1 | /* -*- C++ -*- |
---|
2 | * lemon/minimum_cut.h - Part of LEMON, a generic C++ optimization library |
---|
3 | * |
---|
4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
6 | * |
---|
7 | * Permission to use, modify and distribute this software is granted |
---|
8 | * provided that this copyright notice appears in all copies. For |
---|
9 | * precise terms see the accompanying LICENSE file. |
---|
10 | * |
---|
11 | * This software is provided "AS IS" with no warranty of any kind, |
---|
12 | * express or implied, and with no claim as to its suitability for any |
---|
13 | * purpose. |
---|
14 | * |
---|
15 | */ |
---|
16 | |
---|
17 | #ifndef LEMON_MINIMUM_CUT_H |
---|
18 | #define LEMON_MINIMUM_CUT_H |
---|
19 | |
---|
20 | |
---|
21 | /// \ingroup topology |
---|
22 | /// \file |
---|
23 | /// \brief Maximum cardinality search and minimum cut in undirected graphs. |
---|
24 | |
---|
25 | #include <lemon/list_graph.h> |
---|
26 | #include <lemon/bin_heap.h> |
---|
27 | #include <lemon/linear_heap.h> |
---|
28 | |
---|
29 | #include <lemon/invalid.h> |
---|
30 | #include <lemon/error.h> |
---|
31 | #include <lemon/maps.h> |
---|
32 | |
---|
33 | #include <functional> |
---|
34 | |
---|
35 | namespace lemon { |
---|
36 | |
---|
37 | namespace _minimum_cut_bits { |
---|
38 | |
---|
39 | template <typename CapacityMap> |
---|
40 | struct HeapSelector { |
---|
41 | template <typename Key, typename Value, typename Ref> |
---|
42 | struct Selector { |
---|
43 | typedef BinHeap<Key, Value, Ref, std::greater<Value> > Heap; |
---|
44 | }; |
---|
45 | }; |
---|
46 | |
---|
47 | template <typename CapacityKey> |
---|
48 | struct HeapSelector<ConstMap<CapacityKey, Const<int, 1> > > { |
---|
49 | template <typename Key, typename Value, typename Ref> |
---|
50 | struct Selector { |
---|
51 | typedef LinearHeap<Key, Ref, false > Heap; |
---|
52 | }; |
---|
53 | }; |
---|
54 | |
---|
55 | } |
---|
56 | |
---|
57 | /// \brief Default traits class of MaxCardinalitySearch class. |
---|
58 | /// |
---|
59 | /// Default traits class of MaxCardinalitySearch class. |
---|
60 | /// \param Graph Graph type. |
---|
61 | /// \param CapacityMap Type of length map. |
---|
62 | template <typename _Graph, typename _CapacityMap> |
---|
63 | struct MaxCardinalitySearchDefaultTraits { |
---|
64 | /// The graph type the algorithm runs on. |
---|
65 | typedef _Graph Graph; |
---|
66 | |
---|
67 | /// \brief The type of the map that stores the edge capacities. |
---|
68 | /// |
---|
69 | /// The type of the map that stores the edge capacities. |
---|
70 | /// It must meet the \ref concept::ReadMap "ReadMap" concept. |
---|
71 | typedef _CapacityMap CapacityMap; |
---|
72 | |
---|
73 | /// \brief The type of the capacity of the edges. |
---|
74 | typedef typename CapacityMap::Value Value; |
---|
75 | |
---|
76 | /// \brief The cross reference type used by heap. |
---|
77 | /// |
---|
78 | /// The cross reference type used by heap. |
---|
79 | /// Usually it is \c Graph::NodeMap<int>. |
---|
80 | typedef typename Graph::template NodeMap<int> HeapCrossRef; |
---|
81 | |
---|
82 | /// \brief Instantiates a HeapCrossRef. |
---|
83 | /// |
---|
84 | /// This function instantiates a \ref HeapCrossRef. |
---|
85 | /// \param graph is the graph, to which we would like to define the |
---|
86 | /// HeapCrossRef. |
---|
87 | static HeapCrossRef *createHeapCrossRef(const Graph &graph) { |
---|
88 | return new HeapCrossRef(graph); |
---|
89 | } |
---|
90 | |
---|
91 | /// \brief The heap type used by MaxCardinalitySearch algorithm. |
---|
92 | /// |
---|
93 | /// The heap type used by MaxCardinalitySearch algorithm. It should |
---|
94 | /// maximalize the priorities. The default heap type is |
---|
95 | /// the \ref BinHeap, but it is specialized when the |
---|
96 | /// CapacityMap is ConstMap<Graph::Node, Const<int, 1> > |
---|
97 | /// to LinearHeap. |
---|
98 | /// |
---|
99 | /// \sa MaxCardinalitySearch |
---|
100 | typedef typename _minimum_cut_bits |
---|
101 | ::HeapSelector<CapacityMap> |
---|
102 | ::template Selector<typename Graph::Node, Value, HeapCrossRef> |
---|
103 | ::Heap Heap; |
---|
104 | |
---|
105 | /// \brief Instantiates a Heap. |
---|
106 | /// |
---|
107 | /// This function instantiates a \ref Heap. |
---|
108 | /// \param crossref The cross reference of the heap. |
---|
109 | static Heap *createHeap(HeapCrossRef& crossref) { |
---|
110 | return new Heap(crossref); |
---|
111 | } |
---|
112 | |
---|
113 | /// \brief The type of the map that stores whether a nodes is processed. |
---|
114 | /// |
---|
115 | /// The type of the map that stores whether a nodes is processed. |
---|
116 | /// It must meet the \ref concept::WriteMap "WriteMap" concept. |
---|
117 | /// By default it is a NullMap. |
---|
118 | typedef NullMap<typename Graph::Node, bool> ProcessedMap; |
---|
119 | |
---|
120 | /// \brief Instantiates a ProcessedMap. |
---|
121 | /// |
---|
122 | /// This function instantiates a \ref ProcessedMap. |
---|
123 | /// \param g is the graph, to which |
---|
124 | /// we would like to define the \ref ProcessedMap |
---|
125 | #ifdef DOXYGEN |
---|
126 | static ProcessedMap *createProcessedMap(const Graph &graph) |
---|
127 | #else |
---|
128 | static ProcessedMap *createProcessedMap(const Graph &) |
---|
129 | #endif |
---|
130 | { |
---|
131 | return new ProcessedMap(); |
---|
132 | } |
---|
133 | |
---|
134 | /// \brief The type of the map that stores the cardinalties of the nodes. |
---|
135 | /// |
---|
136 | /// The type of the map that stores the cardinalities of the nodes. |
---|
137 | /// It must meet the \ref concept::WriteMap "WriteMap" concept. |
---|
138 | typedef typename Graph::template NodeMap<Value> CardinalityMap; |
---|
139 | |
---|
140 | /// \brief Instantiates a CardinalityMap. |
---|
141 | /// |
---|
142 | /// This function instantiates a \ref CardinalityMap. |
---|
143 | /// \param graph is the graph, to which we would like to define the \ref |
---|
144 | /// CardinalityMap |
---|
145 | static CardinalityMap *createCardinalityMap(const Graph &graph) { |
---|
146 | return new CardinalityMap(graph); |
---|
147 | } |
---|
148 | |
---|
149 | }; |
---|
150 | |
---|
151 | /// \ingroup topology |
---|
152 | /// |
---|
153 | /// \brief Maximum Cardinality Search algorithm class. |
---|
154 | /// |
---|
155 | /// This class provides an efficient implementation of Maximum Cardinality |
---|
156 | /// Search algorithm. The maximum cardinality search chooses first time any |
---|
157 | /// node of the graph. Then every time chooses that node which connected |
---|
158 | /// to the processed nodes at most in the sum of capacities on the out |
---|
159 | /// edges. If there is a cut in the graph the algorithm should choose |
---|
160 | /// again any unprocessed node of the graph. Each nodes cardinality is |
---|
161 | /// the sum of capacities on the out edges to the nodes which are processed |
---|
162 | /// before the given node. |
---|
163 | /// |
---|
164 | /// The edge capacities are passed to the algorithm using a |
---|
165 | /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any |
---|
166 | /// kind of capacity. |
---|
167 | /// |
---|
168 | /// The type of the capacity is determined by the \ref |
---|
169 | /// concept::ReadMap::Value "Value" of the capacity map. |
---|
170 | /// |
---|
171 | /// It is also possible to change the underlying priority heap. |
---|
172 | /// |
---|
173 | /// |
---|
174 | /// \param _Graph The graph type the algorithm runs on. The default value |
---|
175 | /// is \ref ListGraph. The value of Graph is not used directly by |
---|
176 | /// the search algorithm, it is only passed to |
---|
177 | /// \ref MaxCardinalitySearchDefaultTraits. |
---|
178 | /// \param _CapacityMap This read-only EdgeMap determines the capacities of |
---|
179 | /// the edges. It is read once for each edge, so the map may involve in |
---|
180 | /// relatively time consuming process to compute the edge capacity if |
---|
181 | /// it is necessary. The default map type is \ref |
---|
182 | /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>". The value |
---|
183 | /// of CapacityMap is not used directly by search algorithm, it is only |
---|
184 | /// passed to \ref MaxCardinalitySearchDefaultTraits. |
---|
185 | /// \param _Traits Traits class to set various data types used by the |
---|
186 | /// algorithm. The default traits class is |
---|
187 | /// \ref MaxCardinalitySearchDefaultTraits |
---|
188 | /// "MaxCardinalitySearchDefaultTraits<_Graph, _CapacityMap>". |
---|
189 | /// See \ref MaxCardinalitySearchDefaultTraits |
---|
190 | /// for the documentation of a MaxCardinalitySearch traits class. |
---|
191 | /// |
---|
192 | /// \author Balazs Dezso |
---|
193 | |
---|
194 | #ifdef DOXYGEN |
---|
195 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
---|
196 | #else |
---|
197 | template <typename _Graph = ListUGraph, |
---|
198 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
---|
199 | typename _Traits = |
---|
200 | MaxCardinalitySearchDefaultTraits<_Graph, _CapacityMap> > |
---|
201 | #endif |
---|
202 | class MaxCardinalitySearch { |
---|
203 | public: |
---|
204 | /// \brief \ref Exception for uninitialized parameters. |
---|
205 | /// |
---|
206 | /// This error represents problems in the initialization |
---|
207 | /// of the parameters of the algorithms. |
---|
208 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
209 | public: |
---|
210 | virtual const char* exceptionName() const { |
---|
211 | return "lemon::MaxCardinalitySearch::UninitializedParameter"; |
---|
212 | } |
---|
213 | }; |
---|
214 | |
---|
215 | typedef _Traits Traits; |
---|
216 | ///The type of the underlying graph. |
---|
217 | typedef typename Traits::Graph Graph; |
---|
218 | |
---|
219 | ///The type of the capacity of the edges. |
---|
220 | typedef typename Traits::CapacityMap::Value Value; |
---|
221 | ///The type of the map that stores the edge capacities. |
---|
222 | typedef typename Traits::CapacityMap CapacityMap; |
---|
223 | ///The type of the map indicating if a node is processed. |
---|
224 | typedef typename Traits::ProcessedMap ProcessedMap; |
---|
225 | ///The type of the map that stores the cardinalities of the nodes. |
---|
226 | typedef typename Traits::CardinalityMap CardinalityMap; |
---|
227 | ///The cross reference type used for the current heap. |
---|
228 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
---|
229 | ///The heap type used by the algorithm. It maximize the priorities. |
---|
230 | typedef typename Traits::Heap Heap; |
---|
231 | private: |
---|
232 | /// Pointer to the underlying graph. |
---|
233 | const Graph *_graph; |
---|
234 | /// Pointer to the capacity map |
---|
235 | const CapacityMap *_capacity; |
---|
236 | ///Pointer to the map of cardinality. |
---|
237 | CardinalityMap *_cardinality; |
---|
238 | ///Indicates if \ref _cardinality is locally allocated (\c true) or not. |
---|
239 | bool local_cardinality; |
---|
240 | ///Pointer to the map of processed status of the nodes. |
---|
241 | ProcessedMap *_processed; |
---|
242 | ///Indicates if \ref _processed is locally allocated (\c true) or not. |
---|
243 | bool local_processed; |
---|
244 | ///Pointer to the heap cross references. |
---|
245 | HeapCrossRef *_heap_cross_ref; |
---|
246 | ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not. |
---|
247 | bool local_heap_cross_ref; |
---|
248 | ///Pointer to the heap. |
---|
249 | Heap *_heap; |
---|
250 | ///Indicates if \ref _heap is locally allocated (\c true) or not. |
---|
251 | bool local_heap; |
---|
252 | |
---|
253 | public : |
---|
254 | |
---|
255 | typedef MaxCardinalitySearch Create; |
---|
256 | |
---|
257 | ///\name Named template parameters |
---|
258 | |
---|
259 | ///@{ |
---|
260 | |
---|
261 | template <class T> |
---|
262 | struct DefCardinalityMapTraits : public Traits { |
---|
263 | typedef T CardinalityMap; |
---|
264 | static CardinalityMap *createCardinalityMap(const Graph &) |
---|
265 | { |
---|
266 | throw UninitializedParameter(); |
---|
267 | } |
---|
268 | }; |
---|
269 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
270 | /// CardinalityMap type |
---|
271 | /// |
---|
272 | /// \ref named-templ-param "Named parameter" for setting CardinalityMap |
---|
273 | /// type |
---|
274 | template <class T> |
---|
275 | struct DefCardinalityMap |
---|
276 | : public MaxCardinalitySearch<Graph, CapacityMap, |
---|
277 | DefCardinalityMapTraits<T> > { |
---|
278 | typedef MaxCardinalitySearch<Graph, CapacityMap, |
---|
279 | DefCardinalityMapTraits<T> > Create; |
---|
280 | }; |
---|
281 | |
---|
282 | template <class T> |
---|
283 | struct DefProcessedMapTraits : public Traits { |
---|
284 | typedef T ProcessedMap; |
---|
285 | static ProcessedMap *createProcessedMap(const Graph &) { |
---|
286 | throw UninitializedParameter(); |
---|
287 | } |
---|
288 | }; |
---|
289 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
290 | /// ProcessedMap type |
---|
291 | /// |
---|
292 | /// \ref named-templ-param "Named parameter" for setting ProcessedMap type |
---|
293 | /// |
---|
294 | template <class T> |
---|
295 | struct DefProcessedMap |
---|
296 | : public MaxCardinalitySearch<Graph, CapacityMap, |
---|
297 | DefProcessedMapTraits<T> > { |
---|
298 | typedef MaxCardinalitySearch<Graph, CapacityMap, |
---|
299 | DefProcessedMapTraits<T> > Create; |
---|
300 | }; |
---|
301 | |
---|
302 | template <class H, class CR> |
---|
303 | struct DefHeapTraits : public Traits { |
---|
304 | typedef CR HeapCrossRef; |
---|
305 | typedef H Heap; |
---|
306 | static HeapCrossRef *createHeapCrossRef(const Graph &) { |
---|
307 | throw UninitializedParameter(); |
---|
308 | } |
---|
309 | static Heap *createHeap(HeapCrossRef &) { |
---|
310 | throw UninitializedParameter(); |
---|
311 | } |
---|
312 | }; |
---|
313 | /// \brief \ref named-templ-param "Named parameter" for setting heap |
---|
314 | /// and cross reference type |
---|
315 | /// |
---|
316 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
317 | /// reference type |
---|
318 | template <class H, class CR = typename Graph::template NodeMap<int> > |
---|
319 | struct DefHeap |
---|
320 | : public MaxCardinalitySearch<Graph, CapacityMap, |
---|
321 | DefHeapTraits<H, CR> > { |
---|
322 | typedef MaxCardinalitySearch< Graph, CapacityMap, |
---|
323 | DefHeapTraits<H, CR> > Create; |
---|
324 | }; |
---|
325 | |
---|
326 | template <class H, class CR> |
---|
327 | struct DefStandardHeapTraits : public Traits { |
---|
328 | typedef CR HeapCrossRef; |
---|
329 | typedef H Heap; |
---|
330 | static HeapCrossRef *createHeapCrossRef(const Graph &graph) { |
---|
331 | return new HeapCrossRef(graph); |
---|
332 | } |
---|
333 | static Heap *createHeap(HeapCrossRef &crossref) { |
---|
334 | return new Heap(crossref); |
---|
335 | } |
---|
336 | }; |
---|
337 | |
---|
338 | /// \brief \ref named-templ-param "Named parameter" for setting heap and |
---|
339 | /// cross reference type with automatic allocation |
---|
340 | /// |
---|
341 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
342 | /// reference type. It can allocate the heap and the cross reference |
---|
343 | /// object if the cross reference's constructor waits for the graph as |
---|
344 | /// parameter and the heap's constructor waits for the cross reference. |
---|
345 | template <class H, class CR = typename Graph::template NodeMap<int> > |
---|
346 | struct DefStandardHeap |
---|
347 | : public MaxCardinalitySearch<Graph, CapacityMap, |
---|
348 | DefStandardHeapTraits<H, CR> > { |
---|
349 | typedef MaxCardinalitySearch<Graph, CapacityMap, |
---|
350 | DefStandardHeapTraits<H, CR> > |
---|
351 | Create; |
---|
352 | }; |
---|
353 | |
---|
354 | ///@} |
---|
355 | |
---|
356 | |
---|
357 | protected: |
---|
358 | |
---|
359 | MaxCardinalitySearch() {} |
---|
360 | |
---|
361 | public: |
---|
362 | |
---|
363 | /// \brief Constructor. |
---|
364 | /// |
---|
365 | ///\param _graph the graph the algorithm will run on. |
---|
366 | ///\param _capacity the capacity map used by the algorithm. |
---|
367 | MaxCardinalitySearch(const Graph& graph, const CapacityMap& capacity) : |
---|
368 | _graph(&graph), _capacity(&capacity), |
---|
369 | _cardinality(0), local_cardinality(false), |
---|
370 | _processed(0), local_processed(false), |
---|
371 | _heap_cross_ref(0), local_heap_cross_ref(false), |
---|
372 | _heap(0), local_heap(false) |
---|
373 | { } |
---|
374 | |
---|
375 | /// \brief Destructor. |
---|
376 | ~MaxCardinalitySearch() { |
---|
377 | if(local_cardinality) delete _cardinality; |
---|
378 | if(local_processed) delete _processed; |
---|
379 | if(local_heap_cross_ref) delete _heap_cross_ref; |
---|
380 | if(local_heap) delete _heap; |
---|
381 | } |
---|
382 | |
---|
383 | /// \brief Sets the capacity map. |
---|
384 | /// |
---|
385 | /// Sets the capacity map. |
---|
386 | /// \return <tt> (*this) </tt> |
---|
387 | MaxCardinalitySearch &capacityMap(const CapacityMap &m) { |
---|
388 | _capacity = &m; |
---|
389 | return *this; |
---|
390 | } |
---|
391 | |
---|
392 | /// \brief Sets the map storing the cardinalities calculated by the |
---|
393 | /// algorithm. |
---|
394 | /// |
---|
395 | /// Sets the map storing the cardinalities calculated by the algorithm. |
---|
396 | /// If you don't use this function before calling \ref run(), |
---|
397 | /// it will allocate one. The destuctor deallocates this |
---|
398 | /// automatically allocated map, of course. |
---|
399 | /// \return <tt> (*this) </tt> |
---|
400 | MaxCardinalitySearch &cardinalityMap(CardinalityMap &m) { |
---|
401 | if(local_cardinality) { |
---|
402 | delete _cardinality; |
---|
403 | local_cardinality=false; |
---|
404 | } |
---|
405 | _cardinality = &m; |
---|
406 | return *this; |
---|
407 | } |
---|
408 | |
---|
409 | /// \brief Sets the map storing the processed nodes. |
---|
410 | /// |
---|
411 | /// Sets the map storing the processed nodes. |
---|
412 | /// If you don't use this function before calling \ref run(), |
---|
413 | /// it will allocate one. The destuctor deallocates this |
---|
414 | /// automatically allocated map, of course. |
---|
415 | /// \return <tt> (*this) </tt> |
---|
416 | MaxCardinalitySearch &processedMap(ProcessedMap &m) |
---|
417 | { |
---|
418 | if(local_processed) { |
---|
419 | delete _processed; |
---|
420 | local_processed=false; |
---|
421 | } |
---|
422 | _processed = &m; |
---|
423 | return *this; |
---|
424 | } |
---|
425 | |
---|
426 | /// \brief Sets the heap and the cross reference used by algorithm. |
---|
427 | /// |
---|
428 | /// Sets the heap and the cross reference used by algorithm. |
---|
429 | /// If you don't use this function before calling \ref run(), |
---|
430 | /// it will allocate one. The destuctor deallocates this |
---|
431 | /// automatically allocated map, of course. |
---|
432 | /// \return <tt> (*this) </tt> |
---|
433 | MaxCardinalitySearch &heap(Heap& heap, HeapCrossRef &crossRef) { |
---|
434 | if(local_heap_cross_ref) { |
---|
435 | delete _heap_cross_ref; |
---|
436 | local_heap_cross_ref = false; |
---|
437 | } |
---|
438 | _heap_cross_ref = &crossRef; |
---|
439 | if(local_heap) { |
---|
440 | delete _heap; |
---|
441 | local_heap = false; |
---|
442 | } |
---|
443 | _heap = &heap; |
---|
444 | return *this; |
---|
445 | } |
---|
446 | |
---|
447 | private: |
---|
448 | |
---|
449 | typedef typename Graph::Node Node; |
---|
450 | typedef typename Graph::NodeIt NodeIt; |
---|
451 | typedef typename Graph::Edge Edge; |
---|
452 | typedef typename Graph::InEdgeIt InEdgeIt; |
---|
453 | |
---|
454 | void create_maps() { |
---|
455 | if(!_cardinality) { |
---|
456 | local_cardinality = true; |
---|
457 | _cardinality = Traits::createCardinalityMap(*_graph); |
---|
458 | } |
---|
459 | if(!_processed) { |
---|
460 | local_processed = true; |
---|
461 | _processed = Traits::createProcessedMap(*_graph); |
---|
462 | } |
---|
463 | if (!_heap_cross_ref) { |
---|
464 | local_heap_cross_ref = true; |
---|
465 | _heap_cross_ref = Traits::createHeapCrossRef(*_graph); |
---|
466 | } |
---|
467 | if (!_heap) { |
---|
468 | local_heap = true; |
---|
469 | _heap = Traits::createHeap(*_heap_cross_ref); |
---|
470 | } |
---|
471 | } |
---|
472 | |
---|
473 | void finalizeNodeData(Node node, Value capacity) { |
---|
474 | _processed->set(node, true); |
---|
475 | _cardinality->set(node, capacity); |
---|
476 | } |
---|
477 | |
---|
478 | public: |
---|
479 | /// \name Execution control |
---|
480 | /// The simplest way to execute the algorithm is to use |
---|
481 | /// one of the member functions called \c run(...). |
---|
482 | /// \n |
---|
483 | /// If you need more control on the execution, |
---|
484 | /// first you must call \ref init(), then you can add several source nodes |
---|
485 | /// with \ref addSource(). |
---|
486 | /// Finally \ref start() will perform the actual path |
---|
487 | /// computation. |
---|
488 | |
---|
489 | ///@{ |
---|
490 | |
---|
491 | /// \brief Initializes the internal data structures. |
---|
492 | /// |
---|
493 | /// Initializes the internal data structures. |
---|
494 | void init() { |
---|
495 | create_maps(); |
---|
496 | _heap->clear(); |
---|
497 | for (NodeIt it(*_graph) ; it != INVALID ; ++it) { |
---|
498 | _processed->set(it, false); |
---|
499 | _heap_cross_ref->set(it, Heap::PRE_HEAP); |
---|
500 | } |
---|
501 | } |
---|
502 | |
---|
503 | /// \brief Adds a new source node. |
---|
504 | /// |
---|
505 | /// Adds a new source node to the priority heap. |
---|
506 | /// |
---|
507 | /// It checks if the node has not yet been added to the heap. |
---|
508 | void addSource(Node source, Value capacity = 0) { |
---|
509 | if(_heap->state(source) == Heap::PRE_HEAP) { |
---|
510 | _heap->push(source, capacity); |
---|
511 | } |
---|
512 | } |
---|
513 | |
---|
514 | /// \brief Processes the next node in the priority heap |
---|
515 | /// |
---|
516 | /// Processes the next node in the priority heap. |
---|
517 | /// |
---|
518 | /// \return The processed node. |
---|
519 | /// |
---|
520 | /// \warning The priority heap must not be empty! |
---|
521 | Node processNextNode() { |
---|
522 | Node node = _heap->top(); |
---|
523 | finalizeNodeData(node, _heap->prio()); |
---|
524 | _heap->pop(); |
---|
525 | |
---|
526 | for (InEdgeIt it(*_graph, node); it != INVALID; ++it) { |
---|
527 | Node source = _graph->source(it); |
---|
528 | switch (_heap->state(source)) { |
---|
529 | case Heap::PRE_HEAP: |
---|
530 | _heap->push(source, (*_capacity)[it]); |
---|
531 | break; |
---|
532 | case Heap::IN_HEAP: |
---|
533 | _heap->decrease(source, (*_heap)[source] + (*_capacity)[it]); |
---|
534 | break; |
---|
535 | case Heap::POST_HEAP: |
---|
536 | break; |
---|
537 | } |
---|
538 | } |
---|
539 | return node; |
---|
540 | } |
---|
541 | |
---|
542 | /// \brief Next node to be processed. |
---|
543 | /// |
---|
544 | /// Next node to be processed. |
---|
545 | /// |
---|
546 | /// \return The next node to be processed or INVALID if the |
---|
547 | /// priority heap is empty. |
---|
548 | Node nextNode() { |
---|
549 | return _heap->empty() ? _heap->top() : INVALID; |
---|
550 | } |
---|
551 | |
---|
552 | /// \brief Returns \c false if there are nodes |
---|
553 | /// to be processed in the priority heap |
---|
554 | /// |
---|
555 | /// Returns \c false if there are nodes |
---|
556 | /// to be processed in the priority heap |
---|
557 | bool emptyQueue() { return _heap->empty(); } |
---|
558 | /// \brief Returns the number of the nodes to be processed |
---|
559 | /// in the priority heap |
---|
560 | /// |
---|
561 | /// Returns the number of the nodes to be processed in the priority heap |
---|
562 | int queueSize() { return _heap->size(); } |
---|
563 | |
---|
564 | /// \brief Executes the algorithm. |
---|
565 | /// |
---|
566 | /// Executes the algorithm. |
---|
567 | /// |
---|
568 | ///\pre init() must be called and at least one node should be added |
---|
569 | /// with addSource() before using this function. |
---|
570 | /// |
---|
571 | /// This method runs the Maximum Cardinality Search algorithm from the |
---|
572 | /// source node(s). |
---|
573 | void start() { |
---|
574 | while ( !_heap->empty() ) processNextNode(); |
---|
575 | } |
---|
576 | |
---|
577 | /// \brief Executes the algorithm until \c dest is reached. |
---|
578 | /// |
---|
579 | /// Executes the algorithm until \c dest is reached. |
---|
580 | /// |
---|
581 | /// \pre init() must be called and at least one node should be added |
---|
582 | /// with addSource() before using this function. |
---|
583 | /// |
---|
584 | /// This method runs the %MaxCardinalitySearch algorithm from the source |
---|
585 | /// nodes. |
---|
586 | void start(Node dest) { |
---|
587 | while ( !_heap->empty() && _heap->top()!=dest ) processNextNode(); |
---|
588 | if ( !_heap->empty() ) finalizeNodeData(_heap->top(), _heap->prio()); |
---|
589 | } |
---|
590 | |
---|
591 | /// \brief Executes the algorithm until a condition is met. |
---|
592 | /// |
---|
593 | /// Executes the algorithm until a condition is met. |
---|
594 | /// |
---|
595 | /// \pre init() must be called and at least one node should be added |
---|
596 | /// with addSource() before using this function. |
---|
597 | /// |
---|
598 | /// \param nm must be a bool (or convertible) node map. The algorithm |
---|
599 | /// will stop when it reaches a node \c v with <tt>nm[v]==true</tt>. |
---|
600 | template <typename NodeBoolMap> |
---|
601 | void start(const NodeBoolMap &nm) { |
---|
602 | while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode(); |
---|
603 | if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio()); |
---|
604 | } |
---|
605 | |
---|
606 | /// \brief Runs the maximal cardinality search algorithm from node \c s. |
---|
607 | /// |
---|
608 | /// This method runs the %MaxCardinalitySearch algorithm from a root |
---|
609 | /// node \c s. |
---|
610 | /// |
---|
611 | ///\note d.run(s) is just a shortcut of the following code. |
---|
612 | ///\code |
---|
613 | /// d.init(); |
---|
614 | /// d.addSource(s); |
---|
615 | /// d.start(); |
---|
616 | ///\endcode |
---|
617 | void run(Node s) { |
---|
618 | init(); |
---|
619 | addSource(s); |
---|
620 | start(); |
---|
621 | } |
---|
622 | |
---|
623 | /// \brief Runs the maximal cardinality search algorithm for the |
---|
624 | /// whole graph. |
---|
625 | /// |
---|
626 | /// This method runs the %MaxCardinalitySearch algorithm from all |
---|
627 | /// unprocessed node of the graph. |
---|
628 | /// |
---|
629 | ///\note d.run(s) is just a shortcut of the following code. |
---|
630 | ///\code |
---|
631 | /// d.init(); |
---|
632 | /// for (NodeIt it(graph); it != INVALID; ++it) { |
---|
633 | /// if (!d.reached(it)) { |
---|
634 | /// d.addSource(s); |
---|
635 | /// d.start(); |
---|
636 | /// } |
---|
637 | /// } |
---|
638 | ///\endcode |
---|
639 | void run() { |
---|
640 | init(); |
---|
641 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
---|
642 | if (!reached(it)) { |
---|
643 | addSource(it); |
---|
644 | start(); |
---|
645 | } |
---|
646 | } |
---|
647 | } |
---|
648 | |
---|
649 | ///@} |
---|
650 | |
---|
651 | /// \name Query Functions |
---|
652 | /// The result of the maximum cardinality search algorithm can be |
---|
653 | /// obtained using these functions. |
---|
654 | /// \n |
---|
655 | /// Before the use of these functions, either run() or start() must be |
---|
656 | /// called. |
---|
657 | |
---|
658 | ///@{ |
---|
659 | |
---|
660 | /// \brief The cardinality of a node. |
---|
661 | /// |
---|
662 | /// Returns the cardinality of a node. |
---|
663 | /// \pre \ref run() must be called before using this function. |
---|
664 | /// \warning If node \c v in unreachable from the root the return value |
---|
665 | /// of this funcion is undefined. |
---|
666 | Value cardinality(Node node) const { return (*_cardinality)[node]; } |
---|
667 | |
---|
668 | /// \brief Returns a reference to the NodeMap of cardinalities. |
---|
669 | /// |
---|
670 | /// Returns a reference to the NodeMap of cardinalities. \pre \ref run() |
---|
671 | /// must be called before using this function. |
---|
672 | const CardinalityMap &cardinalityMap() const { return *_cardinality;} |
---|
673 | |
---|
674 | /// \brief Checks if a node is reachable from the root. |
---|
675 | /// |
---|
676 | /// Returns \c true if \c v is reachable from the root. |
---|
677 | /// \warning The source nodes are inditated as unreached. |
---|
678 | /// \pre \ref run() must be called before using this function. |
---|
679 | bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; } |
---|
680 | |
---|
681 | /// \brief Checks if a node is processed. |
---|
682 | /// |
---|
683 | /// Returns \c true if \c v is processed, i.e. the shortest |
---|
684 | /// path to \c v has already found. |
---|
685 | /// \pre \ref run() must be called before using this function. |
---|
686 | bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; } |
---|
687 | |
---|
688 | ///@} |
---|
689 | }; |
---|
690 | |
---|
691 | /// \brief Default traits class of MinimumCut class. |
---|
692 | /// |
---|
693 | /// Default traits class of MinimumCut class. |
---|
694 | /// \param Graph Graph type. |
---|
695 | /// \param CapacityMap Type of length map. |
---|
696 | template <typename _Graph, typename _CapacityMap> |
---|
697 | struct MinimumCutDefaultTraits { |
---|
698 | /// \brief The type of the capacity of the edges. |
---|
699 | typedef typename _CapacityMap::Value Value; |
---|
700 | |
---|
701 | /// The graph type the algorithm runs on. |
---|
702 | typedef _Graph Graph; |
---|
703 | |
---|
704 | /// The WorkGraph type which is an EraseableGraph |
---|
705 | typedef ListUGraph WorkGraph; |
---|
706 | |
---|
707 | /// \brief Instantiates a WorkGraph. |
---|
708 | /// |
---|
709 | /// This function instantiates a \ref WorkGraph. |
---|
710 | static WorkGraph *createWorkGraph() { |
---|
711 | return new WorkGraph(); |
---|
712 | } |
---|
713 | |
---|
714 | /// \brief The type of the map that stores the edge capacities. |
---|
715 | /// |
---|
716 | /// The type of the map that stores the edge capacities. |
---|
717 | /// It must meet the \ref concept::ReadMap "ReadMap" concept. |
---|
718 | typedef _CapacityMap CapacityMap; |
---|
719 | |
---|
720 | /// \brief Instantiates a CapacityMap. |
---|
721 | /// |
---|
722 | /// This function instantiates a \ref CapacityMap. |
---|
723 | #ifdef DOXYGEN |
---|
724 | static CapacityMap *createCapacityMap(const Graph& graph) |
---|
725 | #else |
---|
726 | static CapacityMap *createCapacityMap(const Graph&) |
---|
727 | #endif |
---|
728 | { |
---|
729 | throw UninitializedParameter(); |
---|
730 | } |
---|
731 | |
---|
732 | /// \brief The WorkCapacityMap type |
---|
733 | /// |
---|
734 | /// The type of the map that stores the working edge capacities. |
---|
735 | typedef WorkGraph::UEdgeMap<Value> WorkCapacityMap; |
---|
736 | |
---|
737 | /// \brief Instantiates a WorkCapacityMap. |
---|
738 | /// |
---|
739 | /// This function instantiates a \ref WorkCapacityMap. |
---|
740 | static WorkCapacityMap *createWorkCapacityMap(const WorkGraph& graph) { |
---|
741 | return new WorkCapacityMap(graph); |
---|
742 | } |
---|
743 | |
---|
744 | /// \brief The cross reference type used by heap. |
---|
745 | /// |
---|
746 | /// The cross reference type used by heap. |
---|
747 | /// Usually it is \c Graph::NodeMap<int>. |
---|
748 | typedef WorkGraph::NodeMap<int> HeapCrossRef; |
---|
749 | |
---|
750 | /// \brief Instantiates a HeapCrossRef. |
---|
751 | /// |
---|
752 | /// This function instantiates a \ref HeapCrossRef. |
---|
753 | /// \param graph is the graph, to which we would like to define the |
---|
754 | /// HeapCrossRef. |
---|
755 | static HeapCrossRef *createHeapCrossRef(const WorkGraph &graph) { |
---|
756 | return new HeapCrossRef(graph); |
---|
757 | } |
---|
758 | |
---|
759 | /// \brief The heap type used by MinimumCut algorithm. |
---|
760 | /// |
---|
761 | /// The heap type used by MinimumCut algorithm. It should |
---|
762 | /// maximalize the priorities and the heap's key type is |
---|
763 | /// the work graph's node. |
---|
764 | /// |
---|
765 | /// \sa BinHeap |
---|
766 | /// \sa MinimumCut |
---|
767 | typedef typename _minimum_cut_bits |
---|
768 | ::HeapSelector<CapacityMap> |
---|
769 | ::template Selector<typename WorkGraph::Node, Value, HeapCrossRef> |
---|
770 | ::Heap Heap; |
---|
771 | |
---|
772 | /// \brief Instantiates a Heap. |
---|
773 | /// |
---|
774 | /// This function instantiates a \ref Heap. |
---|
775 | /// \param crossref The cross reference of the heap. |
---|
776 | static Heap *createHeap(HeapCrossRef& crossref) { |
---|
777 | return new Heap(crossref); |
---|
778 | } |
---|
779 | |
---|
780 | /// \brief Map from the WorkGraph's node type to the Graph's node type. |
---|
781 | /// |
---|
782 | /// Map from the WorkGraph's node type to the Graph's node type. |
---|
783 | typedef typename WorkGraph |
---|
784 | ::template NodeMap<typename Graph::Node> NodeRefMap; |
---|
785 | |
---|
786 | /// \brief Instantiates a NodeRefMap. |
---|
787 | /// |
---|
788 | /// This function instantiates a \ref NodeRefMap. |
---|
789 | static NodeRefMap *createNodeRefMap(const WorkGraph& graph) { |
---|
790 | return new NodeRefMap(graph); |
---|
791 | } |
---|
792 | |
---|
793 | /// \brief Map from the Graph's node type to the Graph's node type. |
---|
794 | /// |
---|
795 | /// Map from the Graph's node type to the Graph's node type. |
---|
796 | typedef typename Graph |
---|
797 | ::template NodeMap<typename Graph::Node> ListRefMap; |
---|
798 | |
---|
799 | /// \brief Instantiates a ListRefMap. |
---|
800 | /// |
---|
801 | /// This function instantiates a \ref ListRefMap. |
---|
802 | static ListRefMap *createListRefMap(const Graph& graph) { |
---|
803 | return new ListRefMap(graph); |
---|
804 | } |
---|
805 | |
---|
806 | |
---|
807 | }; |
---|
808 | |
---|
809 | namespace _minimum_cut_bits { |
---|
810 | template <typename _Key> |
---|
811 | class LastTwoMap { |
---|
812 | public: |
---|
813 | typedef _Key Key; |
---|
814 | typedef bool Value; |
---|
815 | |
---|
816 | LastTwoMap(int _num) : num(_num) {} |
---|
817 | void set(const Key& key, bool val) { |
---|
818 | if (!val) return; |
---|
819 | --num; |
---|
820 | if (num > 1) return; |
---|
821 | keys[num] = key; |
---|
822 | } |
---|
823 | |
---|
824 | Key operator[](int index) const { return keys[index]; } |
---|
825 | private: |
---|
826 | Key keys[2]; |
---|
827 | int num; |
---|
828 | }; |
---|
829 | } |
---|
830 | |
---|
831 | /// \ingroup topology |
---|
832 | /// |
---|
833 | /// \brief Calculates the minimum cut in an undirected graph. |
---|
834 | /// |
---|
835 | /// Calculates the minimum cut in an undirected graph. |
---|
836 | /// The algorithm separates the graph's nodes to two partitions with the |
---|
837 | /// minimum sum of edge capacities between the two partitions. The |
---|
838 | /// algorithm can be used to test the network reliability specifically |
---|
839 | /// to test how many links have to be destroyed in the network to split it |
---|
840 | /// at least two distinict subnetwork. |
---|
841 | /// |
---|
842 | /// The complexity of the algorithm is O(n*e*log(n)) but with Fibonacci |
---|
843 | /// heap it can be decreased to O(n*e+n^2*log(n)). When the neutral capacity |
---|
844 | /// map is used then it uses LinearHeap which results O(n*e) time complexity. |
---|
845 | #ifdef DOXYGEN |
---|
846 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
---|
847 | #else |
---|
848 | template <typename _Graph = ListUGraph, |
---|
849 | typename _CapacityMap = typename _Graph::template UEdgeMap<int>, |
---|
850 | typename _Traits = MinimumCutDefaultTraits<_Graph, _CapacityMap> > |
---|
851 | #endif |
---|
852 | class MinimumCut { |
---|
853 | public: |
---|
854 | /// \brief \ref Exception for uninitialized parameters. |
---|
855 | /// |
---|
856 | /// This error represents problems in the initialization |
---|
857 | /// of the parameters of the algorithms. |
---|
858 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
859 | public: |
---|
860 | virtual const char* exceptionName() const { |
---|
861 | return "lemon::MinimumCut::UninitializedParameter"; |
---|
862 | } |
---|
863 | }; |
---|
864 | |
---|
865 | |
---|
866 | private: |
---|
867 | |
---|
868 | typedef _Traits Traits; |
---|
869 | /// The type of the underlying graph. |
---|
870 | typedef typename Traits::Graph Graph; |
---|
871 | |
---|
872 | /// The type of the capacity of the edges. |
---|
873 | typedef typename Traits::CapacityMap::Value Value; |
---|
874 | /// The type of the map that stores the edge capacities. |
---|
875 | typedef typename Traits::CapacityMap CapacityMap; |
---|
876 | /// The type of the work graph |
---|
877 | typedef typename Traits::WorkGraph WorkGraph; |
---|
878 | /// The type of the work capacity map |
---|
879 | typedef typename Traits::WorkCapacityMap WorkCapacityMap; |
---|
880 | /// The cross reference type used for the current heap. |
---|
881 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
---|
882 | /// The heap type used by the max cardinality algorithm. |
---|
883 | typedef typename Traits::Heap Heap; |
---|
884 | /// The node refrefernces between the original and work graph type. |
---|
885 | typedef typename Traits::NodeRefMap NodeRefMap; |
---|
886 | /// The list node refrefernces in the original graph type. |
---|
887 | typedef typename Traits::ListRefMap ListRefMap; |
---|
888 | |
---|
889 | public: |
---|
890 | |
---|
891 | ///\name Named template parameters |
---|
892 | |
---|
893 | ///@{ |
---|
894 | |
---|
895 | struct DefNeutralCapacityTraits : public Traits { |
---|
896 | typedef ConstMap<typename Graph::UEdge, Const<int, 1> > CapacityMap; |
---|
897 | static CapacityMap *createCapacityMap(const Graph&) { |
---|
898 | return new CapacityMap(); |
---|
899 | } |
---|
900 | }; |
---|
901 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
902 | /// the capacity type to constMap<UEdge, int, 1>() |
---|
903 | /// |
---|
904 | /// \ref named-templ-param "Named parameter" for setting |
---|
905 | /// the capacity type to constMap<UEdge, int, 1>() |
---|
906 | struct DefNeutralCapacity |
---|
907 | : public MinimumCut<Graph, CapacityMap, DefNeutralCapacityTraits> { |
---|
908 | typedef MinimumCut<Graph, CapacityMap, DefNeutralCapacityTraits> Create; |
---|
909 | }; |
---|
910 | |
---|
911 | |
---|
912 | template <class H, class CR> |
---|
913 | struct DefHeapTraits : public Traits { |
---|
914 | typedef CR HeapCrossRef; |
---|
915 | typedef H Heap; |
---|
916 | static HeapCrossRef *createHeapCrossRef(const WorkGraph &) { |
---|
917 | throw UninitializedParameter(); |
---|
918 | } |
---|
919 | static Heap *createHeap(HeapCrossRef &) { |
---|
920 | throw UninitializedParameter(); |
---|
921 | } |
---|
922 | }; |
---|
923 | /// \brief \ref named-templ-param "Named parameter" for setting heap |
---|
924 | /// and cross reference type |
---|
925 | /// |
---|
926 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
927 | /// reference type |
---|
928 | template <class H, class CR = typename Graph::template NodeMap<int> > |
---|
929 | struct DefHeap |
---|
930 | : public MinimumCut<Graph, CapacityMap, DefHeapTraits<H, CR> > { |
---|
931 | typedef MinimumCut< Graph, CapacityMap, DefHeapTraits<H, CR> > Create; |
---|
932 | }; |
---|
933 | |
---|
934 | template <class H, class CR> |
---|
935 | struct DefStandardHeapTraits : public Traits { |
---|
936 | typedef CR HeapCrossRef; |
---|
937 | typedef H Heap; |
---|
938 | static HeapCrossRef *createHeapCrossRef(const WorkGraph &graph) { |
---|
939 | return new HeapCrossRef(graph); |
---|
940 | } |
---|
941 | static Heap *createHeap(HeapCrossRef &crossref) { |
---|
942 | return new Heap(crossref); |
---|
943 | } |
---|
944 | }; |
---|
945 | |
---|
946 | /// \brief \ref named-templ-param "Named parameter" for setting heap and |
---|
947 | /// cross reference type with automatic allocation |
---|
948 | /// |
---|
949 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
950 | /// reference type. It can allocate the heap and the cross reference |
---|
951 | /// object if the cross reference's constructor waits for the graph as |
---|
952 | /// parameter and the heap's constructor waits for the cross reference. |
---|
953 | template <class H, class CR = typename Graph::template NodeMap<int> > |
---|
954 | struct DefStandardHeap |
---|
955 | : public MinimumCut<Graph, CapacityMap, DefStandardHeapTraits<H, CR> > { |
---|
956 | typedef MinimumCut<Graph, CapacityMap, DefStandardHeapTraits<H, CR> > |
---|
957 | Create; |
---|
958 | }; |
---|
959 | |
---|
960 | ///@} |
---|
961 | |
---|
962 | |
---|
963 | private: |
---|
964 | /// Pointer to the underlying graph. |
---|
965 | const Graph *_graph; |
---|
966 | /// Pointer to the capacity map |
---|
967 | const CapacityMap *_capacity; |
---|
968 | /// \brief Indicates if \ref _capacity is locally allocated |
---|
969 | /// (\c true) or not. |
---|
970 | bool local_capacity; |
---|
971 | |
---|
972 | /// Pointer to the work graph. |
---|
973 | WorkGraph *_work_graph; |
---|
974 | /// \brief Indicates if \ref _work_graph is locally allocated |
---|
975 | /// (\c true) or not. |
---|
976 | bool local_work_graph; |
---|
977 | /// Pointer to the work capacity map |
---|
978 | WorkCapacityMap *_work_capacity; |
---|
979 | /// \brief Indicates if \ref _work_capacity is locally allocated |
---|
980 | /// (\c true) or not. |
---|
981 | bool local_work_capacity; |
---|
982 | /// Pointer to the heap cross references. |
---|
983 | HeapCrossRef *_heap_cross_ref; |
---|
984 | /// \brief Indicates if \ref _heap_cross_ref is locally allocated |
---|
985 | /// (\c true) or not. |
---|
986 | bool local_heap_cross_ref; |
---|
987 | /// Pointer to the heap. |
---|
988 | Heap *_heap; |
---|
989 | /// Indicates if \ref _heap is locally allocated (\c true) or not. |
---|
990 | bool local_heap; |
---|
991 | |
---|
992 | /// The minimum cut value. |
---|
993 | Value _minimum_cut; |
---|
994 | /// The number of the nodes of the work graph. |
---|
995 | int _node_num; |
---|
996 | /// The first and last node of the min cut in the next list; |
---|
997 | typename Graph::Node _first_node, _last_node; |
---|
998 | |
---|
999 | /// \brief The first and last element in the list associated |
---|
1000 | /// to the work graph node. |
---|
1001 | NodeRefMap *_first, *_last; |
---|
1002 | /// \brief The next node in the node lists. |
---|
1003 | ListRefMap *_next; |
---|
1004 | |
---|
1005 | void create_structures() { |
---|
1006 | if (!_capacity) { |
---|
1007 | local_capacity = true; |
---|
1008 | _capacity = Traits::createCapacityMap(*_graph); |
---|
1009 | } |
---|
1010 | if(!_work_graph) { |
---|
1011 | local_work_graph = true; |
---|
1012 | _work_graph = Traits::createWorkGraph(); |
---|
1013 | } |
---|
1014 | if(!_work_capacity) { |
---|
1015 | local_work_capacity = true; |
---|
1016 | _work_capacity = Traits::createWorkCapacityMap(*_work_graph); |
---|
1017 | } |
---|
1018 | |
---|
1019 | _first = Traits::createNodeRefMap(*_work_graph); |
---|
1020 | _last = Traits::createNodeRefMap(*_work_graph); |
---|
1021 | |
---|
1022 | _next = Traits::createListRefMap(*_graph); |
---|
1023 | |
---|
1024 | typename Graph::template NodeMap<typename WorkGraph::Node> ref(*_graph); |
---|
1025 | |
---|
1026 | for (typename Graph::NodeIt it(*_graph); it != INVALID; ++it) { |
---|
1027 | _next->set(it, INVALID); |
---|
1028 | typename WorkGraph::Node node = _work_graph->addNode(); |
---|
1029 | _first->set(node, it); |
---|
1030 | _last->set(node, it); |
---|
1031 | ref.set(it, node); |
---|
1032 | } |
---|
1033 | |
---|
1034 | for (typename Graph::UEdgeIt it(*_graph); it != INVALID; ++it) { |
---|
1035 | if (_graph->source(it) == _graph->target(it)) continue; |
---|
1036 | typename WorkGraph::UEdge uedge = |
---|
1037 | _work_graph->addEdge(ref[_graph->source(it)], |
---|
1038 | ref[_graph->target(it)]); |
---|
1039 | _work_capacity->set(uedge, (*_capacity)[it]); |
---|
1040 | |
---|
1041 | } |
---|
1042 | |
---|
1043 | if (!_heap_cross_ref) { |
---|
1044 | local_heap_cross_ref = true; |
---|
1045 | _heap_cross_ref = Traits::createHeapCrossRef(*_work_graph); |
---|
1046 | } |
---|
1047 | if (!_heap) { |
---|
1048 | local_heap = true; |
---|
1049 | _heap = Traits::createHeap(*_heap_cross_ref); |
---|
1050 | } |
---|
1051 | } |
---|
1052 | |
---|
1053 | public : |
---|
1054 | |
---|
1055 | typedef MinimumCut Create; |
---|
1056 | |
---|
1057 | |
---|
1058 | /// \brief Constructor. |
---|
1059 | /// |
---|
1060 | ///\param graph the graph the algorithm will run on. |
---|
1061 | ///\param capacity the capacity map used by the algorithm. |
---|
1062 | MinimumCut(const Graph& graph, const CapacityMap& capacity) |
---|
1063 | : _graph(&graph), |
---|
1064 | _capacity(&capacity), local_capacity(false), |
---|
1065 | _work_graph(0), local_work_graph(false), |
---|
1066 | _work_capacity(0), local_work_capacity(false), |
---|
1067 | _heap_cross_ref(0), local_heap_cross_ref(false), |
---|
1068 | _heap(0), local_heap(false), |
---|
1069 | _first(0), _last(0), _next(0) {} |
---|
1070 | |
---|
1071 | /// \brief Constructor. |
---|
1072 | /// |
---|
1073 | /// This constructor can be used only when the Traits class |
---|
1074 | /// defines how can we instantiate a local capacity map. |
---|
1075 | /// If the DefNeutralCapacity used the algorithm automatically |
---|
1076 | /// construct the capacity map. |
---|
1077 | /// |
---|
1078 | ///\param graph the graph the algorithm will run on. |
---|
1079 | MinimumCut(const Graph& graph) |
---|
1080 | : _graph(&graph), |
---|
1081 | _capacity(0), local_capacity(false), |
---|
1082 | _work_graph(0), local_work_graph(false), |
---|
1083 | _work_capacity(0), local_work_capacity(false), |
---|
1084 | _heap_cross_ref(0), local_heap_cross_ref(false), |
---|
1085 | _heap(0), local_heap(false), |
---|
1086 | _first(0), _last(0), _next(0) {} |
---|
1087 | |
---|
1088 | /// \brief Destructor. |
---|
1089 | /// |
---|
1090 | /// Destructor. |
---|
1091 | ~MinimumCut() { |
---|
1092 | if (local_heap) delete _heap; |
---|
1093 | if (local_heap_cross_ref) delete _heap_cross_ref; |
---|
1094 | if (_first) delete _first; |
---|
1095 | if (_last) delete _last; |
---|
1096 | if (_next) delete _next; |
---|
1097 | if (local_work_capacity) delete _work_capacity; |
---|
1098 | if (local_work_graph) delete _work_graph; |
---|
1099 | if (local_capacity) delete _capacity; |
---|
1100 | } |
---|
1101 | |
---|
1102 | /// \brief Sets the heap and the cross reference used by algorithm. |
---|
1103 | /// |
---|
1104 | /// Sets the heap and the cross reference used by algorithm. |
---|
1105 | /// If you don't use this function before calling \ref run(), |
---|
1106 | /// it will allocate one. The destuctor deallocates this |
---|
1107 | /// automatically allocated heap and cross reference, of course. |
---|
1108 | /// \return <tt> (*this) </tt> |
---|
1109 | MinimumCut &heap(Heap& heap, HeapCrossRef &crossRef) |
---|
1110 | { |
---|
1111 | if (local_heap_cross_ref) { |
---|
1112 | delete _heap_cross_ref; |
---|
1113 | local_heap_cross_ref=false; |
---|
1114 | } |
---|
1115 | _heap_cross_ref = &crossRef; |
---|
1116 | if (local_heap) { |
---|
1117 | delete _heap; |
---|
1118 | local_heap=false; |
---|
1119 | } |
---|
1120 | _heap = &heap; |
---|
1121 | return *this; |
---|
1122 | } |
---|
1123 | |
---|
1124 | /// \brief Sets the work graph. |
---|
1125 | /// |
---|
1126 | /// Sets the work graph used by algorithm. |
---|
1127 | /// If you don't use this function before calling \ref run(), |
---|
1128 | /// it will allocate one. The destuctor deallocates this |
---|
1129 | /// automatically allocated graph, of course. |
---|
1130 | /// \return <tt> (*this) </tt> |
---|
1131 | MinimumCut &workGraph(WorkGraph& work_graph) |
---|
1132 | { |
---|
1133 | if(local_work_graph) { |
---|
1134 | delete _work_graph; |
---|
1135 | local_work_graph=false; |
---|
1136 | } |
---|
1137 | _work_graph = &work_graph; |
---|
1138 | return *this; |
---|
1139 | } |
---|
1140 | |
---|
1141 | /// \brief Sets the work capacity map. |
---|
1142 | /// |
---|
1143 | /// Sets the work capacity map used by algorithm. |
---|
1144 | /// If you don't use this function before calling \ref run(), |
---|
1145 | /// it will allocate one. The destuctor deallocates this |
---|
1146 | /// automatically allocated graph, of course. |
---|
1147 | /// \return <tt> (*this) </tt> |
---|
1148 | MinimumCut &workCapacityMap(WorkCapacityMap& work_capacity_map) |
---|
1149 | { |
---|
1150 | if(local_work_capacity) { |
---|
1151 | delete _work_capacity; |
---|
1152 | local_work_capacity=false; |
---|
1153 | } |
---|
1154 | _work_capacity = &work_capacity_map; |
---|
1155 | return *this; |
---|
1156 | } |
---|
1157 | |
---|
1158 | /// \name Execution control |
---|
1159 | /// The simplest way to execute the algorithm is to use |
---|
1160 | /// one of the member functions called \c run(). |
---|
1161 | /// \n |
---|
1162 | /// If you need more control on the execution, |
---|
1163 | /// first you must call \ref init() and then call the start() |
---|
1164 | /// or proper times the processNextPhase() member functions. |
---|
1165 | |
---|
1166 | ///@{ |
---|
1167 | |
---|
1168 | /// \brief Initializes the internal data structures. |
---|
1169 | /// |
---|
1170 | /// Initializes the internal data structures. |
---|
1171 | void init() { |
---|
1172 | create_structures(); |
---|
1173 | _first_node = _last_node = INVALID; |
---|
1174 | _node_num = countNodes(*_graph); |
---|
1175 | } |
---|
1176 | |
---|
1177 | /// \brief Processes the next phase |
---|
1178 | /// |
---|
1179 | /// Processes the next phase in the algorithm. The function |
---|
1180 | /// should be called countNodes(graph) - 1 times to get |
---|
1181 | /// surely the minimum cut in the graph. The |
---|
1182 | /// |
---|
1183 | ///\return %True when the algorithm finished. |
---|
1184 | bool processNextPhase() { |
---|
1185 | if (_node_num <= 1) return true; |
---|
1186 | using namespace _minimum_cut_bits; |
---|
1187 | |
---|
1188 | typedef typename WorkGraph::Node Node; |
---|
1189 | typedef typename WorkGraph::NodeIt NodeIt; |
---|
1190 | typedef typename WorkGraph::UEdge UEdge; |
---|
1191 | typedef typename WorkGraph::IncEdgeIt IncEdgeIt; |
---|
1192 | |
---|
1193 | typedef typename MaxCardinalitySearch<WorkGraph, WorkCapacityMap>:: |
---|
1194 | template DefHeap<Heap, HeapCrossRef>:: |
---|
1195 | template DefCardinalityMap<NullMap<Node, Value> >:: |
---|
1196 | template DefProcessedMap<LastTwoMap<Node> >:: |
---|
1197 | Create MaxCardinalitySearch; |
---|
1198 | |
---|
1199 | MaxCardinalitySearch mcs(*_work_graph, *_work_capacity); |
---|
1200 | for (NodeIt it(*_work_graph); it != INVALID; ++it) { |
---|
1201 | _heap_cross_ref->set(it, Heap::PRE_HEAP); |
---|
1202 | } |
---|
1203 | mcs.heap(*_heap, *_heap_cross_ref); |
---|
1204 | |
---|
1205 | LastTwoMap<Node> last_two_nodes(_node_num); |
---|
1206 | mcs.processedMap(last_two_nodes); |
---|
1207 | |
---|
1208 | NullMap<Node, Value> cardinality; |
---|
1209 | mcs.cardinalityMap(cardinality); |
---|
1210 | |
---|
1211 | mcs.run(); |
---|
1212 | |
---|
1213 | Node new_node = _work_graph->addNode(); |
---|
1214 | |
---|
1215 | typename WorkGraph::template NodeMap<UEdge> edges(*_work_graph, INVALID); |
---|
1216 | |
---|
1217 | Node first_node = last_two_nodes[0]; |
---|
1218 | Node second_node = last_two_nodes[1]; |
---|
1219 | |
---|
1220 | _next->set((*_last)[first_node], (*_first)[second_node]); |
---|
1221 | _first->set(new_node, (*_first)[first_node]); |
---|
1222 | _last->set(new_node, (*_last)[second_node]); |
---|
1223 | |
---|
1224 | Value current_cut = 0; |
---|
1225 | for (IncEdgeIt it(*_work_graph, first_node); it != INVALID; ++it) { |
---|
1226 | Node node = _work_graph->runningNode(it); |
---|
1227 | current_cut += (*_work_capacity)[it]; |
---|
1228 | if (node == second_node) continue; |
---|
1229 | if (edges[node] == INVALID) { |
---|
1230 | edges[node] = _work_graph->addEdge(new_node, node); |
---|
1231 | (*_work_capacity)[edges[node]] = (*_work_capacity)[it]; |
---|
1232 | } else { |
---|
1233 | (*_work_capacity)[edges[node]] += (*_work_capacity)[it]; |
---|
1234 | } |
---|
1235 | } |
---|
1236 | |
---|
1237 | if (_first_node == INVALID || current_cut < _minimum_cut) { |
---|
1238 | _first_node = (*_first)[first_node]; |
---|
1239 | _last_node = (*_last)[first_node]; |
---|
1240 | _minimum_cut = current_cut; |
---|
1241 | } |
---|
1242 | |
---|
1243 | _work_graph->erase(first_node); |
---|
1244 | |
---|
1245 | for (IncEdgeIt it(*_work_graph, second_node); it != INVALID; ++it) { |
---|
1246 | Node node = _work_graph->runningNode(it); |
---|
1247 | if (edges[node] == INVALID) { |
---|
1248 | edges[node] = _work_graph->addEdge(new_node, node); |
---|
1249 | (*_work_capacity)[edges[node]] = (*_work_capacity)[it]; |
---|
1250 | } else { |
---|
1251 | (*_work_capacity)[edges[node]] += (*_work_capacity)[it]; |
---|
1252 | } |
---|
1253 | } |
---|
1254 | _work_graph->erase(second_node); |
---|
1255 | |
---|
1256 | --_node_num; |
---|
1257 | return _node_num == 1; |
---|
1258 | } |
---|
1259 | |
---|
1260 | /// \brief Executes the algorithm. |
---|
1261 | /// |
---|
1262 | /// Executes the algorithm. |
---|
1263 | /// |
---|
1264 | /// \pre init() must be called |
---|
1265 | void start() { |
---|
1266 | while (!processNextPhase()); |
---|
1267 | } |
---|
1268 | |
---|
1269 | |
---|
1270 | /// \brief Runs %MinimumCut algorithm. |
---|
1271 | /// |
---|
1272 | /// This method runs the %Minimum cut algorithm |
---|
1273 | /// |
---|
1274 | /// \note mc.run(s) is just a shortcut of the following code. |
---|
1275 | ///\code |
---|
1276 | /// mc.init(); |
---|
1277 | /// mc.start(); |
---|
1278 | ///\endcode |
---|
1279 | void run() { |
---|
1280 | init(); |
---|
1281 | start(); |
---|
1282 | } |
---|
1283 | |
---|
1284 | ///@} |
---|
1285 | |
---|
1286 | /// \name Query Functions |
---|
1287 | /// The result of the %MinimumCut algorithm can be obtained using these |
---|
1288 | /// functions.\n |
---|
1289 | /// Before the use of these functions, |
---|
1290 | /// either run() or start() must be called. |
---|
1291 | |
---|
1292 | ///@{ |
---|
1293 | |
---|
1294 | /// \brief Returns the minimum cut value. |
---|
1295 | /// |
---|
1296 | /// Returns the minimum cut value if the algorithm finished. |
---|
1297 | /// After the first processNextPhase() it is a value of a |
---|
1298 | /// valid cut in the graph. |
---|
1299 | Value minCut() const { |
---|
1300 | return _minimum_cut; |
---|
1301 | } |
---|
1302 | |
---|
1303 | /// \brief Returns a minimum cut in a NodeMap. |
---|
1304 | /// |
---|
1305 | /// It sets the nodes of one of the two partitions to true in |
---|
1306 | /// the given BoolNodeMap. The map contains a valid cut if the |
---|
1307 | /// map have been setted false previously. |
---|
1308 | template <typename NodeMap> |
---|
1309 | Value quickMinCut(NodeMap& nodeMap) const { |
---|
1310 | for (typename Graph::Node it = _first_node; |
---|
1311 | it != _last_node; it = (*_next)[it]) { |
---|
1312 | nodeMap.set(it, true); |
---|
1313 | } |
---|
1314 | nodeMap.set(_last_node, true); |
---|
1315 | return minCut(); |
---|
1316 | } |
---|
1317 | |
---|
1318 | /// \brief Returns a minimum cut in a NodeMap. |
---|
1319 | /// |
---|
1320 | /// It sets the nodes of one of the two partitions to true and |
---|
1321 | /// the other partition to false. The function first set all of the |
---|
1322 | /// nodes to false and after it call the quickMinCut() member. |
---|
1323 | template <typename NodeMap> |
---|
1324 | Value minCut(NodeMap& nodeMap) const { |
---|
1325 | for (typename Graph::NodeIt it(*_graph); it != INVALID; ++it) { |
---|
1326 | nodeMap.set(it, false); |
---|
1327 | } |
---|
1328 | quickMinCut(nodeMap); |
---|
1329 | return minCut(); |
---|
1330 | } |
---|
1331 | |
---|
1332 | /// \brief Returns a minimum cut in an EdgeMap. |
---|
1333 | /// |
---|
1334 | /// If an undirected edge is cut edge then it will be |
---|
1335 | /// setted to true and the others will be setted to false in the given map. |
---|
1336 | template <typename EdgeMap> |
---|
1337 | Value cutEdges(EdgeMap& edgeMap) const { |
---|
1338 | typename Graph::template NodeMap<bool> cut(*_graph, false); |
---|
1339 | quickMinCut(cut); |
---|
1340 | for (typename Graph::EdgeIt it(*_graph); it != INVALID; ++it) { |
---|
1341 | edgeMap.set(it, cut[_graph->source(it)] ^ cut[_graph->target(it)]); |
---|
1342 | } |
---|
1343 | return minCut(); |
---|
1344 | } |
---|
1345 | |
---|
1346 | ///@} |
---|
1347 | |
---|
1348 | }; |
---|
1349 | } |
---|
1350 | |
---|
1351 | #endif |
---|