1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2007 |
---|
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_MIN_MEAN_CYCLE_H |
---|
20 | #define LEMON_MIN_MEAN_CYCLE_H |
---|
21 | |
---|
22 | /// \ingroup min_cost_flow |
---|
23 | /// |
---|
24 | /// \file |
---|
25 | /// \brief Karp algorithm for finding a minimum mean cycle. |
---|
26 | |
---|
27 | #include <lemon/graph_utils.h> |
---|
28 | #include <lemon/topology.h> |
---|
29 | #include <lemon/path.h> |
---|
30 | |
---|
31 | namespace lemon { |
---|
32 | |
---|
33 | /// \addtogroup min_cost_flow |
---|
34 | /// @{ |
---|
35 | |
---|
36 | /// \brief Implementation of Karp's algorithm for finding a |
---|
37 | /// minimum mean cycle. |
---|
38 | /// |
---|
39 | /// The \ref lemon::MinMeanCycle "MinMeanCycle" implements Karp's |
---|
40 | /// algorithm for finding a minimum mean cycle. |
---|
41 | /// |
---|
42 | /// \param Graph The directed graph type the algorithm runs on. |
---|
43 | /// \param LengthMap The type of the length (cost) map. |
---|
44 | /// |
---|
45 | /// \author Peter Kovacs |
---|
46 | |
---|
47 | #ifdef DOXYGEN |
---|
48 | template <typename Graph, typename LengthMap> |
---|
49 | #else |
---|
50 | template <typename Graph, |
---|
51 | typename LengthMap = typename Graph::template EdgeMap<int> > |
---|
52 | #endif |
---|
53 | |
---|
54 | class MinMeanCycle |
---|
55 | { |
---|
56 | typedef typename Graph::Node Node; |
---|
57 | typedef typename Graph::NodeIt NodeIt; |
---|
58 | typedef typename Graph::Edge Edge; |
---|
59 | typedef typename Graph::EdgeIt EdgeIt; |
---|
60 | typedef typename Graph::InEdgeIt InEdgeIt; |
---|
61 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
62 | |
---|
63 | typedef typename LengthMap::Value Length; |
---|
64 | |
---|
65 | typedef typename Graph::template NodeMap<int> IntNodeMap; |
---|
66 | typedef typename Graph::template NodeMap<Edge> PredNodeMap; |
---|
67 | typedef Path<Graph> Path; |
---|
68 | typedef std::vector<Node> NodeVector; |
---|
69 | typedef typename NodeVector::iterator NodeVectorIt; |
---|
70 | |
---|
71 | protected: |
---|
72 | |
---|
73 | /// \brief Data sturcture for path data. |
---|
74 | struct PathData { |
---|
75 | bool found; |
---|
76 | Length dist; |
---|
77 | Edge pred; |
---|
78 | PathData(bool _found = false, Length _dist = 0) : |
---|
79 | found(_found), dist(_dist), pred(INVALID) {} |
---|
80 | PathData(bool _found, Length _dist, Edge _pred) : |
---|
81 | found(_found), dist(_dist), pred(_pred) {} |
---|
82 | }; |
---|
83 | |
---|
84 | private: |
---|
85 | |
---|
86 | typedef typename Graph::template NodeMap<std::vector<PathData> > PathVectorNodeMap; |
---|
87 | |
---|
88 | protected: |
---|
89 | |
---|
90 | /// \brief Node map for storing path data. |
---|
91 | /// |
---|
92 | /// Node map for storing path data of all nodes in the current |
---|
93 | /// component. dmap[v][k] is the length of a shortest directed walk |
---|
94 | /// to node v from the starting node containing exactly k edges. |
---|
95 | PathVectorNodeMap dmap; |
---|
96 | |
---|
97 | /// \brief The directed graph the algorithm runs on. |
---|
98 | const Graph& graph; |
---|
99 | /// \brief The length of the edges. |
---|
100 | const LengthMap& length; |
---|
101 | |
---|
102 | /// \brief The total length of the found cycle. |
---|
103 | Length cycle_length; |
---|
104 | /// \brief The number of edges in the found cycle. |
---|
105 | int cycle_size; |
---|
106 | /// \brief The found cycle. |
---|
107 | Path *cycle_path; |
---|
108 | /// \brief The found cycle. |
---|
109 | bool local_path; |
---|
110 | |
---|
111 | /// \brief Node map for identifying strongly connected components. |
---|
112 | IntNodeMap comp; |
---|
113 | /// \brief The number of strongly connected components. |
---|
114 | int comp_num; |
---|
115 | /// \brief %Counter for identifying the current component. |
---|
116 | int comp_cnt; |
---|
117 | /// \brief Nodes of the current component. |
---|
118 | NodeVector nodes; |
---|
119 | /// \brief The processed nodes in the last round. |
---|
120 | NodeVector process; |
---|
121 | |
---|
122 | public : |
---|
123 | |
---|
124 | /// \brief The constructor of the class. |
---|
125 | /// |
---|
126 | /// The constructor of the class. |
---|
127 | /// |
---|
128 | /// \param _graph The directed graph the algorithm runs on. |
---|
129 | /// \param _length The length (cost) of the edges. |
---|
130 | MinMeanCycle( const Graph& _graph, |
---|
131 | const LengthMap& _length ) : |
---|
132 | graph(_graph), length(_length), dmap(_graph), |
---|
133 | cycle_length(0), cycle_size(-1), comp(_graph), |
---|
134 | cycle_path(NULL), local_path(false) |
---|
135 | { } |
---|
136 | |
---|
137 | /// \brief The destructor of the class. |
---|
138 | ~MinMeanCycle() { |
---|
139 | if (local_path) delete cycle_path; |
---|
140 | } |
---|
141 | |
---|
142 | protected: |
---|
143 | |
---|
144 | /// \brief Initializes the internal data structures. |
---|
145 | void init() { |
---|
146 | comp_num = stronglyConnectedComponents(graph, comp); |
---|
147 | if (!cycle_path) { |
---|
148 | local_path = true; |
---|
149 | cycle_path = new Path; |
---|
150 | } |
---|
151 | } |
---|
152 | |
---|
153 | /// \brief Initializes the internal data structures for the current |
---|
154 | /// component. |
---|
155 | void initCurrent() { |
---|
156 | nodes.clear(); |
---|
157 | // Finding the nodes of the current component |
---|
158 | for (NodeIt v(graph); v != INVALID; ++v) { |
---|
159 | if (comp[v] == comp_cnt) nodes.push_back(v); |
---|
160 | } |
---|
161 | |
---|
162 | // Creating vectors for all nodes |
---|
163 | int n = nodes.size(); |
---|
164 | for (NodeVectorIt vi = nodes.begin(); vi != nodes.end(); ++vi) { |
---|
165 | dmap[*vi].resize(n + 1); |
---|
166 | } |
---|
167 | } |
---|
168 | |
---|
169 | /// \brief Processes all rounds of computing required path data. |
---|
170 | void processRounds() { |
---|
171 | dmap[nodes[0]][0] = PathData(true, 0); |
---|
172 | process.clear(); |
---|
173 | for (OutEdgeIt oe(graph, nodes[0]); oe != INVALID; ++oe) { |
---|
174 | Node v = graph.target(oe); |
---|
175 | if (comp[v] != comp_cnt || v == nodes[0]) continue; |
---|
176 | dmap[v][1] = PathData(true, length[oe], oe); |
---|
177 | process.push_back(v); |
---|
178 | } |
---|
179 | int n = nodes.size(), k; |
---|
180 | for (k = 2; k <= n && process.size() < n; ++k) { |
---|
181 | processNextBuildRound(k); |
---|
182 | } |
---|
183 | for ( ; k <= n; ++k) { |
---|
184 | processNextFullRound(k); |
---|
185 | } |
---|
186 | } |
---|
187 | |
---|
188 | /// \brief Processes one round of computing required path data and |
---|
189 | /// rebuilds \ref process vector. |
---|
190 | void processNextBuildRound(int k) { |
---|
191 | NodeVector next; |
---|
192 | for (NodeVectorIt ui = process.begin(); ui != process.end(); ++ui) { |
---|
193 | for (OutEdgeIt oe(graph, *ui); oe != INVALID; ++oe) { |
---|
194 | Node v = graph.target(oe); |
---|
195 | if (comp[v] != comp_cnt) continue; |
---|
196 | if ( !dmap[v][k].found || (dmap[v][k].dist > dmap[*ui][k-1].dist + length[oe]) ) { |
---|
197 | if (!dmap[v][k].found) next.push_back(v); |
---|
198 | dmap[v][k] = PathData(true, dmap[*ui][k-1].dist + length[oe], oe); |
---|
199 | } |
---|
200 | } |
---|
201 | } |
---|
202 | process.swap(next); |
---|
203 | } |
---|
204 | |
---|
205 | /// \brief Processes one round of computing required path data |
---|
206 | /// using \ref nodes vector instead of \ref process vector. |
---|
207 | void processNextFullRound(int k) { |
---|
208 | for (NodeVectorIt ui = nodes.begin(); ui != nodes.end(); ++ui) { |
---|
209 | for (OutEdgeIt oe(graph, *ui); oe != INVALID; ++oe) { |
---|
210 | Node v = graph.target(oe); |
---|
211 | if (comp[v] != comp_cnt) continue; |
---|
212 | if ( !dmap[v][k].found || (dmap[v][k].dist > dmap[*ui][k-1].dist + length[oe]) ) { |
---|
213 | dmap[v][k] = PathData(true, dmap[*ui][k-1].dist + length[oe], oe); |
---|
214 | } |
---|
215 | } |
---|
216 | } |
---|
217 | } |
---|
218 | |
---|
219 | /// \brief Finds the minimum cycle mean value according to the path |
---|
220 | /// data stored in \ref dmap. |
---|
221 | /// |
---|
222 | /// Finds the minimum cycle mean value according to the path data |
---|
223 | /// stored in \ref dmap. |
---|
224 | /// |
---|
225 | /// \retval min_length The total length of the found cycle. |
---|
226 | /// \retval min_size The number of edges in the found cycle. |
---|
227 | /// \retval min_node A node for obtaining a critical cycle. |
---|
228 | /// |
---|
229 | /// \return \c true if a cycle exists in the graph. |
---|
230 | bool findMinCycleMean(Length &min_length, int &min_size, Node &min_node) { |
---|
231 | bool found_min = false; |
---|
232 | for (NodeVectorIt vi = nodes.begin(); vi != nodes.end(); ++vi) { |
---|
233 | Length len; |
---|
234 | int size; |
---|
235 | bool found_one = false; |
---|
236 | int n = nodes.size(); |
---|
237 | for (int k = 0; k < n; ++k) { |
---|
238 | Length _len = dmap[*vi][n].dist - dmap[*vi][k].dist; |
---|
239 | int _size = n - k; |
---|
240 | if ( dmap[*vi][n].found && dmap[*vi][k].found && (!found_one || len * _size < _len * size) ) { |
---|
241 | found_one = true; |
---|
242 | len = _len; |
---|
243 | size = _size; |
---|
244 | } |
---|
245 | } |
---|
246 | if (found_one && (!found_min || len * min_size < min_length * size)) { |
---|
247 | found_min = true; |
---|
248 | min_length = len; |
---|
249 | min_size = size; |
---|
250 | min_node = *vi; |
---|
251 | } |
---|
252 | } |
---|
253 | return found_min; |
---|
254 | } |
---|
255 | |
---|
256 | /// \brief Finds a critical (minimum mean) cycle according to the |
---|
257 | /// path data stored in \ref dmap. |
---|
258 | void findCycle(const Node &min_n) { |
---|
259 | IntNodeMap reached(graph, -1); |
---|
260 | int r = reached[min_n] = dmap[min_n].size() - 1; |
---|
261 | Node u = graph.source(dmap[min_n][r].pred); |
---|
262 | while (reached[u] < 0) { |
---|
263 | reached[u] = --r; |
---|
264 | u = graph.source(dmap[u][r].pred); |
---|
265 | } |
---|
266 | r = reached[u]; |
---|
267 | Edge ce = dmap[u][r].pred; |
---|
268 | cycle_path->addFront(ce); |
---|
269 | Node v; |
---|
270 | while ((v = graph.source(ce)) != u) { |
---|
271 | ce = dmap[v][--r].pred; |
---|
272 | cycle_path->addFront(ce); |
---|
273 | } |
---|
274 | } |
---|
275 | |
---|
276 | public: |
---|
277 | |
---|
278 | /// \brief Runs the algorithm. |
---|
279 | /// |
---|
280 | /// Runs the algorithm. |
---|
281 | /// |
---|
282 | /// \return \c true if a cycle exists in the graph. |
---|
283 | bool run() { |
---|
284 | init(); |
---|
285 | // Searching for the minimum mean cycle in all components |
---|
286 | bool found_cycle = false; |
---|
287 | Node cycle_node; |
---|
288 | for (comp_cnt = 0; comp_cnt < comp_num; ++comp_cnt) { |
---|
289 | |
---|
290 | initCurrent(); |
---|
291 | processRounds(); |
---|
292 | |
---|
293 | Length min_length; |
---|
294 | int min_size; |
---|
295 | Node min_node; |
---|
296 | bool found_min = findMinCycleMean(min_length, min_size, min_node); |
---|
297 | |
---|
298 | if ( found_min && (!found_cycle || min_length * cycle_size < cycle_length * min_size) ) { |
---|
299 | found_cycle = true; |
---|
300 | cycle_length = min_length; |
---|
301 | cycle_size = min_size; |
---|
302 | cycle_node = min_node; |
---|
303 | } |
---|
304 | } |
---|
305 | if (found_cycle) findCycle(cycle_node); |
---|
306 | return found_cycle; |
---|
307 | } |
---|
308 | |
---|
309 | /// \brief Returns the total length of the found critical cycle. |
---|
310 | /// |
---|
311 | /// Returns the total length of the found critical cycle. |
---|
312 | /// |
---|
313 | /// \pre \ref run() must be called before using this function. |
---|
314 | Length cycleLength() const { |
---|
315 | return cycle_length; |
---|
316 | } |
---|
317 | |
---|
318 | /// \brief Returns the number of edges in the found critical |
---|
319 | /// cycle. |
---|
320 | /// |
---|
321 | /// Returns the number of edges in the found critical cycle. |
---|
322 | /// |
---|
323 | /// \pre \ref run() must be called before using this function. |
---|
324 | int cycleEdgeNum() const { |
---|
325 | return cycle_size; |
---|
326 | } |
---|
327 | |
---|
328 | /// \brief Returns the mean length of the found critical cycle. |
---|
329 | /// |
---|
330 | /// Returns the mean length of the found critical cycle. |
---|
331 | /// |
---|
332 | /// \pre \ref run() must be called before using this function. |
---|
333 | /// |
---|
334 | /// \warning LengthMap::Value must be convertible to double. |
---|
335 | double minMean() const { |
---|
336 | return (double)cycle_length / (double)cycle_size; |
---|
337 | } |
---|
338 | |
---|
339 | /// \brief Returns a const reference to the \ref lemon::Path "Path" |
---|
340 | /// structure of the found flow. |
---|
341 | /// |
---|
342 | /// Returns a const reference to the \ref lemon::Path "Path" |
---|
343 | /// structure of the found flow. |
---|
344 | /// |
---|
345 | /// \pre \ref run() must be called before using this function. |
---|
346 | /// |
---|
347 | /// \sa \ref cyclePath() |
---|
348 | const Path &cycle() const { |
---|
349 | return *cycle_path; |
---|
350 | } |
---|
351 | |
---|
352 | /// \brief Sets the \ref lemon::Path "Path" structure storing the |
---|
353 | /// found cycle. |
---|
354 | /// |
---|
355 | /// Sets the \ref lemon::Path "Path" structure storing the found |
---|
356 | /// cycle. If you don't use this function before calling |
---|
357 | /// \ref run(), it will allocate one. The destuctor deallocates |
---|
358 | /// this automatically allocated map, of course. |
---|
359 | /// |
---|
360 | /// \note The algorithm calls only the \ref lemon::Path::addFront() |
---|
361 | /// "addFront()" method of the given \ref lemon::Path "Path" |
---|
362 | /// structure. |
---|
363 | /// |
---|
364 | /// \return \c (*this) |
---|
365 | MinMeanCycle &cyclePath(Path& path) { |
---|
366 | if (local_path) { |
---|
367 | delete cycle_path; |
---|
368 | local_path = false; |
---|
369 | } |
---|
370 | cycle_path = &path; |
---|
371 | return *this; |
---|
372 | } |
---|
373 | |
---|
374 | }; //class MinMeanCycle |
---|
375 | |
---|
376 | ///@} |
---|
377 | |
---|
378 | } //namespace lemon |
---|
379 | |
---|
380 | #endif //LEMON_MIN_MEAN_CYCLE_H |
---|