeTree(n); |
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| 581 | _dt->addCost(n, _max_value); |
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| 582 | } |
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| 583 | |
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| 584 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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| 585 | _flow->set(e, flowMap[e]); |
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| 586 | } |
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| 587 | _flow_value = 0; |
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| 588 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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| 589 | _flow_value += (*_flow)[jt]; |
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| 590 | } |
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| 591 | for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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| 592 | _flow_value -= (*_flow)[jt]; |
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| 593 | } |
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| 594 | } |
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| 595 | |
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| 596 | /// \brief Initializes the algorithm |
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| 597 | /// |
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| 598 | /// Initializes the flow to the \c flowMap. The \c flowMap should |
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| 599 | /// contain a feasible flow, ie. in each node excluding the source |
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| 600 | /// and the target the incoming flow should be equal to the |
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| 601 | /// outgoing flow. |
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| 602 | /// \return %False when the given flowMap does not contain |
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| 603 | /// feasible flow. |
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| 604 | template <typename FlowMap> |
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| 605 | bool checkedFlowInit(const FlowMap& flowMap) { |
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| 606 | createStructures(); |
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| 607 | |
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| 608 | _dt->clear(); |
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| 609 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 610 | _dt->makeTree(n); |
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| 611 | _dt->addCost(n, _max_value); |
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| 612 | } |
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| 613 | |
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| 614 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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| 615 | _flow->set(e, flowMap[e]); |
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| 616 | } |
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| 617 | for (NodeIt it(_graph); it != INVALID; ++it) { |
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| 618 | if (it == _source || it == _target) continue; |
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| 619 | Value outFlow = 0; |
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| 620 | for (OutEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
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| 621 | outFlow += (*_flow)[jt]; |
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| 622 | } |
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| 623 | Value inFlow = 0; |
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| 624 | for (InEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
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| 625 | inFlow += (*_flow)[jt]; |
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| 626 | } |
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| 627 | if (_tolerance.different(outFlow, inFlow)) { |
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| 628 | return false; |
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| 629 | } |
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| 630 | } |
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| 631 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
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| 632 | if (_tolerance.less((*_flow)[it], 0)) return false; |
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| 633 | if (_tolerance.less((*_capacity)[it], (*_flow)[it])) return false; |
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| 634 | } |
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| 635 | _flow_value = 0; |
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| 636 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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| 637 | _flow_value += (*_flow)[jt]; |
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| 638 | } |
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| 639 | for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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| 640 | _flow_value -= (*_flow)[jt]; |
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| 641 | } |
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| 642 | return true; |
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| 643 | } |
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| 644 | |
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| 645 | /// \brief Executes the algorithm |
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| 646 | /// |
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| 647 | /// It runs augmenting phases by adding blocking flow until the |
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| 648 | /// optimal solution is reached. |
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| 649 | void start() { |
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| 650 | while (augment()); |
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| 651 | } |
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| 652 | |
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| 653 | /// \brief Augments the flow with a blocking flow on a layered |
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| 654 | /// graph. |
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| 655 | /// |
---|
| 656 | /// This function builds a layered graph and then find a blocking |
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| 657 | /// flow on this graph. The number of the levels in the layered |
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| 658 | /// graph is strictly increasing in each augmenting phase |
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| 659 | /// therefore the number of the augmentings is at most \f$ n-1 |
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| 660 | /// \f$. The length of each phase is at most \f$ O(m \log(n)) |
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| 661 | /// \f$, that the overall time complexity is \f$ O(nm \log(n)) \f$. |
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| 662 | /// \return %False when there is not residual path between the |
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| 663 | /// source and the target so the current flow is a feasible and |
---|
| 664 | /// optimal solution. |
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| 665 | bool augment() { |
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| 666 | Node n; |
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| 667 | |
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| 668 | if (createLayeredGraph()) { |
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| 669 | |
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| 670 | Timer bf_timer; |
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| 671 | initEdges(); |
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| 672 | |
---|
| 673 | n = _dt->findRoot(_source); |
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| 674 | while (true) { |
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| 675 | Edge e; |
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| 676 | if (n == _target) { |
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| 677 | augmentPath(); |
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| 678 | } else if (!advance(n)) { |
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| 679 | if (n != _source) { |
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| 680 | retreat(n); |
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| 681 | } else { |
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| 682 | break; |
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| 683 | } |
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| 684 | } |
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| 685 | n = _dt->findRoot(_source); |
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| 686 | } |
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| 687 | extractTrees(); |
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| 688 | |
---|
| 689 | return true; |
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| 690 | } else { |
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| 691 | return false; |
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| 692 | } |
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| 693 | } |
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| 694 | |
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| 695 | /// \brief runs the algorithm. |
---|
| 696 | /// |
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| 697 | /// It is just a shorthand for: |
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| 698 | /// |
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| 699 | ///\code |
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| 700 | /// ek.init(); |
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| 701 | /// ek.start(); |
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| 702 | ///\endcode |
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| 703 | void run() { |
---|
| 704 | init(); |
---|
| 705 | start(); |
---|
| 706 | } |
---|
| 707 | |
---|
| 708 | /// @} |
---|
| 709 | |
---|
[2522] | 710 | /// \name Query Functions |
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| 711 | /// The result of the Dinitz-Sleator-Tarjan algorithm can be |
---|
| 712 | /// obtained using these functions. |
---|
| 713 | /// \n |
---|
[2514] | 714 | /// Before the use of these functions, |
---|
| 715 | /// either run() or start() must be called. |
---|
| 716 | |
---|
| 717 | ///@{ |
---|
| 718 | |
---|
| 719 | /// \brief Returns the value of the maximum flow. |
---|
| 720 | /// |
---|
| 721 | /// Returns the value of the maximum flow by returning the excess |
---|
| 722 | /// of the target node \c t. This value equals to the value of |
---|
| 723 | /// the maximum flow already after the first phase. |
---|
| 724 | Value flowValue() const { |
---|
| 725 | return _flow_value; |
---|
| 726 | } |
---|
| 727 | |
---|
| 728 | |
---|
| 729 | /// \brief Returns the flow on the edge. |
---|
| 730 | /// |
---|
| 731 | /// Sets the \c flowMap to the flow on the edges. This method can |
---|
| 732 | /// be called after the second phase of algorithm. |
---|
| 733 | Value flow(const Edge& edge) const { |
---|
| 734 | return (*_flow)[edge]; |
---|
| 735 | } |
---|
| 736 | |
---|
| 737 | /// \brief Returns true when the node is on the source side of minimum cut. |
---|
| 738 | /// |
---|
| 739 | |
---|
| 740 | /// Returns true when the node is on the source side of minimum |
---|
| 741 | /// cut. This method can be called both after running \ref |
---|
| 742 | /// startFirstPhase() and \ref startSecondPhase(). |
---|
| 743 | bool minCut(const Node& node) const { |
---|
| 744 | return (*_level)[node] == -2; |
---|
| 745 | } |
---|
| 746 | |
---|
| 747 | /// \brief Returns a minimum value cut. |
---|
| 748 | /// |
---|
| 749 | /// Sets \c cut to the characteristic vector of a minimum value cut |
---|
| 750 | /// It simply calls the minMinCut member. |
---|
| 751 | /// \retval cut Write node bool map. |
---|
| 752 | template <typename CutMap> |
---|
| 753 | void minCutMap(CutMap& cutMap) const { |
---|
| 754 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 755 | cutMap.set(n, (*_level)[n] == -2); |
---|
| 756 | } |
---|
| 757 | cutMap.set(_source, true); |
---|
| 758 | } |
---|
| 759 | |
---|
| 760 | /// @} |
---|
| 761 | |
---|
| 762 | }; |
---|
| 763 | } |
---|
| 764 | |
---|
| 765 | #endif |
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