1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2006 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
9 | * Permission to use, modify and distribute this software is granted |
---|
10 | * provided that this copyright notice appears in all copies. For |
---|
11 | * precise terms see the accompanying LICENSE file. |
---|
12 | * |
---|
13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
14 | * express or implied, and with no claim as to its suitability for any |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | #ifndef LEMON_STEINER_H |
---|
20 | #define LEMON_STEINER_H |
---|
21 | |
---|
22 | ///\ingroup approx |
---|
23 | ///\file |
---|
24 | ///\brief Algorithm for the 2-approximation of Steiner Tree problem. |
---|
25 | /// |
---|
26 | |
---|
27 | #include <lemon/smart_graph.h> |
---|
28 | #include <lemon/graph_utils.h> |
---|
29 | #include <lemon/error.h> |
---|
30 | |
---|
31 | #include <lemon/ugraph_adaptor.h> |
---|
32 | #include <lemon/maps.h> |
---|
33 | |
---|
34 | #include <lemon/dijkstra.h> |
---|
35 | #include <lemon/prim.h> |
---|
36 | |
---|
37 | |
---|
38 | namespace lemon { |
---|
39 | |
---|
40 | /// \ingroup approx |
---|
41 | |
---|
42 | /// \brief Algorithm for the 2-approximation of Steiner Tree problem |
---|
43 | /// |
---|
44 | /// The Steiner-tree problem is the next: Given a connected |
---|
45 | /// undirected graph, a cost function on the edges and a subset of |
---|
46 | /// the nodes. Construct a tree with minimum cost which covers the |
---|
47 | /// given subset of the nodes. The problem is NP-hard moreover |
---|
48 | /// it is APX-complete too. |
---|
49 | /// |
---|
50 | /// Mehlhorn's approximation algorithm is implemented in this class, |
---|
51 | /// which gives a 2-approximation for the Steiner-tree problem. The |
---|
52 | /// algorithm's time complexity is O(nlog(n)+e). |
---|
53 | template <typename UGraph, |
---|
54 | typename CostMap = typename UGraph:: template UEdgeMap<double> > |
---|
55 | class SteinerTree { |
---|
56 | public: |
---|
57 | |
---|
58 | UGRAPH_TYPEDEFS(typename UGraph) |
---|
59 | |
---|
60 | typedef typename CostMap::Value Value; |
---|
61 | |
---|
62 | private: |
---|
63 | |
---|
64 | class CompMap { |
---|
65 | public: |
---|
66 | typedef Node Key; |
---|
67 | typedef Edge Value; |
---|
68 | |
---|
69 | private: |
---|
70 | const UGraph& _graph; |
---|
71 | typename UGraph::template NodeMap<int> _comp; |
---|
72 | |
---|
73 | public: |
---|
74 | CompMap(const UGraph& graph) : _graph(graph), _comp(graph) {} |
---|
75 | |
---|
76 | void set(const Node& node, const Edge& edge) { |
---|
77 | if (edge != INVALID) { |
---|
78 | _comp.set(node, _comp[_graph.source(edge)]); |
---|
79 | } else { |
---|
80 | _comp.set(node, -1); |
---|
81 | } |
---|
82 | } |
---|
83 | |
---|
84 | int comp(const Node& node) const { return _comp[node]; } |
---|
85 | void comp(const Node& node, int value) { _comp.set(node, value); } |
---|
86 | }; |
---|
87 | |
---|
88 | typedef typename UGraph::template NodeMap<Edge> PredMap; |
---|
89 | |
---|
90 | typedef ForkWriteMap<PredMap, CompMap> ForkedMap; |
---|
91 | |
---|
92 | |
---|
93 | struct External { |
---|
94 | int source, target; |
---|
95 | UEdge uedge; |
---|
96 | Value value; |
---|
97 | |
---|
98 | External(int s, int t, const UEdge& e, const Value& v) |
---|
99 | : source(s), target(t), uedge(e), value(v) {} |
---|
100 | }; |
---|
101 | |
---|
102 | struct ExternalLess { |
---|
103 | bool operator()(const External& left, const External& right) const { |
---|
104 | return (left.source < right.source) || |
---|
105 | (left.source == right.source && left.target < right.target); |
---|
106 | } |
---|
107 | }; |
---|
108 | |
---|
109 | |
---|
110 | typedef typename UGraph::template NodeMap<bool> FilterMap; |
---|
111 | |
---|
112 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
---|
113 | |
---|
114 | const UGraph& _graph; |
---|
115 | const CostMap& _cost; |
---|
116 | |
---|
117 | typename Dijkstra<UGraph, CostMap>:: |
---|
118 | template DefPredMap<ForkedMap>::Create _dijkstra; |
---|
119 | |
---|
120 | PredMap* _pred; |
---|
121 | CompMap* _comp; |
---|
122 | ForkedMap* _forked; |
---|
123 | |
---|
124 | int _terminal_num; |
---|
125 | |
---|
126 | FilterMap *_filter; |
---|
127 | TreeMap *_tree; |
---|
128 | |
---|
129 | public: |
---|
130 | |
---|
131 | /// \brief Constructor |
---|
132 | |
---|
133 | /// Constructor |
---|
134 | /// |
---|
135 | SteinerTree(const UGraph &graph, const CostMap &cost) |
---|
136 | : _graph(graph), _cost(cost), _dijkstra(graph, _cost), |
---|
137 | _pred(0), _comp(0), _forked(0), _filter(0), _tree(0) {} |
---|
138 | |
---|
139 | /// \brief Initializes the internal data structures. |
---|
140 | /// |
---|
141 | /// Initializes the internal data structures. |
---|
142 | void init() { |
---|
143 | if (!_pred) _pred = new PredMap(_graph); |
---|
144 | if (!_comp) _comp = new CompMap(_graph); |
---|
145 | if (!_forked) _forked = new ForkedMap(*_pred, *_comp); |
---|
146 | if (!_filter) _filter = new FilterMap(_graph); |
---|
147 | if (!_tree) _tree = new TreeMap(_graph); |
---|
148 | _dijkstra.predMap(*_forked); |
---|
149 | _dijkstra.init(); |
---|
150 | _terminal_num = 0; |
---|
151 | for (NodeIt it(_graph); it != INVALID; ++it) { |
---|
152 | _filter->set(it, false); |
---|
153 | } |
---|
154 | } |
---|
155 | |
---|
156 | /// \brief Adds a new terminal node. |
---|
157 | /// |
---|
158 | /// Adds a new terminal node to the Steiner-tree problem. |
---|
159 | void addTerminal(const Node& node) { |
---|
160 | if (!_dijkstra.reached(node)) { |
---|
161 | _dijkstra.addSource(node); |
---|
162 | _comp->comp(node, _terminal_num); |
---|
163 | ++_terminal_num; |
---|
164 | } |
---|
165 | } |
---|
166 | |
---|
167 | /// \brief Executes the algorithm. |
---|
168 | /// |
---|
169 | /// Executes the algorithm. |
---|
170 | /// |
---|
171 | /// \pre init() must be called and at least some nodes should be |
---|
172 | /// added with addTerminal() before using this function. |
---|
173 | /// |
---|
174 | /// This method constructs an approximation of the Steiner-Tree. |
---|
175 | void start() { |
---|
176 | _dijkstra.start(); |
---|
177 | |
---|
178 | std::vector<External> externals; |
---|
179 | for (UEdgeIt it(_graph); it != INVALID; ++it) { |
---|
180 | Node s = _graph.source(it); |
---|
181 | Node t = _graph.target(it); |
---|
182 | if (_comp->comp(s) == _comp->comp(t)) continue; |
---|
183 | |
---|
184 | Value cost = _dijkstra.dist(s) + _dijkstra.dist(t) + _cost[it]; |
---|
185 | |
---|
186 | if (_comp->comp(s) < _comp->comp(t)) { |
---|
187 | externals.push_back(External(_comp->comp(s), _comp->comp(t), |
---|
188 | it, cost)); |
---|
189 | } else { |
---|
190 | externals.push_back(External(_comp->comp(t), _comp->comp(s), |
---|
191 | it, cost)); |
---|
192 | } |
---|
193 | } |
---|
194 | std::sort(externals.begin(), externals.end(), ExternalLess()); |
---|
195 | |
---|
196 | SmartUGraph aux_graph; |
---|
197 | std::vector<SmartUGraph::Node> aux_nodes; |
---|
198 | |
---|
199 | for (int i = 0; i < _terminal_num; ++i) { |
---|
200 | aux_nodes.push_back(aux_graph.addNode()); |
---|
201 | } |
---|
202 | |
---|
203 | SmartUGraph::UEdgeMap<Value> aux_cost(aux_graph); |
---|
204 | SmartUGraph::UEdgeMap<UEdge> cross(aux_graph); |
---|
205 | { |
---|
206 | int i = 0; |
---|
207 | while (i < int(externals.size())) { |
---|
208 | int sn = externals[i].source; |
---|
209 | int tn = externals[i].target; |
---|
210 | Value ev = externals[i].value; |
---|
211 | UEdge ee = externals[i].uedge; |
---|
212 | ++i; |
---|
213 | while (i < int(externals.size()) && |
---|
214 | sn == externals[i].source && tn == externals[i].target) { |
---|
215 | if (externals[i].value < ev) { |
---|
216 | ev = externals[i].value; |
---|
217 | ee = externals[i].uedge; |
---|
218 | } |
---|
219 | ++i; |
---|
220 | } |
---|
221 | SmartUGraph::UEdge ne = |
---|
222 | aux_graph.addEdge(aux_nodes[sn], aux_nodes[tn]); |
---|
223 | aux_cost.set(ne, ev); |
---|
224 | cross.set(ne, ee); |
---|
225 | } |
---|
226 | } |
---|
227 | |
---|
228 | std::vector<SmartUGraph::UEdge> aux_tree_edges; |
---|
229 | BackInserterBoolMap<std::vector<SmartUGraph::UEdge> > |
---|
230 | aux_tree_map(aux_tree_edges); |
---|
231 | prim(aux_graph, aux_cost, aux_tree_map); |
---|
232 | |
---|
233 | for (std::vector<SmartUGraph::UEdge>::iterator |
---|
234 | it = aux_tree_edges.begin(); it != aux_tree_edges.end(); ++it) { |
---|
235 | Node node; |
---|
236 | node = _graph.source(cross[*it]); |
---|
237 | while (node != INVALID && !(*_filter)[node]) { |
---|
238 | _filter->set(node, true); |
---|
239 | node = (*_pred)[node] != INVALID ? |
---|
240 | _graph.source((*_pred)[node]) : INVALID; |
---|
241 | } |
---|
242 | node = _graph.target(cross[*it]); |
---|
243 | while (node != INVALID && !(*_filter)[node]) { |
---|
244 | _filter->set(node, true); |
---|
245 | node = (*_pred)[node] != INVALID ? |
---|
246 | _graph.source((*_pred)[node]) : INVALID; |
---|
247 | } |
---|
248 | } |
---|
249 | |
---|
250 | prim(nodeSubUGraphAdaptor(_graph, *_filter), _cost, *_tree); |
---|
251 | |
---|
252 | } |
---|
253 | |
---|
254 | /// \brief Checks if an edge is in the Steiner-tree or not. |
---|
255 | /// |
---|
256 | /// Checks if an edge is in the Steiner-tree or not. |
---|
257 | /// \param e is the edge that will be checked |
---|
258 | /// \return \c true if e is in the Steiner-tree, \c false otherwise |
---|
259 | bool tree(UEdge e){ |
---|
260 | return (*_tree)[e]; |
---|
261 | } |
---|
262 | |
---|
263 | /// \brief Checks if the node is in the Steiner-tree or not. |
---|
264 | /// |
---|
265 | /// Checks if a node is in the Steiner-tree or not. |
---|
266 | /// \param n is the node that will be checked |
---|
267 | /// \return \c true if n is in the Steiner-tree, \c false otherwise |
---|
268 | bool tree(Node n){ |
---|
269 | return (*_filter)[n]; |
---|
270 | } |
---|
271 | |
---|
272 | |
---|
273 | }; |
---|
274 | |
---|
275 | } //END OF NAMESPACE LEMON |
---|
276 | |
---|
277 | #endif |
---|