1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library. |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2009 |
---|
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_SUURBALLE_H |
---|
20 | #define LEMON_SUURBALLE_H |
---|
21 | |
---|
22 | ///\ingroup shortest_path |
---|
23 | ///\file |
---|
24 | ///\brief An algorithm for finding arc-disjoint paths between two |
---|
25 | /// nodes having minimum total length. |
---|
26 | |
---|
27 | #include <vector> |
---|
28 | #include <lemon/bin_heap.h> |
---|
29 | #include <lemon/path.h> |
---|
30 | |
---|
31 | namespace lemon { |
---|
32 | |
---|
33 | /// \addtogroup shortest_path |
---|
34 | /// @{ |
---|
35 | |
---|
36 | /// \brief Algorithm for finding arc-disjoint paths between two nodes |
---|
37 | /// having minimum total length. |
---|
38 | /// |
---|
39 | /// \ref lemon::Suurballe "Suurballe" implements an algorithm for |
---|
40 | /// finding arc-disjoint paths having minimum total length (cost) |
---|
41 | /// from a given source node to a given target node in a digraph. |
---|
42 | /// |
---|
43 | /// In fact, this implementation is the specialization of the |
---|
44 | /// \ref CapacityScaling "successive shortest path" algorithm. |
---|
45 | /// |
---|
46 | /// \tparam Digraph The digraph type the algorithm runs on. |
---|
47 | /// The default value is \c ListDigraph. |
---|
48 | /// \tparam LengthMap The type of the length (cost) map. |
---|
49 | /// The default value is <tt>Digraph::ArcMap<int></tt>. |
---|
50 | /// |
---|
51 | /// \warning Length values should be \e non-negative \e integers. |
---|
52 | /// |
---|
53 | /// \note For finding node-disjoint paths this algorithm can be used |
---|
54 | /// with \ref SplitNodes. |
---|
55 | #ifdef DOXYGEN |
---|
56 | template <typename Digraph, typename LengthMap> |
---|
57 | #else |
---|
58 | template < typename Digraph = ListDigraph, |
---|
59 | typename LengthMap = typename Digraph::template ArcMap<int> > |
---|
60 | #endif |
---|
61 | class Suurballe |
---|
62 | { |
---|
63 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
---|
64 | |
---|
65 | typedef typename LengthMap::Value Length; |
---|
66 | typedef ConstMap<Arc, int> ConstArcMap; |
---|
67 | typedef typename Digraph::template NodeMap<Arc> PredMap; |
---|
68 | |
---|
69 | public: |
---|
70 | |
---|
71 | /// The type of the flow map. |
---|
72 | typedef typename Digraph::template ArcMap<int> FlowMap; |
---|
73 | /// The type of the potential map. |
---|
74 | typedef typename Digraph::template NodeMap<Length> PotentialMap; |
---|
75 | /// The type of the path structures. |
---|
76 | typedef SimplePath<Digraph> Path; |
---|
77 | |
---|
78 | private: |
---|
79 | |
---|
80 | /// \brief Special implementation of the Dijkstra algorithm |
---|
81 | /// for finding shortest paths in the residual network. |
---|
82 | /// |
---|
83 | /// \ref ResidualDijkstra is a special implementation of the |
---|
84 | /// \ref Dijkstra algorithm for finding shortest paths in the |
---|
85 | /// residual network of the digraph with respect to the reduced arc |
---|
86 | /// lengths and modifying the node potentials according to the |
---|
87 | /// distance of the nodes. |
---|
88 | class ResidualDijkstra |
---|
89 | { |
---|
90 | typedef typename Digraph::template NodeMap<int> HeapCrossRef; |
---|
91 | typedef BinHeap<Length, HeapCrossRef> Heap; |
---|
92 | |
---|
93 | private: |
---|
94 | |
---|
95 | // The digraph the algorithm runs on |
---|
96 | const Digraph &_graph; |
---|
97 | |
---|
98 | // The main maps |
---|
99 | const FlowMap &_flow; |
---|
100 | const LengthMap &_length; |
---|
101 | PotentialMap &_potential; |
---|
102 | |
---|
103 | // The distance map |
---|
104 | PotentialMap _dist; |
---|
105 | // The pred arc map |
---|
106 | PredMap &_pred; |
---|
107 | // The processed (i.e. permanently labeled) nodes |
---|
108 | std::vector<Node> _proc_nodes; |
---|
109 | |
---|
110 | Node _s; |
---|
111 | Node _t; |
---|
112 | |
---|
113 | public: |
---|
114 | |
---|
115 | /// Constructor. |
---|
116 | ResidualDijkstra( const Digraph &digraph, |
---|
117 | const FlowMap &flow, |
---|
118 | const LengthMap &length, |
---|
119 | PotentialMap &potential, |
---|
120 | PredMap &pred, |
---|
121 | Node s, Node t ) : |
---|
122 | _graph(digraph), _flow(flow), _length(length), _potential(potential), |
---|
123 | _dist(digraph), _pred(pred), _s(s), _t(t) {} |
---|
124 | |
---|
125 | /// \brief Run the algorithm. It returns \c true if a path is found |
---|
126 | /// from the source node to the target node. |
---|
127 | bool run() { |
---|
128 | HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP); |
---|
129 | Heap heap(heap_cross_ref); |
---|
130 | heap.push(_s, 0); |
---|
131 | _pred[_s] = INVALID; |
---|
132 | _proc_nodes.clear(); |
---|
133 | |
---|
134 | // Process nodes |
---|
135 | while (!heap.empty() && heap.top() != _t) { |
---|
136 | Node u = heap.top(), v; |
---|
137 | Length d = heap.prio() + _potential[u], nd; |
---|
138 | _dist[u] = heap.prio(); |
---|
139 | heap.pop(); |
---|
140 | _proc_nodes.push_back(u); |
---|
141 | |
---|
142 | // Traverse outgoing arcs |
---|
143 | for (OutArcIt e(_graph, u); e != INVALID; ++e) { |
---|
144 | if (_flow[e] == 0) { |
---|
145 | v = _graph.target(e); |
---|
146 | switch(heap.state(v)) { |
---|
147 | case Heap::PRE_HEAP: |
---|
148 | heap.push(v, d + _length[e] - _potential[v]); |
---|
149 | _pred[v] = e; |
---|
150 | break; |
---|
151 | case Heap::IN_HEAP: |
---|
152 | nd = d + _length[e] - _potential[v]; |
---|
153 | if (nd < heap[v]) { |
---|
154 | heap.decrease(v, nd); |
---|
155 | _pred[v] = e; |
---|
156 | } |
---|
157 | break; |
---|
158 | case Heap::POST_HEAP: |
---|
159 | break; |
---|
160 | } |
---|
161 | } |
---|
162 | } |
---|
163 | |
---|
164 | // Traverse incoming arcs |
---|
165 | for (InArcIt e(_graph, u); e != INVALID; ++e) { |
---|
166 | if (_flow[e] == 1) { |
---|
167 | v = _graph.source(e); |
---|
168 | switch(heap.state(v)) { |
---|
169 | case Heap::PRE_HEAP: |
---|
170 | heap.push(v, d - _length[e] - _potential[v]); |
---|
171 | _pred[v] = e; |
---|
172 | break; |
---|
173 | case Heap::IN_HEAP: |
---|
174 | nd = d - _length[e] - _potential[v]; |
---|
175 | if (nd < heap[v]) { |
---|
176 | heap.decrease(v, nd); |
---|
177 | _pred[v] = e; |
---|
178 | } |
---|
179 | break; |
---|
180 | case Heap::POST_HEAP: |
---|
181 | break; |
---|
182 | } |
---|
183 | } |
---|
184 | } |
---|
185 | } |
---|
186 | if (heap.empty()) return false; |
---|
187 | |
---|
188 | // Update potentials of processed nodes |
---|
189 | Length t_dist = heap.prio(); |
---|
190 | for (int i = 0; i < int(_proc_nodes.size()); ++i) |
---|
191 | _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist; |
---|
192 | return true; |
---|
193 | } |
---|
194 | |
---|
195 | }; //class ResidualDijkstra |
---|
196 | |
---|
197 | private: |
---|
198 | |
---|
199 | // The digraph the algorithm runs on |
---|
200 | const Digraph &_graph; |
---|
201 | // The length map |
---|
202 | const LengthMap &_length; |
---|
203 | |
---|
204 | // Arc map of the current flow |
---|
205 | FlowMap *_flow; |
---|
206 | bool _local_flow; |
---|
207 | // Node map of the current potentials |
---|
208 | PotentialMap *_potential; |
---|
209 | bool _local_potential; |
---|
210 | |
---|
211 | // The source node |
---|
212 | Node _source; |
---|
213 | // The target node |
---|
214 | Node _target; |
---|
215 | |
---|
216 | // Container to store the found paths |
---|
217 | std::vector< SimplePath<Digraph> > paths; |
---|
218 | int _path_num; |
---|
219 | |
---|
220 | // The pred arc map |
---|
221 | PredMap _pred; |
---|
222 | // Implementation of the Dijkstra algorithm for finding augmenting |
---|
223 | // shortest paths in the residual network |
---|
224 | ResidualDijkstra *_dijkstra; |
---|
225 | |
---|
226 | public: |
---|
227 | |
---|
228 | /// \brief Constructor. |
---|
229 | /// |
---|
230 | /// Constructor. |
---|
231 | /// |
---|
232 | /// \param digraph The digraph the algorithm runs on. |
---|
233 | /// \param length The length (cost) values of the arcs. |
---|
234 | /// \param s The source node. |
---|
235 | /// \param t The target node. |
---|
236 | Suurballe( const Digraph &digraph, |
---|
237 | const LengthMap &length, |
---|
238 | Node s, Node t ) : |
---|
239 | _graph(digraph), _length(length), _flow(0), _local_flow(false), |
---|
240 | _potential(0), _local_potential(false), _source(s), _target(t), |
---|
241 | _pred(digraph) {} |
---|
242 | |
---|
243 | /// Destructor. |
---|
244 | ~Suurballe() { |
---|
245 | if (_local_flow) delete _flow; |
---|
246 | if (_local_potential) delete _potential; |
---|
247 | delete _dijkstra; |
---|
248 | } |
---|
249 | |
---|
250 | /// \brief Set the flow map. |
---|
251 | /// |
---|
252 | /// This function sets the flow map. |
---|
253 | /// |
---|
254 | /// The found flow contains only 0 and 1 values. It is the union of |
---|
255 | /// the found arc-disjoint paths. |
---|
256 | /// |
---|
257 | /// \return \c (*this) |
---|
258 | Suurballe& flowMap(FlowMap &map) { |
---|
259 | if (_local_flow) { |
---|
260 | delete _flow; |
---|
261 | _local_flow = false; |
---|
262 | } |
---|
263 | _flow = ↦ |
---|
264 | return *this; |
---|
265 | } |
---|
266 | |
---|
267 | /// \brief Set the potential map. |
---|
268 | /// |
---|
269 | /// This function sets the potential map. |
---|
270 | /// |
---|
271 | /// The potentials provide the dual solution of the underlying |
---|
272 | /// minimum cost flow problem. |
---|
273 | /// |
---|
274 | /// \return \c (*this) |
---|
275 | Suurballe& potentialMap(PotentialMap &map) { |
---|
276 | if (_local_potential) { |
---|
277 | delete _potential; |
---|
278 | _local_potential = false; |
---|
279 | } |
---|
280 | _potential = ↦ |
---|
281 | return *this; |
---|
282 | } |
---|
283 | |
---|
284 | /// \name Execution control |
---|
285 | /// The simplest way to execute the algorithm is to call the run() |
---|
286 | /// function. |
---|
287 | /// \n |
---|
288 | /// If you only need the flow that is the union of the found |
---|
289 | /// arc-disjoint paths, you may call init() and findFlow(). |
---|
290 | |
---|
291 | /// @{ |
---|
292 | |
---|
293 | /// \brief Run the algorithm. |
---|
294 | /// |
---|
295 | /// This function runs the algorithm. |
---|
296 | /// |
---|
297 | /// \param k The number of paths to be found. |
---|
298 | /// |
---|
299 | /// \return \c k if there are at least \c k arc-disjoint paths from |
---|
300 | /// \c s to \c t in the digraph. Otherwise it returns the number of |
---|
301 | /// arc-disjoint paths found. |
---|
302 | /// |
---|
303 | /// \note Apart from the return value, <tt>s.run(k)</tt> is just a |
---|
304 | /// shortcut of the following code. |
---|
305 | /// \code |
---|
306 | /// s.init(); |
---|
307 | /// s.findFlow(k); |
---|
308 | /// s.findPaths(); |
---|
309 | /// \endcode |
---|
310 | int run(int k = 2) { |
---|
311 | init(); |
---|
312 | findFlow(k); |
---|
313 | findPaths(); |
---|
314 | return _path_num; |
---|
315 | } |
---|
316 | |
---|
317 | /// \brief Initialize the algorithm. |
---|
318 | /// |
---|
319 | /// This function initializes the algorithm. |
---|
320 | void init() { |
---|
321 | // Initialize maps |
---|
322 | if (!_flow) { |
---|
323 | _flow = new FlowMap(_graph); |
---|
324 | _local_flow = true; |
---|
325 | } |
---|
326 | if (!_potential) { |
---|
327 | _potential = new PotentialMap(_graph); |
---|
328 | _local_potential = true; |
---|
329 | } |
---|
330 | for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0; |
---|
331 | for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0; |
---|
332 | |
---|
333 | _dijkstra = new ResidualDijkstra( _graph, *_flow, _length, |
---|
334 | *_potential, _pred, |
---|
335 | _source, _target ); |
---|
336 | } |
---|
337 | |
---|
338 | /// \brief Execute the successive shortest path algorithm to find |
---|
339 | /// an optimal flow. |
---|
340 | /// |
---|
341 | /// This function executes the successive shortest path algorithm to |
---|
342 | /// find a minimum cost flow, which is the union of \c k or less |
---|
343 | /// arc-disjoint paths. |
---|
344 | /// |
---|
345 | /// \return \c k if there are at least \c k arc-disjoint paths from |
---|
346 | /// \c s to \c t in the digraph. Otherwise it returns the number of |
---|
347 | /// arc-disjoint paths found. |
---|
348 | /// |
---|
349 | /// \pre \ref init() must be called before using this function. |
---|
350 | int findFlow(int k = 2) { |
---|
351 | // Find shortest paths |
---|
352 | _path_num = 0; |
---|
353 | while (_path_num < k) { |
---|
354 | // Run Dijkstra |
---|
355 | if (!_dijkstra->run()) break; |
---|
356 | ++_path_num; |
---|
357 | |
---|
358 | // Set the flow along the found shortest path |
---|
359 | Node u = _target; |
---|
360 | Arc e; |
---|
361 | while ((e = _pred[u]) != INVALID) { |
---|
362 | if (u == _graph.target(e)) { |
---|
363 | (*_flow)[e] = 1; |
---|
364 | u = _graph.source(e); |
---|
365 | } else { |
---|
366 | (*_flow)[e] = 0; |
---|
367 | u = _graph.target(e); |
---|
368 | } |
---|
369 | } |
---|
370 | } |
---|
371 | return _path_num; |
---|
372 | } |
---|
373 | |
---|
374 | /// \brief Compute the paths from the flow. |
---|
375 | /// |
---|
376 | /// This function computes the paths from the flow. |
---|
377 | /// |
---|
378 | /// \pre \ref init() and \ref findFlow() must be called before using |
---|
379 | /// this function. |
---|
380 | void findPaths() { |
---|
381 | // Create the residual flow map (the union of the paths not found |
---|
382 | // so far) |
---|
383 | FlowMap res_flow(_graph); |
---|
384 | for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a]; |
---|
385 | |
---|
386 | paths.clear(); |
---|
387 | paths.resize(_path_num); |
---|
388 | for (int i = 0; i < _path_num; ++i) { |
---|
389 | Node n = _source; |
---|
390 | while (n != _target) { |
---|
391 | OutArcIt e(_graph, n); |
---|
392 | for ( ; res_flow[e] == 0; ++e) ; |
---|
393 | n = _graph.target(e); |
---|
394 | paths[i].addBack(e); |
---|
395 | res_flow[e] = 0; |
---|
396 | } |
---|
397 | } |
---|
398 | } |
---|
399 | |
---|
400 | /// @} |
---|
401 | |
---|
402 | /// \name Query Functions |
---|
403 | /// The results of the algorithm can be obtained using these |
---|
404 | /// functions. |
---|
405 | /// \n The algorithm should be executed before using them. |
---|
406 | |
---|
407 | /// @{ |
---|
408 | |
---|
409 | /// \brief Return a const reference to the arc map storing the |
---|
410 | /// found flow. |
---|
411 | /// |
---|
412 | /// This function returns a const reference to the arc map storing |
---|
413 | /// the flow that is the union of the found arc-disjoint paths. |
---|
414 | /// |
---|
415 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
416 | /// this function. |
---|
417 | const FlowMap& flowMap() const { |
---|
418 | return *_flow; |
---|
419 | } |
---|
420 | |
---|
421 | /// \brief Return a const reference to the node map storing the |
---|
422 | /// found potentials (the dual solution). |
---|
423 | /// |
---|
424 | /// This function returns a const reference to the node map storing |
---|
425 | /// the found potentials that provide the dual solution of the |
---|
426 | /// underlying minimum cost flow problem. |
---|
427 | /// |
---|
428 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
429 | /// this function. |
---|
430 | const PotentialMap& potentialMap() const { |
---|
431 | return *_potential; |
---|
432 | } |
---|
433 | |
---|
434 | /// \brief Return the flow on the given arc. |
---|
435 | /// |
---|
436 | /// This function returns the flow on the given arc. |
---|
437 | /// It is \c 1 if the arc is involved in one of the found paths, |
---|
438 | /// otherwise it is \c 0. |
---|
439 | /// |
---|
440 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
441 | /// this function. |
---|
442 | int flow(const Arc& arc) const { |
---|
443 | return (*_flow)[arc]; |
---|
444 | } |
---|
445 | |
---|
446 | /// \brief Return the potential of the given node. |
---|
447 | /// |
---|
448 | /// This function returns the potential of the given node. |
---|
449 | /// |
---|
450 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
451 | /// this function. |
---|
452 | Length potential(const Node& node) const { |
---|
453 | return (*_potential)[node]; |
---|
454 | } |
---|
455 | |
---|
456 | /// \brief Return the total length (cost) of the found paths (flow). |
---|
457 | /// |
---|
458 | /// This function returns the total length (cost) of the found paths |
---|
459 | /// (flow). The complexity of the function is \f$ O(e) \f$. |
---|
460 | /// |
---|
461 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
462 | /// this function. |
---|
463 | Length totalLength() const { |
---|
464 | Length c = 0; |
---|
465 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
466 | c += (*_flow)[e] * _length[e]; |
---|
467 | return c; |
---|
468 | } |
---|
469 | |
---|
470 | /// \brief Return the number of the found paths. |
---|
471 | /// |
---|
472 | /// This function returns the number of the found paths. |
---|
473 | /// |
---|
474 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
475 | /// this function. |
---|
476 | int pathNum() const { |
---|
477 | return _path_num; |
---|
478 | } |
---|
479 | |
---|
480 | /// \brief Return a const reference to the specified path. |
---|
481 | /// |
---|
482 | /// This function returns a const reference to the specified path. |
---|
483 | /// |
---|
484 | /// \param i The function returns the \c i-th path. |
---|
485 | /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>. |
---|
486 | /// |
---|
487 | /// \pre \ref run() or \ref findPaths() must be called before using |
---|
488 | /// this function. |
---|
489 | Path path(int i) const { |
---|
490 | return paths[i]; |
---|
491 | } |
---|
492 | |
---|
493 | /// @} |
---|
494 | |
---|
495 | }; //class Suurballe |
---|
496 | |
---|
497 | ///@} |
---|
498 | |
---|
499 | } //namespace lemon |
---|
500 | |
---|
501 | #endif //LEMON_SUURBALLE_H |
---|