[2382] | 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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[2553] | 5 | * Copyright (C) 2003-2008 |
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[2382] | 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_STEINER_H |
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| 20 | #define LEMON_STEINER_H |
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| 21 | |
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| 22 | ///\ingroup approx |
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| 23 | ///\file |
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| 24 | ///\brief Algorithm for the 2-approximation of Steiner Tree problem. |
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| 25 | /// |
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| 26 | |
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| 27 | #include <lemon/smart_graph.h> |
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| 28 | #include <lemon/graph_utils.h> |
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| 29 | #include <lemon/error.h> |
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| 30 | |
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| 31 | #include <lemon/ugraph_adaptor.h> |
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| 32 | #include <lemon/maps.h> |
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| 33 | |
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| 34 | #include <lemon/dijkstra.h> |
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| 35 | #include <lemon/prim.h> |
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| 36 | |
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| 37 | |
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| 38 | namespace lemon { |
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| 39 | |
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| 40 | /// \ingroup approx |
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| 41 | |
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| 42 | /// \brief Algorithm for the 2-approximation of Steiner Tree problem |
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| 43 | /// |
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| 44 | /// The Steiner-tree problem is the next: Given a connected |
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| 45 | /// undirected graph, a cost function on the edges and a subset of |
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| 46 | /// the nodes. Construct a tree with minimum cost which covers the |
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| 47 | /// given subset of the nodes. The problem is NP-hard moreover |
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| 48 | /// it is APX-complete too. |
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| 49 | /// |
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| 50 | /// Mehlhorn's approximation algorithm is implemented in this class, |
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| 51 | /// which gives a 2-approximation for the Steiner-tree problem. The |
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| 52 | /// algorithm's time complexity is O(nlog(n)+e). |
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| 53 | template <typename UGraph, |
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| 54 | typename CostMap = typename UGraph:: template UEdgeMap<double> > |
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| 55 | class SteinerTree { |
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| 56 | public: |
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| 57 | |
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[2510] | 58 | UGRAPH_TYPEDEFS(typename UGraph); |
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[2382] | 59 | |
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| 60 | typedef typename CostMap::Value Value; |
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| 61 | |
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| 62 | private: |
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| 63 | |
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| 64 | class CompMap { |
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| 65 | public: |
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| 66 | typedef Node Key; |
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| 67 | typedef Edge Value; |
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| 68 | |
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| 69 | private: |
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| 70 | const UGraph& _graph; |
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| 71 | typename UGraph::template NodeMap<int> _comp; |
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| 72 | |
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| 73 | public: |
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| 74 | CompMap(const UGraph& graph) : _graph(graph), _comp(graph) {} |
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| 75 | |
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| 76 | void set(const Node& node, const Edge& edge) { |
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| 77 | if (edge != INVALID) { |
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| 78 | _comp.set(node, _comp[_graph.source(edge)]); |
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| 79 | } else { |
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| 80 | _comp.set(node, -1); |
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| 81 | } |
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| 82 | } |
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| 83 | |
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| 84 | int comp(const Node& node) const { return _comp[node]; } |
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| 85 | void comp(const Node& node, int value) { _comp.set(node, value); } |
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| 86 | }; |
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| 87 | |
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| 88 | typedef typename UGraph::template NodeMap<Edge> PredMap; |
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| 89 | |
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| 90 | typedef ForkWriteMap<PredMap, CompMap> ForkedMap; |
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| 91 | |
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| 92 | |
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| 93 | struct External { |
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| 94 | int source, target; |
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| 95 | UEdge uedge; |
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| 96 | Value value; |
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| 97 | |
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| 98 | External(int s, int t, const UEdge& e, const Value& v) |
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| 99 | : source(s), target(t), uedge(e), value(v) {} |
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| 100 | }; |
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| 101 | |
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| 102 | struct ExternalLess { |
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| 103 | bool operator()(const External& left, const External& right) const { |
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| 104 | return (left.source < right.source) || |
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| 105 | (left.source == right.source && left.target < right.target); |
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| 106 | } |
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| 107 | }; |
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| 108 | |
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| 109 | |
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| 110 | typedef typename UGraph::template NodeMap<bool> FilterMap; |
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| 111 | |
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| 112 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
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| 113 | |
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| 114 | const UGraph& _graph; |
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| 115 | const CostMap& _cost; |
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| 116 | |
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| 117 | typename Dijkstra<UGraph, CostMap>:: |
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| 118 | template DefPredMap<ForkedMap>::Create _dijkstra; |
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| 119 | |
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| 120 | PredMap* _pred; |
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| 121 | CompMap* _comp; |
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| 122 | ForkedMap* _forked; |
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| 123 | |
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| 124 | int _terminal_num; |
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| 125 | |
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| 126 | FilterMap *_filter; |
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| 127 | TreeMap *_tree; |
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| 128 | |
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[2399] | 129 | Value _value; |
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| 130 | |
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[2382] | 131 | public: |
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| 132 | |
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| 133 | /// \brief Constructor |
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| 134 | |
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| 135 | /// Constructor |
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| 136 | /// |
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| 137 | SteinerTree(const UGraph &graph, const CostMap &cost) |
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| 138 | : _graph(graph), _cost(cost), _dijkstra(graph, _cost), |
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| 139 | _pred(0), _comp(0), _forked(0), _filter(0), _tree(0) {} |
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| 140 | |
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| 141 | /// \brief Initializes the internal data structures. |
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| 142 | /// |
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| 143 | /// Initializes the internal data structures. |
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| 144 | void init() { |
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| 145 | if (!_pred) _pred = new PredMap(_graph); |
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| 146 | if (!_comp) _comp = new CompMap(_graph); |
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| 147 | if (!_forked) _forked = new ForkedMap(*_pred, *_comp); |
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| 148 | if (!_filter) _filter = new FilterMap(_graph); |
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| 149 | if (!_tree) _tree = new TreeMap(_graph); |
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| 150 | _dijkstra.predMap(*_forked); |
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| 151 | _dijkstra.init(); |
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| 152 | _terminal_num = 0; |
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| 153 | for (NodeIt it(_graph); it != INVALID; ++it) { |
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| 154 | _filter->set(it, false); |
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| 155 | } |
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| 156 | } |
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| 157 | |
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| 158 | /// \brief Adds a new terminal node. |
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| 159 | /// |
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| 160 | /// Adds a new terminal node to the Steiner-tree problem. |
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| 161 | void addTerminal(const Node& node) { |
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| 162 | if (!_dijkstra.reached(node)) { |
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| 163 | _dijkstra.addSource(node); |
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| 164 | _comp->comp(node, _terminal_num); |
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| 165 | ++_terminal_num; |
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| 166 | } |
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| 167 | } |
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| 168 | |
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| 169 | /// \brief Executes the algorithm. |
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| 170 | /// |
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| 171 | /// Executes the algorithm. |
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| 172 | /// |
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| 173 | /// \pre init() must be called and at least some nodes should be |
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| 174 | /// added with addTerminal() before using this function. |
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| 175 | /// |
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| 176 | /// This method constructs an approximation of the Steiner-Tree. |
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| 177 | void start() { |
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| 178 | _dijkstra.start(); |
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| 179 | |
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| 180 | std::vector<External> externals; |
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| 181 | for (UEdgeIt it(_graph); it != INVALID; ++it) { |
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| 182 | Node s = _graph.source(it); |
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| 183 | Node t = _graph.target(it); |
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| 184 | if (_comp->comp(s) == _comp->comp(t)) continue; |
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| 185 | |
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| 186 | Value cost = _dijkstra.dist(s) + _dijkstra.dist(t) + _cost[it]; |
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| 187 | |
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| 188 | if (_comp->comp(s) < _comp->comp(t)) { |
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| 189 | externals.push_back(External(_comp->comp(s), _comp->comp(t), |
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| 190 | it, cost)); |
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| 191 | } else { |
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| 192 | externals.push_back(External(_comp->comp(t), _comp->comp(s), |
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| 193 | it, cost)); |
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| 194 | } |
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| 195 | } |
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| 196 | std::sort(externals.begin(), externals.end(), ExternalLess()); |
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| 197 | |
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| 198 | SmartUGraph aux_graph; |
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| 199 | std::vector<SmartUGraph::Node> aux_nodes; |
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| 200 | |
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| 201 | for (int i = 0; i < _terminal_num; ++i) { |
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| 202 | aux_nodes.push_back(aux_graph.addNode()); |
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| 203 | } |
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| 204 | |
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| 205 | SmartUGraph::UEdgeMap<Value> aux_cost(aux_graph); |
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| 206 | SmartUGraph::UEdgeMap<UEdge> cross(aux_graph); |
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| 207 | { |
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| 208 | int i = 0; |
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[2386] | 209 | while (i < int(externals.size())) { |
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[2382] | 210 | int sn = externals[i].source; |
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| 211 | int tn = externals[i].target; |
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| 212 | Value ev = externals[i].value; |
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| 213 | UEdge ee = externals[i].uedge; |
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| 214 | ++i; |
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[2386] | 215 | while (i < int(externals.size()) && |
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[2382] | 216 | sn == externals[i].source && tn == externals[i].target) { |
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| 217 | if (externals[i].value < ev) { |
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| 218 | ev = externals[i].value; |
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| 219 | ee = externals[i].uedge; |
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| 220 | } |
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| 221 | ++i; |
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| 222 | } |
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| 223 | SmartUGraph::UEdge ne = |
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| 224 | aux_graph.addEdge(aux_nodes[sn], aux_nodes[tn]); |
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| 225 | aux_cost.set(ne, ev); |
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| 226 | cross.set(ne, ee); |
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| 227 | } |
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| 228 | } |
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| 229 | |
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| 230 | std::vector<SmartUGraph::UEdge> aux_tree_edges; |
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| 231 | BackInserterBoolMap<std::vector<SmartUGraph::UEdge> > |
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| 232 | aux_tree_map(aux_tree_edges); |
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| 233 | prim(aux_graph, aux_cost, aux_tree_map); |
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| 234 | |
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| 235 | for (std::vector<SmartUGraph::UEdge>::iterator |
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| 236 | it = aux_tree_edges.begin(); it != aux_tree_edges.end(); ++it) { |
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| 237 | Node node; |
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| 238 | node = _graph.source(cross[*it]); |
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| 239 | while (node != INVALID && !(*_filter)[node]) { |
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| 240 | _filter->set(node, true); |
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| 241 | node = (*_pred)[node] != INVALID ? |
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| 242 | _graph.source((*_pred)[node]) : INVALID; |
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| 243 | } |
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| 244 | node = _graph.target(cross[*it]); |
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| 245 | while (node != INVALID && !(*_filter)[node]) { |
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| 246 | _filter->set(node, true); |
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| 247 | node = (*_pred)[node] != INVALID ? |
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| 248 | _graph.source((*_pred)[node]) : INVALID; |
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| 249 | } |
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| 250 | } |
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| 251 | |
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[2399] | 252 | _value = prim(nodeSubUGraphAdaptor(_graph, *_filter), _cost, *_tree); |
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[2382] | 253 | |
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| 254 | } |
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| 255 | |
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| 256 | /// \brief Checks if an edge is in the Steiner-tree or not. |
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| 257 | /// |
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| 258 | /// Checks if an edge is in the Steiner-tree or not. |
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| 259 | /// \param e is the edge that will be checked |
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| 260 | /// \return \c true if e is in the Steiner-tree, \c false otherwise |
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| 261 | bool tree(UEdge e){ |
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| 262 | return (*_tree)[e]; |
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| 263 | } |
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| 264 | |
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| 265 | /// \brief Checks if the node is in the Steiner-tree or not. |
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| 266 | /// |
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| 267 | /// Checks if a node is in the Steiner-tree or not. |
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| 268 | /// \param n is the node that will be checked |
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| 269 | /// \return \c true if n is in the Steiner-tree, \c false otherwise |
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| 270 | bool tree(Node n){ |
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| 271 | return (*_filter)[n]; |
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| 272 | } |
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[2399] | 273 | |
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| 274 | /// \brief Checks if the node is a Steiner-node. |
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| 275 | /// |
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| 276 | /// Checks if the node is a Steiner-node (i.e. a tree node but |
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| 277 | /// not terminal). |
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| 278 | /// \param n is the node that will be checked |
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| 279 | /// \return \c true if n is a Steiner-node, \c false otherwise |
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| 280 | bool steiner(Node n){ |
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| 281 | return (*_filter)[n] && (*_pred)[n] != INVALID; |
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| 282 | } |
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| 283 | |
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| 284 | /// \brief Checks if the node is a terminal. |
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| 285 | /// |
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| 286 | /// Checks if the node is a terminal. |
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| 287 | /// \param n is the node that will be checked |
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| 288 | /// \return \c true if n is a terminal, \c false otherwise |
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| 289 | bool terminal(Node n){ |
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| 290 | return _dijkstra.reached(n) && (*_pred)[n] == INVALID; |
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| 291 | } |
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[2382] | 292 | |
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[2399] | 293 | /// \brief The total cost of the tree |
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| 294 | /// |
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| 295 | /// The total cost of the constructed tree. The calculated value does |
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| 296 | /// not exceed the double of the optimal value. |
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| 297 | Value treeValue() const { |
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| 298 | return _value; |
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| 299 | } |
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| 300 | |
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[2382] | 301 | }; |
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| 302 | |
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| 303 | } //END OF NAMESPACE LEMON |
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| 304 | |
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| 305 | #endif |
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