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) 2003-2010 |
---|
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_NAGAMOCHI_IBARAKI_H |
---|
20 | #define LEMON_NAGAMOCHI_IBARAKI_H |
---|
21 | |
---|
22 | |
---|
23 | /// \ingroup min_cut |
---|
24 | /// \file |
---|
25 | /// \brief Implementation of the Nagamochi-Ibaraki algorithm. |
---|
26 | |
---|
27 | #include <lemon/core.h> |
---|
28 | #include <lemon/bin_heap.h> |
---|
29 | #include <lemon/bucket_heap.h> |
---|
30 | #include <lemon/maps.h> |
---|
31 | #include <lemon/radix_sort.h> |
---|
32 | #include <lemon/unionfind.h> |
---|
33 | |
---|
34 | #include <cassert> |
---|
35 | |
---|
36 | namespace lemon { |
---|
37 | |
---|
38 | /// \brief Default traits class for NagamochiIbaraki class. |
---|
39 | /// |
---|
40 | /// Default traits class for NagamochiIbaraki class. |
---|
41 | /// \param GR The undirected graph type. |
---|
42 | /// \param CM Type of capacity map. |
---|
43 | template <typename GR, typename CM> |
---|
44 | struct NagamochiIbarakiDefaultTraits { |
---|
45 | /// The type of the capacity map. |
---|
46 | typedef typename CM::Value Value; |
---|
47 | |
---|
48 | /// The undirected graph type the algorithm runs on. |
---|
49 | typedef GR Graph; |
---|
50 | |
---|
51 | /// \brief The type of the map that stores the edge capacities. |
---|
52 | /// |
---|
53 | /// The type of the map that stores the edge capacities. |
---|
54 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
---|
55 | typedef CM CapacityMap; |
---|
56 | |
---|
57 | /// \brief Instantiates a CapacityMap. |
---|
58 | /// |
---|
59 | /// This function instantiates a \ref CapacityMap. |
---|
60 | #ifdef DOXYGEN |
---|
61 | static CapacityMap *createCapacityMap(const Graph& graph) |
---|
62 | #else |
---|
63 | static CapacityMap *createCapacityMap(const Graph&) |
---|
64 | #endif |
---|
65 | { |
---|
66 | LEMON_ASSERT(false, "CapacityMap is not initialized"); |
---|
67 | return 0; // ignore warnings |
---|
68 | } |
---|
69 | |
---|
70 | /// \brief The cross reference type used by heap. |
---|
71 | /// |
---|
72 | /// The cross reference type used by heap. |
---|
73 | /// Usually \c Graph::NodeMap<int>. |
---|
74 | typedef typename Graph::template NodeMap<int> HeapCrossRef; |
---|
75 | |
---|
76 | /// \brief Instantiates a HeapCrossRef. |
---|
77 | /// |
---|
78 | /// This function instantiates a \ref HeapCrossRef. |
---|
79 | /// \param g is the graph, to which we would like to define the |
---|
80 | /// \ref HeapCrossRef. |
---|
81 | static HeapCrossRef *createHeapCrossRef(const Graph& g) { |
---|
82 | return new HeapCrossRef(g); |
---|
83 | } |
---|
84 | |
---|
85 | /// \brief The heap type used by NagamochiIbaraki algorithm. |
---|
86 | /// |
---|
87 | /// The heap type used by NagamochiIbaraki algorithm. It has to |
---|
88 | /// maximize the priorities. |
---|
89 | /// |
---|
90 | /// \sa BinHeap |
---|
91 | /// \sa NagamochiIbaraki |
---|
92 | typedef BinHeap<Value, HeapCrossRef, std::greater<Value> > Heap; |
---|
93 | |
---|
94 | /// \brief Instantiates a Heap. |
---|
95 | /// |
---|
96 | /// This function instantiates a \ref Heap. |
---|
97 | /// \param r is the cross reference of the heap. |
---|
98 | static Heap *createHeap(HeapCrossRef& r) { |
---|
99 | return new Heap(r); |
---|
100 | } |
---|
101 | }; |
---|
102 | |
---|
103 | /// \ingroup min_cut |
---|
104 | /// |
---|
105 | /// \brief Calculates the minimum cut in an undirected graph. |
---|
106 | /// |
---|
107 | /// Calculates the minimum cut in an undirected graph with the |
---|
108 | /// Nagamochi-Ibaraki algorithm. The algorithm separates the graph's |
---|
109 | /// nodes into two partitions with the minimum sum of edge capacities |
---|
110 | /// between the two partitions. The algorithm can be used to test |
---|
111 | /// the network reliability, especially to test how many links have |
---|
112 | /// to be destroyed in the network to split it to at least two |
---|
113 | /// distinict subnetworks. |
---|
114 | /// |
---|
115 | /// The complexity of the algorithm is \f$ O(nm\log(n)) \f$ but with |
---|
116 | /// \ref FibHeap "Fibonacci heap" it can be decreased to |
---|
117 | /// \f$ O(nm+n^2\log(n)) \f$. When the edges have unit capacities, |
---|
118 | /// \c BucketHeap can be used which yields \f$ O(nm) \f$ time |
---|
119 | /// complexity. |
---|
120 | /// |
---|
121 | /// \warning The value type of the capacity map should be able to |
---|
122 | /// hold any cut value of the graph, otherwise the result can |
---|
123 | /// overflow. |
---|
124 | /// \note This capacity is supposed to be integer type. |
---|
125 | #ifdef DOXYGEN |
---|
126 | template <typename GR, typename CM, typename TR> |
---|
127 | #else |
---|
128 | template <typename GR, |
---|
129 | typename CM = typename GR::template EdgeMap<int>, |
---|
130 | typename TR = NagamochiIbarakiDefaultTraits<GR, CM> > |
---|
131 | #endif |
---|
132 | class NagamochiIbaraki { |
---|
133 | public: |
---|
134 | |
---|
135 | typedef TR Traits; |
---|
136 | /// The type of the underlying graph. |
---|
137 | typedef typename Traits::Graph Graph; |
---|
138 | |
---|
139 | /// The type of the capacity map. |
---|
140 | typedef typename Traits::CapacityMap CapacityMap; |
---|
141 | /// The value type of the capacity map. |
---|
142 | typedef typename Traits::CapacityMap::Value Value; |
---|
143 | |
---|
144 | /// The heap type used by the algorithm. |
---|
145 | typedef typename Traits::Heap Heap; |
---|
146 | /// The cross reference type used for the heap. |
---|
147 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
---|
148 | |
---|
149 | ///\name Named template parameters |
---|
150 | |
---|
151 | ///@{ |
---|
152 | |
---|
153 | struct SetUnitCapacityTraits : public Traits { |
---|
154 | typedef ConstMap<typename Graph::Edge, Const<int, 1> > CapacityMap; |
---|
155 | static CapacityMap *createCapacityMap(const Graph&) { |
---|
156 | return new CapacityMap(); |
---|
157 | } |
---|
158 | }; |
---|
159 | |
---|
160 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
161 | /// the capacity map to a constMap<Edge, int, 1>() instance |
---|
162 | /// |
---|
163 | /// \ref named-templ-param "Named parameter" for setting |
---|
164 | /// the capacity map to a constMap<Edge, int, 1>() instance |
---|
165 | struct SetUnitCapacity |
---|
166 | : public NagamochiIbaraki<Graph, CapacityMap, |
---|
167 | SetUnitCapacityTraits> { |
---|
168 | typedef NagamochiIbaraki<Graph, CapacityMap, |
---|
169 | SetUnitCapacityTraits> Create; |
---|
170 | }; |
---|
171 | |
---|
172 | |
---|
173 | template <class H, class CR> |
---|
174 | struct SetHeapTraits : public Traits { |
---|
175 | typedef CR HeapCrossRef; |
---|
176 | typedef H Heap; |
---|
177 | static HeapCrossRef *createHeapCrossRef(int num) { |
---|
178 | LEMON_ASSERT(false, "HeapCrossRef is not initialized"); |
---|
179 | return 0; // ignore warnings |
---|
180 | } |
---|
181 | static Heap *createHeap(HeapCrossRef &) { |
---|
182 | LEMON_ASSERT(false, "Heap is not initialized"); |
---|
183 | return 0; // ignore warnings |
---|
184 | } |
---|
185 | }; |
---|
186 | |
---|
187 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
188 | /// heap and cross reference type |
---|
189 | /// |
---|
190 | /// \ref named-templ-param "Named parameter" for setting heap and |
---|
191 | /// cross reference type. The heap has to maximize the priorities. |
---|
192 | template <class H, class CR = RangeMap<int> > |
---|
193 | struct SetHeap |
---|
194 | : public NagamochiIbaraki<Graph, CapacityMap, SetHeapTraits<H, CR> > { |
---|
195 | typedef NagamochiIbaraki< Graph, CapacityMap, SetHeapTraits<H, CR> > |
---|
196 | Create; |
---|
197 | }; |
---|
198 | |
---|
199 | template <class H, class CR> |
---|
200 | struct SetStandardHeapTraits : public Traits { |
---|
201 | typedef CR HeapCrossRef; |
---|
202 | typedef H Heap; |
---|
203 | static HeapCrossRef *createHeapCrossRef(int size) { |
---|
204 | return new HeapCrossRef(size); |
---|
205 | } |
---|
206 | static Heap *createHeap(HeapCrossRef &crossref) { |
---|
207 | return new Heap(crossref); |
---|
208 | } |
---|
209 | }; |
---|
210 | |
---|
211 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
212 | /// heap and cross reference type with automatic allocation |
---|
213 | /// |
---|
214 | /// \ref named-templ-param "Named parameter" for setting heap and |
---|
215 | /// cross reference type with automatic allocation. They should |
---|
216 | /// have standard constructor interfaces to be able to |
---|
217 | /// automatically created by the algorithm (i.e. the graph should |
---|
218 | /// be passed to the constructor of the cross reference and the |
---|
219 | /// cross reference should be passed to the constructor of the |
---|
220 | /// heap). However, external heap and cross reference objects |
---|
221 | /// could also be passed to the algorithm using the \ref heap() |
---|
222 | /// function before calling \ref run() or \ref init(). The heap |
---|
223 | /// has to maximize the priorities. |
---|
224 | /// \sa SetHeap |
---|
225 | template <class H, class CR = RangeMap<int> > |
---|
226 | struct SetStandardHeap |
---|
227 | : public NagamochiIbaraki<Graph, CapacityMap, |
---|
228 | SetStandardHeapTraits<H, CR> > { |
---|
229 | typedef NagamochiIbaraki<Graph, CapacityMap, |
---|
230 | SetStandardHeapTraits<H, CR> > Create; |
---|
231 | }; |
---|
232 | |
---|
233 | ///@} |
---|
234 | |
---|
235 | |
---|
236 | private: |
---|
237 | |
---|
238 | const Graph &_graph; |
---|
239 | const CapacityMap *_capacity; |
---|
240 | bool _local_capacity; // unit capacity |
---|
241 | |
---|
242 | struct ArcData { |
---|
243 | typename Graph::Node target; |
---|
244 | int prev, next; |
---|
245 | }; |
---|
246 | struct EdgeData { |
---|
247 | Value capacity; |
---|
248 | Value cut; |
---|
249 | }; |
---|
250 | |
---|
251 | struct NodeData { |
---|
252 | int first_arc; |
---|
253 | typename Graph::Node prev, next; |
---|
254 | int curr_arc; |
---|
255 | typename Graph::Node last_rep; |
---|
256 | Value sum; |
---|
257 | }; |
---|
258 | |
---|
259 | typename Graph::template NodeMap<NodeData> *_nodes; |
---|
260 | std::vector<ArcData> _arcs; |
---|
261 | std::vector<EdgeData> _edges; |
---|
262 | |
---|
263 | typename Graph::Node _first_node; |
---|
264 | int _node_num; |
---|
265 | |
---|
266 | Value _min_cut; |
---|
267 | |
---|
268 | HeapCrossRef *_heap_cross_ref; |
---|
269 | bool _local_heap_cross_ref; |
---|
270 | Heap *_heap; |
---|
271 | bool _local_heap; |
---|
272 | |
---|
273 | typedef typename Graph::template NodeMap<typename Graph::Node> NodeList; |
---|
274 | NodeList *_next_rep; |
---|
275 | |
---|
276 | typedef typename Graph::template NodeMap<bool> MinCutMap; |
---|
277 | MinCutMap *_cut_map; |
---|
278 | |
---|
279 | void createStructures() { |
---|
280 | if (!_nodes) { |
---|
281 | _nodes = new (typename Graph::template NodeMap<NodeData>)(_graph); |
---|
282 | } |
---|
283 | if (!_capacity) { |
---|
284 | _local_capacity = true; |
---|
285 | _capacity = Traits::createCapacityMap(_graph); |
---|
286 | } |
---|
287 | if (!_heap_cross_ref) { |
---|
288 | _local_heap_cross_ref = true; |
---|
289 | _heap_cross_ref = Traits::createHeapCrossRef(_graph); |
---|
290 | } |
---|
291 | if (!_heap) { |
---|
292 | _local_heap = true; |
---|
293 | _heap = Traits::createHeap(*_heap_cross_ref); |
---|
294 | } |
---|
295 | if (!_next_rep) { |
---|
296 | _next_rep = new NodeList(_graph); |
---|
297 | } |
---|
298 | if (!_cut_map) { |
---|
299 | _cut_map = new MinCutMap(_graph); |
---|
300 | } |
---|
301 | } |
---|
302 | |
---|
303 | public : |
---|
304 | |
---|
305 | typedef NagamochiIbaraki Create; |
---|
306 | |
---|
307 | |
---|
308 | /// \brief Constructor. |
---|
309 | /// |
---|
310 | /// \param graph The graph the algorithm runs on. |
---|
311 | /// \param capacity The capacity map used by the algorithm. |
---|
312 | NagamochiIbaraki(const Graph& graph, const CapacityMap& capacity) |
---|
313 | : _graph(graph), _capacity(&capacity), _local_capacity(false), |
---|
314 | _nodes(0), _arcs(), _edges(), _min_cut(), |
---|
315 | _heap_cross_ref(0), _local_heap_cross_ref(false), |
---|
316 | _heap(0), _local_heap(false), |
---|
317 | _next_rep(0), _cut_map(0) {} |
---|
318 | |
---|
319 | /// \brief Constructor. |
---|
320 | /// |
---|
321 | /// This constructor can be used only when the Traits class |
---|
322 | /// defines how can the local capacity map be instantiated. |
---|
323 | /// If the SetUnitCapacity used the algorithm automatically |
---|
324 | /// constructs the capacity map. |
---|
325 | /// |
---|
326 | ///\param graph The graph the algorithm runs on. |
---|
327 | NagamochiIbaraki(const Graph& graph) |
---|
328 | : _graph(graph), _capacity(0), _local_capacity(false), |
---|
329 | _nodes(0), _arcs(), _edges(), _min_cut(), |
---|
330 | _heap_cross_ref(0), _local_heap_cross_ref(false), |
---|
331 | _heap(0), _local_heap(false), |
---|
332 | _next_rep(0), _cut_map(0) {} |
---|
333 | |
---|
334 | /// \brief Destructor. |
---|
335 | /// |
---|
336 | /// Destructor. |
---|
337 | ~NagamochiIbaraki() { |
---|
338 | if (_local_capacity) delete _capacity; |
---|
339 | if (_nodes) delete _nodes; |
---|
340 | if (_local_heap) delete _heap; |
---|
341 | if (_local_heap_cross_ref) delete _heap_cross_ref; |
---|
342 | if (_next_rep) delete _next_rep; |
---|
343 | if (_cut_map) delete _cut_map; |
---|
344 | } |
---|
345 | |
---|
346 | /// \brief Sets the heap and the cross reference used by algorithm. |
---|
347 | /// |
---|
348 | /// Sets the heap and the cross reference used by algorithm. |
---|
349 | /// If you don't use this function before calling \ref run(), |
---|
350 | /// it will allocate one. The destuctor deallocates this |
---|
351 | /// automatically allocated heap and cross reference, of course. |
---|
352 | /// \return <tt> (*this) </tt> |
---|
353 | NagamochiIbaraki &heap(Heap& hp, HeapCrossRef &cr) |
---|
354 | { |
---|
355 | if (_local_heap_cross_ref) { |
---|
356 | delete _heap_cross_ref; |
---|
357 | _local_heap_cross_ref = false; |
---|
358 | } |
---|
359 | _heap_cross_ref = &cr; |
---|
360 | if (_local_heap) { |
---|
361 | delete _heap; |
---|
362 | _local_heap = false; |
---|
363 | } |
---|
364 | _heap = &hp; |
---|
365 | return *this; |
---|
366 | } |
---|
367 | |
---|
368 | /// \name Execution control |
---|
369 | /// The simplest way to execute the algorithm is to use |
---|
370 | /// one of the member functions called \c run(). |
---|
371 | /// \n |
---|
372 | /// If you need more control on the execution, |
---|
373 | /// first you must call \ref init() and then call the start() |
---|
374 | /// or proper times the processNextPhase() member functions. |
---|
375 | |
---|
376 | ///@{ |
---|
377 | |
---|
378 | /// \brief Initializes the internal data structures. |
---|
379 | /// |
---|
380 | /// Initializes the internal data structures. |
---|
381 | void init() { |
---|
382 | createStructures(); |
---|
383 | |
---|
384 | int edge_num = countEdges(_graph); |
---|
385 | _edges.resize(edge_num); |
---|
386 | _arcs.resize(2 * edge_num); |
---|
387 | |
---|
388 | typename Graph::Node prev = INVALID; |
---|
389 | _node_num = 0; |
---|
390 | for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) { |
---|
391 | (*_cut_map)[n] = false; |
---|
392 | (*_next_rep)[n] = INVALID; |
---|
393 | (*_nodes)[n].last_rep = n; |
---|
394 | (*_nodes)[n].first_arc = -1; |
---|
395 | (*_nodes)[n].curr_arc = -1; |
---|
396 | (*_nodes)[n].prev = prev; |
---|
397 | if (prev != INVALID) { |
---|
398 | (*_nodes)[prev].next = n; |
---|
399 | } |
---|
400 | (*_nodes)[n].next = INVALID; |
---|
401 | (*_nodes)[n].sum = 0; |
---|
402 | prev = n; |
---|
403 | ++_node_num; |
---|
404 | } |
---|
405 | |
---|
406 | _first_node = typename Graph::NodeIt(_graph); |
---|
407 | |
---|
408 | int index = 0; |
---|
409 | for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) { |
---|
410 | for (typename Graph::OutArcIt a(_graph, n); a != INVALID; ++a) { |
---|
411 | typename Graph::Node m = _graph.target(a); |
---|
412 | |
---|
413 | if (!(n < m)) continue; |
---|
414 | |
---|
415 | (*_nodes)[n].sum += (*_capacity)[a]; |
---|
416 | (*_nodes)[m].sum += (*_capacity)[a]; |
---|
417 | |
---|
418 | int c = (*_nodes)[m].curr_arc; |
---|
419 | if (c != -1 && _arcs[c ^ 1].target == n) { |
---|
420 | _edges[c >> 1].capacity += (*_capacity)[a]; |
---|
421 | } else { |
---|
422 | _edges[index].capacity = (*_capacity)[a]; |
---|
423 | |
---|
424 | _arcs[index << 1].prev = -1; |
---|
425 | if ((*_nodes)[n].first_arc != -1) { |
---|
426 | _arcs[(*_nodes)[n].first_arc].prev = (index << 1); |
---|
427 | } |
---|
428 | _arcs[index << 1].next = (*_nodes)[n].first_arc; |
---|
429 | (*_nodes)[n].first_arc = (index << 1); |
---|
430 | _arcs[index << 1].target = m; |
---|
431 | |
---|
432 | (*_nodes)[m].curr_arc = (index << 1); |
---|
433 | |
---|
434 | _arcs[(index << 1) | 1].prev = -1; |
---|
435 | if ((*_nodes)[m].first_arc != -1) { |
---|
436 | _arcs[(*_nodes)[m].first_arc].prev = ((index << 1) | 1); |
---|
437 | } |
---|
438 | _arcs[(index << 1) | 1].next = (*_nodes)[m].first_arc; |
---|
439 | (*_nodes)[m].first_arc = ((index << 1) | 1); |
---|
440 | _arcs[(index << 1) | 1].target = n; |
---|
441 | |
---|
442 | ++index; |
---|
443 | } |
---|
444 | } |
---|
445 | } |
---|
446 | |
---|
447 | typename Graph::Node cut_node = INVALID; |
---|
448 | _min_cut = std::numeric_limits<Value>::max(); |
---|
449 | |
---|
450 | for (typename Graph::Node n = _first_node; |
---|
451 | n != INVALID; n = (*_nodes)[n].next) { |
---|
452 | if ((*_nodes)[n].sum < _min_cut) { |
---|
453 | cut_node = n; |
---|
454 | _min_cut = (*_nodes)[n].sum; |
---|
455 | } |
---|
456 | } |
---|
457 | (*_cut_map)[cut_node] = true; |
---|
458 | if (_min_cut == 0) { |
---|
459 | _first_node = INVALID; |
---|
460 | } |
---|
461 | } |
---|
462 | |
---|
463 | public: |
---|
464 | |
---|
465 | /// \brief Processes the next phase |
---|
466 | /// |
---|
467 | /// Processes the next phase in the algorithm. It must be called |
---|
468 | /// at most one less the number of the nodes in the graph. |
---|
469 | /// |
---|
470 | ///\return %True when the algorithm finished. |
---|
471 | bool processNextPhase() { |
---|
472 | if (_first_node == INVALID) return true; |
---|
473 | |
---|
474 | _heap->clear(); |
---|
475 | for (typename Graph::Node n = _first_node; |
---|
476 | n != INVALID; n = (*_nodes)[n].next) { |
---|
477 | (*_heap_cross_ref)[n] = Heap::PRE_HEAP; |
---|
478 | } |
---|
479 | |
---|
480 | std::vector<typename Graph::Node> order; |
---|
481 | order.reserve(_node_num); |
---|
482 | int sep = 0; |
---|
483 | |
---|
484 | Value alpha = 0; |
---|
485 | Value pmc = std::numeric_limits<Value>::max(); |
---|
486 | |
---|
487 | _heap->push(_first_node, static_cast<Value>(0)); |
---|
488 | while (!_heap->empty()) { |
---|
489 | typename Graph::Node n = _heap->top(); |
---|
490 | Value v = _heap->prio(); |
---|
491 | |
---|
492 | _heap->pop(); |
---|
493 | for (int a = (*_nodes)[n].first_arc; a != -1; a = _arcs[a].next) { |
---|
494 | switch (_heap->state(_arcs[a].target)) { |
---|
495 | case Heap::PRE_HEAP: |
---|
496 | { |
---|
497 | Value nv = _edges[a >> 1].capacity; |
---|
498 | _heap->push(_arcs[a].target, nv); |
---|
499 | _edges[a >> 1].cut = nv; |
---|
500 | } break; |
---|
501 | case Heap::IN_HEAP: |
---|
502 | { |
---|
503 | Value nv = _edges[a >> 1].capacity + (*_heap)[_arcs[a].target]; |
---|
504 | _heap->decrease(_arcs[a].target, nv); |
---|
505 | _edges[a >> 1].cut = nv; |
---|
506 | } break; |
---|
507 | case Heap::POST_HEAP: |
---|
508 | break; |
---|
509 | } |
---|
510 | } |
---|
511 | |
---|
512 | alpha += (*_nodes)[n].sum; |
---|
513 | alpha -= 2 * v; |
---|
514 | |
---|
515 | order.push_back(n); |
---|
516 | if (!_heap->empty()) { |
---|
517 | if (alpha < pmc) { |
---|
518 | pmc = alpha; |
---|
519 | sep = order.size(); |
---|
520 | } |
---|
521 | } |
---|
522 | } |
---|
523 | |
---|
524 | if (static_cast<int>(order.size()) < _node_num) { |
---|
525 | _first_node = INVALID; |
---|
526 | for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) { |
---|
527 | (*_cut_map)[n] = false; |
---|
528 | } |
---|
529 | for (int i = 0; i < static_cast<int>(order.size()); ++i) { |
---|
530 | typename Graph::Node n = order[i]; |
---|
531 | while (n != INVALID) { |
---|
532 | (*_cut_map)[n] = true; |
---|
533 | n = (*_next_rep)[n]; |
---|
534 | } |
---|
535 | } |
---|
536 | _min_cut = 0; |
---|
537 | return true; |
---|
538 | } |
---|
539 | |
---|
540 | if (pmc < _min_cut) { |
---|
541 | for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) { |
---|
542 | (*_cut_map)[n] = false; |
---|
543 | } |
---|
544 | for (int i = 0; i < sep; ++i) { |
---|
545 | typename Graph::Node n = order[i]; |
---|
546 | while (n != INVALID) { |
---|
547 | (*_cut_map)[n] = true; |
---|
548 | n = (*_next_rep)[n]; |
---|
549 | } |
---|
550 | } |
---|
551 | _min_cut = pmc; |
---|
552 | } |
---|
553 | |
---|
554 | for (typename Graph::Node n = _first_node; |
---|
555 | n != INVALID; n = (*_nodes)[n].next) { |
---|
556 | bool merged = false; |
---|
557 | for (int a = (*_nodes)[n].first_arc; a != -1; a = _arcs[a].next) { |
---|
558 | if (!(_edges[a >> 1].cut < pmc)) { |
---|
559 | if (!merged) { |
---|
560 | for (int b = (*_nodes)[n].first_arc; b != -1; b = _arcs[b].next) { |
---|
561 | (*_nodes)[_arcs[b].target].curr_arc = b; |
---|
562 | } |
---|
563 | merged = true; |
---|
564 | } |
---|
565 | typename Graph::Node m = _arcs[a].target; |
---|
566 | int nb = 0; |
---|
567 | for (int b = (*_nodes)[m].first_arc; b != -1; b = nb) { |
---|
568 | nb = _arcs[b].next; |
---|
569 | if ((b ^ a) == 1) continue; |
---|
570 | typename Graph::Node o = _arcs[b].target; |
---|
571 | int c = (*_nodes)[o].curr_arc; |
---|
572 | if (c != -1 && _arcs[c ^ 1].target == n) { |
---|
573 | _edges[c >> 1].capacity += _edges[b >> 1].capacity; |
---|
574 | (*_nodes)[n].sum += _edges[b >> 1].capacity; |
---|
575 | if (_edges[b >> 1].cut < _edges[c >> 1].cut) { |
---|
576 | _edges[b >> 1].cut = _edges[c >> 1].cut; |
---|
577 | } |
---|
578 | if (_arcs[b ^ 1].prev != -1) { |
---|
579 | _arcs[_arcs[b ^ 1].prev].next = _arcs[b ^ 1].next; |
---|
580 | } else { |
---|
581 | (*_nodes)[o].first_arc = _arcs[b ^ 1].next; |
---|
582 | } |
---|
583 | if (_arcs[b ^ 1].next != -1) { |
---|
584 | _arcs[_arcs[b ^ 1].next].prev = _arcs[b ^ 1].prev; |
---|
585 | } |
---|
586 | } else { |
---|
587 | if (_arcs[a].next != -1) { |
---|
588 | _arcs[_arcs[a].next].prev = b; |
---|
589 | } |
---|
590 | _arcs[b].next = _arcs[a].next; |
---|
591 | _arcs[b].prev = a; |
---|
592 | _arcs[a].next = b; |
---|
593 | _arcs[b ^ 1].target = n; |
---|
594 | |
---|
595 | (*_nodes)[n].sum += _edges[b >> 1].capacity; |
---|
596 | (*_nodes)[o].curr_arc = b; |
---|
597 | } |
---|
598 | } |
---|
599 | |
---|
600 | if (_arcs[a].prev != -1) { |
---|
601 | _arcs[_arcs[a].prev].next = _arcs[a].next; |
---|
602 | } else { |
---|
603 | (*_nodes)[n].first_arc = _arcs[a].next; |
---|
604 | } |
---|
605 | if (_arcs[a].next != -1) { |
---|
606 | _arcs[_arcs[a].next].prev = _arcs[a].prev; |
---|
607 | } |
---|
608 | |
---|
609 | (*_nodes)[n].sum -= _edges[a >> 1].capacity; |
---|
610 | (*_next_rep)[(*_nodes)[n].last_rep] = m; |
---|
611 | (*_nodes)[n].last_rep = (*_nodes)[m].last_rep; |
---|
612 | |
---|
613 | if ((*_nodes)[m].prev != INVALID) { |
---|
614 | (*_nodes)[(*_nodes)[m].prev].next = (*_nodes)[m].next; |
---|
615 | } else{ |
---|
616 | _first_node = (*_nodes)[m].next; |
---|
617 | } |
---|
618 | if ((*_nodes)[m].next != INVALID) { |
---|
619 | (*_nodes)[(*_nodes)[m].next].prev = (*_nodes)[m].prev; |
---|
620 | } |
---|
621 | --_node_num; |
---|
622 | } |
---|
623 | } |
---|
624 | } |
---|
625 | |
---|
626 | if (_node_num == 1) { |
---|
627 | _first_node = INVALID; |
---|
628 | return true; |
---|
629 | } |
---|
630 | |
---|
631 | return false; |
---|
632 | } |
---|
633 | |
---|
634 | /// \brief Executes the algorithm. |
---|
635 | /// |
---|
636 | /// Executes the algorithm. |
---|
637 | /// |
---|
638 | /// \pre init() must be called |
---|
639 | void start() { |
---|
640 | while (!processNextPhase()) {} |
---|
641 | } |
---|
642 | |
---|
643 | |
---|
644 | /// \brief Runs %NagamochiIbaraki algorithm. |
---|
645 | /// |
---|
646 | /// This method runs the %Min cut algorithm |
---|
647 | /// |
---|
648 | /// \note mc.run(s) is just a shortcut of the following code. |
---|
649 | ///\code |
---|
650 | /// mc.init(); |
---|
651 | /// mc.start(); |
---|
652 | ///\endcode |
---|
653 | void run() { |
---|
654 | init(); |
---|
655 | start(); |
---|
656 | } |
---|
657 | |
---|
658 | ///@} |
---|
659 | |
---|
660 | /// \name Query Functions |
---|
661 | /// |
---|
662 | /// The result of the %NagamochiIbaraki |
---|
663 | /// algorithm can be obtained using these functions.\n |
---|
664 | /// Before the use of these functions, either run() or start() |
---|
665 | /// must be called. |
---|
666 | |
---|
667 | ///@{ |
---|
668 | |
---|
669 | /// \brief Returns the min cut value. |
---|
670 | /// |
---|
671 | /// Returns the min cut value if the algorithm finished. |
---|
672 | /// After the first processNextPhase() it is a value of a |
---|
673 | /// valid cut in the graph. |
---|
674 | Value minCutValue() const { |
---|
675 | return _min_cut; |
---|
676 | } |
---|
677 | |
---|
678 | /// \brief Returns a min cut in a NodeMap. |
---|
679 | /// |
---|
680 | /// It sets the nodes of one of the two partitions to true and |
---|
681 | /// the other partition to false. |
---|
682 | /// \param cutMap A \ref concepts::WriteMap "writable" node map with |
---|
683 | /// \c bool (or convertible) value type. |
---|
684 | template <typename CutMap> |
---|
685 | Value minCutMap(CutMap& cutMap) const { |
---|
686 | for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) { |
---|
687 | cutMap.set(n, (*_cut_map)[n]); |
---|
688 | } |
---|
689 | return minCutValue(); |
---|
690 | } |
---|
691 | |
---|
692 | ///@} |
---|
693 | |
---|
694 | }; |
---|
695 | } |
---|
696 | |
---|
697 | #endif |
---|