1 // -*- C++ -*- |
|
2 #ifndef LEMON_MAX_FLOW_H |
|
3 #define LEMON_MAX_FLOW_H |
|
4 |
|
5 #include <vector> |
|
6 #include <queue> |
|
7 #include <stack> |
|
8 |
|
9 #include <lemon/graph_wrapper.h> |
|
10 #include <bfs_dfs.h> |
|
11 #include <lemon/invalid.h> |
|
12 #include <lemon/maps.h> |
|
13 #include <lemon/for_each_macros.h> |
|
14 |
|
15 /// \file |
|
16 /// \brief Maximum flow algorithms. |
|
17 /// \ingroup galgs |
|
18 |
|
19 namespace lemon { |
|
20 |
|
21 /// \addtogroup galgs |
|
22 /// @{ |
|
23 ///Maximum flow algorithms class. |
|
24 |
|
25 ///This class provides various algorithms for finding a flow of |
|
26 ///maximum value in a directed graph. The \e source node, the \e |
|
27 ///target node, the \e capacity of the edges and the \e starting \e |
|
28 ///flow value of the edges should be passed to the algorithm through the |
|
29 ///constructor. It is possible to change these quantities using the |
|
30 ///functions \ref resetSource, \ref resetTarget, \ref resetCap and |
|
31 ///\ref resetFlow. Before any subsequent runs of any algorithm of |
|
32 ///the class \ref resetFlow should be called. |
|
33 |
|
34 ///After running an algorithm of the class, the actual flow value |
|
35 ///can be obtained by calling \ref flowValue(). The minimum |
|
36 ///value cut can be written into a \c node map of \c bools by |
|
37 ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes |
|
38 ///the inclusionwise minimum and maximum of the minimum value |
|
39 ///cuts, resp.) |
|
40 ///\param Graph The directed graph type the algorithm runs on. |
|
41 ///\param Num The number type of the capacities and the flow values. |
|
42 ///\param CapMap The capacity map type. |
|
43 ///\param FlowMap The flow map type. |
|
44 ///\author Marton Makai, Jacint Szabo |
|
45 template <typename Graph, typename Num, |
|
46 typename CapMap=typename Graph::template EdgeMap<Num>, |
|
47 typename FlowMap=typename Graph::template EdgeMap<Num> > |
|
48 class MaxFlow { |
|
49 protected: |
|
50 typedef typename Graph::Node Node; |
|
51 typedef typename Graph::NodeIt NodeIt; |
|
52 typedef typename Graph::EdgeIt EdgeIt; |
|
53 typedef typename Graph::OutEdgeIt OutEdgeIt; |
|
54 typedef typename Graph::InEdgeIt InEdgeIt; |
|
55 |
|
56 typedef typename std::vector<std::stack<Node> > VecStack; |
|
57 typedef typename Graph::template NodeMap<Node> NNMap; |
|
58 typedef typename std::vector<Node> VecNode; |
|
59 |
|
60 const Graph* g; |
|
61 Node s; |
|
62 Node t; |
|
63 const CapMap* capacity; |
|
64 FlowMap* flow; |
|
65 int n; //the number of nodes of G |
|
66 typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
|
67 //typedef ExpResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
|
68 typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt; |
|
69 typedef typename ResGW::Edge ResGWEdge; |
|
70 //typedef typename ResGW::template NodeMap<bool> ReachedMap; |
|
71 typedef typename Graph::template NodeMap<int> ReachedMap; |
|
72 |
|
73 |
|
74 //level works as a bool map in augmenting path algorithms and is |
|
75 //used by bfs for storing reached information. In preflow, it |
|
76 //shows the levels of nodes. |
|
77 ReachedMap level; |
|
78 |
|
79 //excess is needed only in preflow |
|
80 typename Graph::template NodeMap<Num> excess; |
|
81 |
|
82 //fixme |
|
83 // protected: |
|
84 // MaxFlow() { } |
|
85 // void set(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
|
86 // FlowMap& _flow) |
|
87 // { |
|
88 // g=&_G; |
|
89 // s=_s; |
|
90 // t=_t; |
|
91 // capacity=&_capacity; |
|
92 // flow=&_flow; |
|
93 // n=_G.nodeNum; |
|
94 // level.set (_G); //kellene vmi ilyesmi fv |
|
95 // excess(_G,0); //itt is |
|
96 // } |
|
97 |
|
98 // constants used for heuristics |
|
99 static const int H0=20; |
|
100 static const int H1=1; |
|
101 |
|
102 public: |
|
103 |
|
104 ///Indicates the property of the starting flow. |
|
105 |
|
106 ///Indicates the property of the starting flow. The meanings are as follows: |
|
107 ///- \c ZERO_FLOW: constant zero flow |
|
108 ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to |
|
109 ///the sum of the out-flows in every node except the \e source and |
|
110 ///the \e target. |
|
111 ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at |
|
112 ///least the sum of the out-flows in every node except the \e source. |
|
113 ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be |
|
114 ///set to the constant zero flow in the beginning of the algorithm in this case. |
|
115 enum FlowEnum{ |
|
116 ZERO_FLOW, |
|
117 GEN_FLOW, |
|
118 PRE_FLOW, |
|
119 NO_FLOW |
|
120 }; |
|
121 |
|
122 enum StatusEnum { |
|
123 AFTER_NOTHING, |
|
124 AFTER_AUGMENTING, |
|
125 AFTER_FAST_AUGMENTING, |
|
126 AFTER_PRE_FLOW_PHASE_1, |
|
127 AFTER_PRE_FLOW_PHASE_2 |
|
128 }; |
|
129 |
|
130 /// Don not needle this flag only if necessary. |
|
131 StatusEnum status; |
|
132 int number_of_augmentations; |
|
133 |
|
134 |
|
135 template<typename IntMap> |
|
136 class TrickyReachedMap { |
|
137 protected: |
|
138 IntMap* map; |
|
139 int* number_of_augmentations; |
|
140 public: |
|
141 TrickyReachedMap(IntMap& _map, int& _number_of_augmentations) : |
|
142 map(&_map), number_of_augmentations(&_number_of_augmentations) { } |
|
143 void set(const Node& n, bool b) { |
|
144 if (b) |
|
145 map->set(n, *number_of_augmentations); |
|
146 else |
|
147 map->set(n, *number_of_augmentations-1); |
|
148 } |
|
149 bool operator[](const Node& n) const { |
|
150 return (*map)[n]==*number_of_augmentations; |
|
151 } |
|
152 }; |
|
153 |
|
154 ///Constructor |
|
155 |
|
156 ///\todo Document, please. |
|
157 /// |
|
158 MaxFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
|
159 FlowMap& _flow) : |
|
160 g(&_G), s(_s), t(_t), capacity(&_capacity), |
|
161 flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0), |
|
162 status(AFTER_NOTHING), number_of_augmentations(0) { } |
|
163 |
|
164 ///Runs a maximum flow algorithm. |
|
165 |
|
166 ///Runs a preflow algorithm, which is the fastest maximum flow |
|
167 ///algorithm up-to-date. The default for \c fe is ZERO_FLOW. |
|
168 ///\pre The starting flow must be |
|
169 /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
|
170 /// - an arbitary flow if \c fe is \c GEN_FLOW, |
|
171 /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
|
172 /// - any map if \c fe is NO_FLOW. |
|
173 void run(FlowEnum fe=ZERO_FLOW) { |
|
174 preflow(fe); |
|
175 } |
|
176 |
|
177 |
|
178 ///Runs a preflow algorithm. |
|
179 |
|
180 ///Runs a preflow algorithm. The preflow algorithms provide the |
|
181 ///fastest way to compute a maximum flow in a directed graph. |
|
182 ///\pre The starting flow must be |
|
183 /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
|
184 /// - an arbitary flow if \c fe is \c GEN_FLOW, |
|
185 /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
|
186 /// - any map if \c fe is NO_FLOW. |
|
187 /// |
|
188 ///\todo NO_FLOW should be the default flow. |
|
189 void preflow(FlowEnum fe) { |
|
190 preflowPhase1(fe); |
|
191 preflowPhase2(); |
|
192 } |
|
193 // Heuristics: |
|
194 // 2 phase |
|
195 // gap |
|
196 // list 'level_list' on the nodes on level i implemented by hand |
|
197 // stack 'active' on the active nodes on level i |
|
198 // runs heuristic 'highest label' for H1*n relabels |
|
199 // runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
|
200 // Parameters H0 and H1 are initialized to 20 and 1. |
|
201 |
|
202 ///Runs the first phase of the preflow algorithm. |
|
203 |
|
204 ///The preflow algorithm consists of two phases, this method runs the |
|
205 ///first phase. After the first phase the maximum flow value and a |
|
206 ///minimum value cut can already be computed, though a maximum flow |
|
207 ///is net yet obtained. So after calling this method \ref flowValue |
|
208 ///and \ref actMinCut gives proper results. |
|
209 ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not |
|
210 ///give minimum value cuts unless calling \ref preflowPhase2. |
|
211 ///\pre The starting flow must be |
|
212 /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
|
213 /// - an arbitary flow if \c fe is \c GEN_FLOW, |
|
214 /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
|
215 /// - any map if \c fe is NO_FLOW. |
|
216 void preflowPhase1(FlowEnum fe); |
|
217 |
|
218 ///Runs the second phase of the preflow algorithm. |
|
219 |
|
220 ///The preflow algorithm consists of two phases, this method runs |
|
221 ///the second phase. After calling \ref preflowPhase1 and then |
|
222 ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut, |
|
223 ///\ref minMinCut and \ref maxMinCut give proper results. |
|
224 ///\pre \ref preflowPhase1 must be called before. |
|
225 void preflowPhase2(); |
|
226 |
|
227 /// Starting from a flow, this method searches for an augmenting path |
|
228 /// according to the Edmonds-Karp algorithm |
|
229 /// and augments the flow on if any. |
|
230 /// The return value shows if the augmentation was succesful. |
|
231 bool augmentOnShortestPath(); |
|
232 bool augmentOnShortestPath2(); |
|
233 |
|
234 /// Starting from a flow, this method searches for an augmenting blocking |
|
235 /// flow according to Dinits' algorithm and augments the flow on if any. |
|
236 /// The blocking flow is computed in a physically constructed |
|
237 /// residual graph of type \c Mutablegraph. |
|
238 /// The return value show sif the augmentation was succesful. |
|
239 template<typename MutableGraph> bool augmentOnBlockingFlow(); |
|
240 |
|
241 /// The same as \c augmentOnBlockingFlow<MutableGraph> but the |
|
242 /// residual graph is not constructed physically. |
|
243 /// The return value shows if the augmentation was succesful. |
|
244 bool augmentOnBlockingFlow2(); |
|
245 |
|
246 /// Returns the maximum value of a flow. |
|
247 |
|
248 /// Returns the maximum value of a flow, by counting the |
|
249 /// over-flow of the target node \ref t. |
|
250 /// It can be called already after running \ref preflowPhase1. |
|
251 Num flowValue() const { |
|
252 Num a=0; |
|
253 FOR_EACH_INC_LOC(InEdgeIt, e, *g, t) a+=(*flow)[e]; |
|
254 FOR_EACH_INC_LOC(OutEdgeIt, e, *g, t) a-=(*flow)[e]; |
|
255 return a; |
|
256 //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan |
|
257 } |
|
258 |
|
259 ///Returns a minimum value cut after calling \ref preflowPhase1. |
|
260 |
|
261 ///After the first phase of the preflow algorithm the maximum flow |
|
262 ///value and a minimum value cut can already be computed. This |
|
263 ///method can be called after running \ref preflowPhase1 for |
|
264 ///obtaining a minimum value cut. |
|
265 /// \warning Gives proper result only right after calling \ref |
|
266 /// preflowPhase1. |
|
267 /// \todo We have to make some status variable which shows the |
|
268 /// actual state |
|
269 /// of the class. This enables us to determine which methods are valid |
|
270 /// for MinCut computation |
|
271 template<typename _CutMap> |
|
272 void actMinCut(_CutMap& M) const { |
|
273 NodeIt v; |
|
274 switch (status) { |
|
275 case AFTER_PRE_FLOW_PHASE_1: |
|
276 for(g->first(v); g->valid(v); g->next(v)) { |
|
277 if (level[v] < n) { |
|
278 M.set(v, false); |
|
279 } else { |
|
280 M.set(v, true); |
|
281 } |
|
282 } |
|
283 break; |
|
284 case AFTER_PRE_FLOW_PHASE_2: |
|
285 case AFTER_NOTHING: |
|
286 minMinCut(M); |
|
287 break; |
|
288 case AFTER_AUGMENTING: |
|
289 for(g->first(v); g->valid(v); g->next(v)) { |
|
290 if (level[v]) { |
|
291 M.set(v, true); |
|
292 } else { |
|
293 M.set(v, false); |
|
294 } |
|
295 } |
|
296 break; |
|
297 case AFTER_FAST_AUGMENTING: |
|
298 for(g->first(v); g->valid(v); g->next(v)) { |
|
299 if (level[v]==number_of_augmentations) { |
|
300 M.set(v, true); |
|
301 } else { |
|
302 M.set(v, false); |
|
303 } |
|
304 } |
|
305 break; |
|
306 } |
|
307 } |
|
308 |
|
309 ///Returns the inclusionwise minimum of the minimum value cuts. |
|
310 |
|
311 ///Sets \c M to the characteristic vector of the minimum value cut |
|
312 ///which is inclusionwise minimum. It is computed by processing |
|
313 ///a bfs from the source node \c s in the residual graph. |
|
314 ///\pre M should be a node map of bools initialized to false. |
|
315 ///\pre \c flow must be a maximum flow. |
|
316 template<typename _CutMap> |
|
317 void minMinCut(_CutMap& M) const { |
|
318 std::queue<Node> queue; |
|
319 |
|
320 M.set(s,true); |
|
321 queue.push(s); |
|
322 |
|
323 while (!queue.empty()) { |
|
324 Node w=queue.front(); |
|
325 queue.pop(); |
|
326 |
|
327 OutEdgeIt e; |
|
328 for(g->first(e,w) ; g->valid(e); g->next(e)) { |
|
329 Node v=g->target(e); |
|
330 if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
|
331 queue.push(v); |
|
332 M.set(v, true); |
|
333 } |
|
334 } |
|
335 |
|
336 InEdgeIt f; |
|
337 for(g->first(f,w) ; g->valid(f); g->next(f)) { |
|
338 Node v=g->source(f); |
|
339 if (!M[v] && (*flow)[f] > 0 ) { |
|
340 queue.push(v); |
|
341 M.set(v, true); |
|
342 } |
|
343 } |
|
344 } |
|
345 } |
|
346 |
|
347 ///Returns the inclusionwise maximum of the minimum value cuts. |
|
348 |
|
349 ///Sets \c M to the characteristic vector of the minimum value cut |
|
350 ///which is inclusionwise maximum. It is computed by processing a |
|
351 ///backward bfs from the target node \c t in the residual graph. |
|
352 ///\pre M should be a node map of bools initialized to false. |
|
353 ///\pre \c flow must be a maximum flow. |
|
354 template<typename _CutMap> |
|
355 void maxMinCut(_CutMap& M) const { |
|
356 |
|
357 NodeIt v; |
|
358 for(g->first(v) ; g->valid(v); g->next(v)) { |
|
359 M.set(v, true); |
|
360 } |
|
361 |
|
362 std::queue<Node> queue; |
|
363 |
|
364 M.set(t,false); |
|
365 queue.push(t); |
|
366 |
|
367 while (!queue.empty()) { |
|
368 Node w=queue.front(); |
|
369 queue.pop(); |
|
370 |
|
371 InEdgeIt e; |
|
372 for(g->first(e,w) ; g->valid(e); g->next(e)) { |
|
373 Node v=g->source(e); |
|
374 if (M[v] && (*flow)[e] < (*capacity)[e] ) { |
|
375 queue.push(v); |
|
376 M.set(v, false); |
|
377 } |
|
378 } |
|
379 |
|
380 OutEdgeIt f; |
|
381 for(g->first(f,w) ; g->valid(f); g->next(f)) { |
|
382 Node v=g->target(f); |
|
383 if (M[v] && (*flow)[f] > 0 ) { |
|
384 queue.push(v); |
|
385 M.set(v, false); |
|
386 } |
|
387 } |
|
388 } |
|
389 } |
|
390 |
|
391 ///Returns a minimum value cut. |
|
392 |
|
393 ///Sets \c M to the characteristic vector of a minimum value cut. |
|
394 ///\pre M should be a node map of bools initialized to false. |
|
395 ///\pre \c flow must be a maximum flow. |
|
396 template<typename CutMap> |
|
397 void minCut(CutMap& M) const { minMinCut(M); } |
|
398 |
|
399 ///Resets the source node to \c _s. |
|
400 |
|
401 ///Resets the source node to \c _s. |
|
402 /// |
|
403 void resetSource(Node _s) { s=_s; status=AFTER_NOTHING; } |
|
404 |
|
405 ///Resets the target node to \c _t. |
|
406 |
|
407 ///Resets the target node to \c _t. |
|
408 /// |
|
409 void resetTarget(Node _t) { t=_t; status=AFTER_NOTHING; } |
|
410 |
|
411 /// Resets the edge map of the capacities to _cap. |
|
412 |
|
413 /// Resets the edge map of the capacities to _cap. |
|
414 /// |
|
415 void resetCap(const CapMap& _cap) { capacity=&_cap; status=AFTER_NOTHING; } |
|
416 |
|
417 /// Resets the edge map of the flows to _flow. |
|
418 |
|
419 /// Resets the edge map of the flows to _flow. |
|
420 /// |
|
421 void resetFlow(FlowMap& _flow) { flow=&_flow; status=AFTER_NOTHING; } |
|
422 |
|
423 |
|
424 private: |
|
425 |
|
426 int push(Node w, VecStack& active) { |
|
427 |
|
428 int lev=level[w]; |
|
429 Num exc=excess[w]; |
|
430 int newlevel=n; //bound on the next level of w |
|
431 |
|
432 OutEdgeIt e; |
|
433 for(g->first(e,w); g->valid(e); g->next(e)) { |
|
434 |
|
435 if ( (*flow)[e] >= (*capacity)[e] ) continue; |
|
436 Node v=g->target(e); |
|
437 |
|
438 if( lev > level[v] ) { //Push is allowed now |
|
439 |
|
440 if ( excess[v]<=0 && v!=t && v!=s ) { |
|
441 int lev_v=level[v]; |
|
442 active[lev_v].push(v); |
|
443 } |
|
444 |
|
445 Num cap=(*capacity)[e]; |
|
446 Num flo=(*flow)[e]; |
|
447 Num remcap=cap-flo; |
|
448 |
|
449 if ( remcap >= exc ) { //A nonsaturating push. |
|
450 |
|
451 flow->set(e, flo+exc); |
|
452 excess.set(v, excess[v]+exc); |
|
453 exc=0; |
|
454 break; |
|
455 |
|
456 } else { //A saturating push. |
|
457 flow->set(e, cap); |
|
458 excess.set(v, excess[v]+remcap); |
|
459 exc-=remcap; |
|
460 } |
|
461 } else if ( newlevel > level[v] ) newlevel = level[v]; |
|
462 } //for out edges wv |
|
463 |
|
464 if ( exc > 0 ) { |
|
465 InEdgeIt e; |
|
466 for(g->first(e,w); g->valid(e); g->next(e)) { |
|
467 |
|
468 if( (*flow)[e] <= 0 ) continue; |
|
469 Node v=g->source(e); |
|
470 |
|
471 if( lev > level[v] ) { //Push is allowed now |
|
472 |
|
473 if ( excess[v]<=0 && v!=t && v!=s ) { |
|
474 int lev_v=level[v]; |
|
475 active[lev_v].push(v); |
|
476 } |
|
477 |
|
478 Num flo=(*flow)[e]; |
|
479 |
|
480 if ( flo >= exc ) { //A nonsaturating push. |
|
481 |
|
482 flow->set(e, flo-exc); |
|
483 excess.set(v, excess[v]+exc); |
|
484 exc=0; |
|
485 break; |
|
486 } else { //A saturating push. |
|
487 |
|
488 excess.set(v, excess[v]+flo); |
|
489 exc-=flo; |
|
490 flow->set(e,0); |
|
491 } |
|
492 } else if ( newlevel > level[v] ) newlevel = level[v]; |
|
493 } //for in edges vw |
|
494 |
|
495 } // if w still has excess after the out edge for cycle |
|
496 |
|
497 excess.set(w, exc); |
|
498 |
|
499 return newlevel; |
|
500 } |
|
501 |
|
502 |
|
503 void preflowPreproc(FlowEnum fe, VecStack& active, |
|
504 VecNode& level_list, NNMap& left, NNMap& right) |
|
505 { |
|
506 std::queue<Node> bfs_queue; |
|
507 |
|
508 switch (fe) { |
|
509 case NO_FLOW: //flow is already set to const zero in this case |
|
510 case ZERO_FLOW: |
|
511 { |
|
512 //Reverse_bfs from t, to find the starting level. |
|
513 level.set(t,0); |
|
514 bfs_queue.push(t); |
|
515 |
|
516 while (!bfs_queue.empty()) { |
|
517 |
|
518 Node v=bfs_queue.front(); |
|
519 bfs_queue.pop(); |
|
520 int l=level[v]+1; |
|
521 |
|
522 InEdgeIt e; |
|
523 for(g->first(e,v); g->valid(e); g->next(e)) { |
|
524 Node w=g->source(e); |
|
525 if ( level[w] == n && w != s ) { |
|
526 bfs_queue.push(w); |
|
527 Node first=level_list[l]; |
|
528 if ( g->valid(first) ) left.set(first,w); |
|
529 right.set(w,first); |
|
530 level_list[l]=w; |
|
531 level.set(w, l); |
|
532 } |
|
533 } |
|
534 } |
|
535 |
|
536 //the starting flow |
|
537 OutEdgeIt e; |
|
538 for(g->first(e,s); g->valid(e); g->next(e)) |
|
539 { |
|
540 Num c=(*capacity)[e]; |
|
541 if ( c <= 0 ) continue; |
|
542 Node w=g->target(e); |
|
543 if ( level[w] < n ) { |
|
544 if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
|
545 flow->set(e, c); |
|
546 excess.set(w, excess[w]+c); |
|
547 } |
|
548 } |
|
549 break; |
|
550 } |
|
551 |
|
552 case GEN_FLOW: |
|
553 case PRE_FLOW: |
|
554 { |
|
555 //Reverse_bfs from t in the residual graph, |
|
556 //to find the starting level. |
|
557 level.set(t,0); |
|
558 bfs_queue.push(t); |
|
559 |
|
560 while (!bfs_queue.empty()) { |
|
561 |
|
562 Node v=bfs_queue.front(); |
|
563 bfs_queue.pop(); |
|
564 int l=level[v]+1; |
|
565 |
|
566 InEdgeIt e; |
|
567 for(g->first(e,v); g->valid(e); g->next(e)) { |
|
568 if ( (*capacity)[e] <= (*flow)[e] ) continue; |
|
569 Node w=g->source(e); |
|
570 if ( level[w] == n && w != s ) { |
|
571 bfs_queue.push(w); |
|
572 Node first=level_list[l]; |
|
573 if ( g->valid(first) ) left.set(first,w); |
|
574 right.set(w,first); |
|
575 level_list[l]=w; |
|
576 level.set(w, l); |
|
577 } |
|
578 } |
|
579 |
|
580 OutEdgeIt f; |
|
581 for(g->first(f,v); g->valid(f); g->next(f)) { |
|
582 if ( 0 >= (*flow)[f] ) continue; |
|
583 Node w=g->target(f); |
|
584 if ( level[w] == n && w != s ) { |
|
585 bfs_queue.push(w); |
|
586 Node first=level_list[l]; |
|
587 if ( g->valid(first) ) left.set(first,w); |
|
588 right.set(w,first); |
|
589 level_list[l]=w; |
|
590 level.set(w, l); |
|
591 } |
|
592 } |
|
593 } |
|
594 |
|
595 |
|
596 //the starting flow |
|
597 OutEdgeIt e; |
|
598 for(g->first(e,s); g->valid(e); g->next(e)) |
|
599 { |
|
600 Num rem=(*capacity)[e]-(*flow)[e]; |
|
601 if ( rem <= 0 ) continue; |
|
602 Node w=g->target(e); |
|
603 if ( level[w] < n ) { |
|
604 if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
|
605 flow->set(e, (*capacity)[e]); |
|
606 excess.set(w, excess[w]+rem); |
|
607 } |
|
608 } |
|
609 |
|
610 InEdgeIt f; |
|
611 for(g->first(f,s); g->valid(f); g->next(f)) |
|
612 { |
|
613 if ( (*flow)[f] <= 0 ) continue; |
|
614 Node w=g->source(f); |
|
615 if ( level[w] < n ) { |
|
616 if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
|
617 excess.set(w, excess[w]+(*flow)[f]); |
|
618 flow->set(f, 0); |
|
619 } |
|
620 } |
|
621 break; |
|
622 } //case PRE_FLOW |
|
623 } |
|
624 } //preflowPreproc |
|
625 |
|
626 |
|
627 |
|
628 void relabel(Node w, int newlevel, VecStack& active, |
|
629 VecNode& level_list, NNMap& left, |
|
630 NNMap& right, int& b, int& k, bool what_heur ) |
|
631 { |
|
632 |
|
633 Num lev=level[w]; |
|
634 |
|
635 Node right_n=right[w]; |
|
636 Node left_n=left[w]; |
|
637 |
|
638 //unlacing starts |
|
639 if ( g->valid(right_n) ) { |
|
640 if ( g->valid(left_n) ) { |
|
641 right.set(left_n, right_n); |
|
642 left.set(right_n, left_n); |
|
643 } else { |
|
644 level_list[lev]=right_n; |
|
645 left.set(right_n, INVALID); |
|
646 } |
|
647 } else { |
|
648 if ( g->valid(left_n) ) { |
|
649 right.set(left_n, INVALID); |
|
650 } else { |
|
651 level_list[lev]=INVALID; |
|
652 } |
|
653 } |
|
654 //unlacing ends |
|
655 |
|
656 if ( !g->valid(level_list[lev]) ) { |
|
657 |
|
658 //gapping starts |
|
659 for (int i=lev; i!=k ; ) { |
|
660 Node v=level_list[++i]; |
|
661 while ( g->valid(v) ) { |
|
662 level.set(v,n); |
|
663 v=right[v]; |
|
664 } |
|
665 level_list[i]=INVALID; |
|
666 if ( !what_heur ) { |
|
667 while ( !active[i].empty() ) { |
|
668 active[i].pop(); //FIXME: ezt szebben kene |
|
669 } |
|
670 } |
|
671 } |
|
672 |
|
673 level.set(w,n); |
|
674 b=lev-1; |
|
675 k=b; |
|
676 //gapping ends |
|
677 |
|
678 } else { |
|
679 |
|
680 if ( newlevel == n ) level.set(w,n); |
|
681 else { |
|
682 level.set(w,++newlevel); |
|
683 active[newlevel].push(w); |
|
684 if ( what_heur ) b=newlevel; |
|
685 if ( k < newlevel ) ++k; //now k=newlevel |
|
686 Node first=level_list[newlevel]; |
|
687 if ( g->valid(first) ) left.set(first,w); |
|
688 right.set(w,first); |
|
689 left.set(w,INVALID); |
|
690 level_list[newlevel]=w; |
|
691 } |
|
692 } |
|
693 |
|
694 } //relabel |
|
695 |
|
696 |
|
697 template<typename MapGraphWrapper> |
|
698 class DistanceMap { |
|
699 protected: |
|
700 const MapGraphWrapper* g; |
|
701 typename MapGraphWrapper::template NodeMap<int> dist; |
|
702 public: |
|
703 DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { } |
|
704 void set(const typename MapGraphWrapper::Node& n, int a) { |
|
705 dist.set(n, a); |
|
706 } |
|
707 int operator[](const typename MapGraphWrapper::Node& n) const { |
|
708 return dist[n]; |
|
709 } |
|
710 // int get(const typename MapGraphWrapper::Node& n) const { |
|
711 // return dist[n]; } |
|
712 // bool get(const typename MapGraphWrapper::Edge& e) const { |
|
713 // return (dist.get(g->source(e))<dist.get(g->target(e))); } |
|
714 bool operator[](const typename MapGraphWrapper::Edge& e) const { |
|
715 return (dist[g->source(e)]<dist[g->target(e)]); |
|
716 } |
|
717 }; |
|
718 |
|
719 }; |
|
720 |
|
721 |
|
722 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
723 void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase1(FlowEnum fe) |
|
724 { |
|
725 |
|
726 int heur0=(int)(H0*n); //time while running 'bound decrease' |
|
727 int heur1=(int)(H1*n); //time while running 'highest label' |
|
728 int heur=heur1; //starting time interval (#of relabels) |
|
729 int numrelabel=0; |
|
730 |
|
731 bool what_heur=1; |
|
732 //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
|
733 |
|
734 bool end=false; |
|
735 //Needed for 'bound decrease', true means no active nodes are above bound |
|
736 //b. |
|
737 |
|
738 int k=n-2; //bound on the highest level under n containing a node |
|
739 int b=k; //bound on the highest level under n of an active node |
|
740 |
|
741 VecStack active(n); |
|
742 |
|
743 NNMap left(*g, INVALID); |
|
744 NNMap right(*g, INVALID); |
|
745 VecNode level_list(n,INVALID); |
|
746 //List of the nodes in level i<n, set to n. |
|
747 |
|
748 NodeIt v; |
|
749 for(g->first(v); g->valid(v); g->next(v)) level.set(v,n); |
|
750 //setting each node to level n |
|
751 |
|
752 if ( fe == NO_FLOW ) { |
|
753 EdgeIt e; |
|
754 for(g->first(e); g->valid(e); g->next(e)) flow->set(e,0); |
|
755 } |
|
756 |
|
757 switch (fe) { //computing the excess |
|
758 case PRE_FLOW: |
|
759 { |
|
760 NodeIt v; |
|
761 for(g->first(v); g->valid(v); g->next(v)) { |
|
762 Num exc=0; |
|
763 |
|
764 InEdgeIt e; |
|
765 for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
|
766 OutEdgeIt f; |
|
767 for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
|
768 |
|
769 excess.set(v,exc); |
|
770 |
|
771 //putting the active nodes into the stack |
|
772 int lev=level[v]; |
|
773 if ( exc > 0 && lev < n && v != t ) active[lev].push(v); |
|
774 } |
|
775 break; |
|
776 } |
|
777 case GEN_FLOW: |
|
778 { |
|
779 NodeIt v; |
|
780 for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
|
781 |
|
782 Num exc=0; |
|
783 InEdgeIt e; |
|
784 for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
|
785 OutEdgeIt f; |
|
786 for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
|
787 excess.set(t,exc); |
|
788 break; |
|
789 } |
|
790 case ZERO_FLOW: |
|
791 case NO_FLOW: |
|
792 { |
|
793 NodeIt v; |
|
794 for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
|
795 break; |
|
796 } |
|
797 } |
|
798 |
|
799 preflowPreproc(fe, active, level_list, left, right); |
|
800 //End of preprocessing |
|
801 |
|
802 |
|
803 //Push/relabel on the highest level active nodes. |
|
804 while ( true ) { |
|
805 if ( b == 0 ) { |
|
806 if ( !what_heur && !end && k > 0 ) { |
|
807 b=k; |
|
808 end=true; |
|
809 } else break; |
|
810 } |
|
811 |
|
812 if ( active[b].empty() ) --b; |
|
813 else { |
|
814 end=false; |
|
815 Node w=active[b].top(); |
|
816 active[b].pop(); |
|
817 int newlevel=push(w,active); |
|
818 if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list, |
|
819 left, right, b, k, what_heur); |
|
820 |
|
821 ++numrelabel; |
|
822 if ( numrelabel >= heur ) { |
|
823 numrelabel=0; |
|
824 if ( what_heur ) { |
|
825 what_heur=0; |
|
826 heur=heur0; |
|
827 end=false; |
|
828 } else { |
|
829 what_heur=1; |
|
830 heur=heur1; |
|
831 b=k; |
|
832 } |
|
833 } |
|
834 } |
|
835 } |
|
836 |
|
837 status=AFTER_PRE_FLOW_PHASE_1; |
|
838 } |
|
839 |
|
840 |
|
841 |
|
842 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
843 void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase2() |
|
844 { |
|
845 |
|
846 int k=n-2; //bound on the highest level under n containing a node |
|
847 int b=k; //bound on the highest level under n of an active node |
|
848 |
|
849 VecStack active(n); |
|
850 level.set(s,0); |
|
851 std::queue<Node> bfs_queue; |
|
852 bfs_queue.push(s); |
|
853 |
|
854 while (!bfs_queue.empty()) { |
|
855 |
|
856 Node v=bfs_queue.front(); |
|
857 bfs_queue.pop(); |
|
858 int l=level[v]+1; |
|
859 |
|
860 InEdgeIt e; |
|
861 for(g->first(e,v); g->valid(e); g->next(e)) { |
|
862 if ( (*capacity)[e] <= (*flow)[e] ) continue; |
|
863 Node u=g->source(e); |
|
864 if ( level[u] >= n ) { |
|
865 bfs_queue.push(u); |
|
866 level.set(u, l); |
|
867 if ( excess[u] > 0 ) active[l].push(u); |
|
868 } |
|
869 } |
|
870 |
|
871 OutEdgeIt f; |
|
872 for(g->first(f,v); g->valid(f); g->next(f)) { |
|
873 if ( 0 >= (*flow)[f] ) continue; |
|
874 Node u=g->target(f); |
|
875 if ( level[u] >= n ) { |
|
876 bfs_queue.push(u); |
|
877 level.set(u, l); |
|
878 if ( excess[u] > 0 ) active[l].push(u); |
|
879 } |
|
880 } |
|
881 } |
|
882 b=n-2; |
|
883 |
|
884 while ( true ) { |
|
885 |
|
886 if ( b == 0 ) break; |
|
887 |
|
888 if ( active[b].empty() ) --b; |
|
889 else { |
|
890 Node w=active[b].top(); |
|
891 active[b].pop(); |
|
892 int newlevel=push(w,active); |
|
893 |
|
894 //relabel |
|
895 if ( excess[w] > 0 ) { |
|
896 level.set(w,++newlevel); |
|
897 active[newlevel].push(w); |
|
898 b=newlevel; |
|
899 } |
|
900 } // if stack[b] is nonempty |
|
901 } // while(true) |
|
902 |
|
903 status=AFTER_PRE_FLOW_PHASE_2; |
|
904 } |
|
905 |
|
906 |
|
907 |
|
908 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
909 bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath() |
|
910 { |
|
911 ResGW res_graph(*g, *capacity, *flow); |
|
912 bool _augment=false; |
|
913 |
|
914 //ReachedMap level(res_graph); |
|
915 FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
|
916 BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
|
917 bfs.pushAndSetReached(s); |
|
918 |
|
919 typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); |
|
920 pred.set(s, INVALID); |
|
921 |
|
922 typename ResGW::template NodeMap<Num> free(res_graph); |
|
923 |
|
924 //searching for augmenting path |
|
925 while ( !bfs.finished() ) { |
|
926 ResGWOutEdgeIt e=bfs; |
|
927 if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
|
928 Node v=res_graph.source(e); |
|
929 Node w=res_graph.target(e); |
|
930 pred.set(w, e); |
|
931 if (res_graph.valid(pred[v])) { |
|
932 free.set(w, std::min(free[v], res_graph.resCap(e))); |
|
933 } else { |
|
934 free.set(w, res_graph.resCap(e)); |
|
935 } |
|
936 if (res_graph.target(e)==t) { _augment=true; break; } |
|
937 } |
|
938 |
|
939 ++bfs; |
|
940 } //end of searching augmenting path |
|
941 |
|
942 if (_augment) { |
|
943 Node n=t; |
|
944 Num augment_value=free[t]; |
|
945 while (res_graph.valid(pred[n])) { |
|
946 ResGWEdge e=pred[n]; |
|
947 res_graph.augment(e, augment_value); |
|
948 n=res_graph.source(e); |
|
949 } |
|
950 } |
|
951 |
|
952 status=AFTER_AUGMENTING; |
|
953 return _augment; |
|
954 } |
|
955 |
|
956 |
|
957 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
958 bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath2() |
|
959 { |
|
960 ResGW res_graph(*g, *capacity, *flow); |
|
961 bool _augment=false; |
|
962 |
|
963 if (status!=AFTER_FAST_AUGMENTING) { |
|
964 FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
|
965 number_of_augmentations=1; |
|
966 } else { |
|
967 ++number_of_augmentations; |
|
968 } |
|
969 TrickyReachedMap<ReachedMap> |
|
970 tricky_reached_map(level, number_of_augmentations); |
|
971 //ReachedMap level(res_graph); |
|
972 // FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
|
973 BfsIterator<ResGW, TrickyReachedMap<ReachedMap> > |
|
974 bfs(res_graph, tricky_reached_map); |
|
975 bfs.pushAndSetReached(s); |
|
976 |
|
977 typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); |
|
978 pred.set(s, INVALID); |
|
979 |
|
980 typename ResGW::template NodeMap<Num> free(res_graph); |
|
981 |
|
982 //searching for augmenting path |
|
983 while ( !bfs.finished() ) { |
|
984 ResGWOutEdgeIt e=bfs; |
|
985 if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
|
986 Node v=res_graph.source(e); |
|
987 Node w=res_graph.target(e); |
|
988 pred.set(w, e); |
|
989 if (res_graph.valid(pred[v])) { |
|
990 free.set(w, std::min(free[v], res_graph.resCap(e))); |
|
991 } else { |
|
992 free.set(w, res_graph.resCap(e)); |
|
993 } |
|
994 if (res_graph.target(e)==t) { _augment=true; break; } |
|
995 } |
|
996 |
|
997 ++bfs; |
|
998 } //end of searching augmenting path |
|
999 |
|
1000 if (_augment) { |
|
1001 Node n=t; |
|
1002 Num augment_value=free[t]; |
|
1003 while (res_graph.valid(pred[n])) { |
|
1004 ResGWEdge e=pred[n]; |
|
1005 res_graph.augment(e, augment_value); |
|
1006 n=res_graph.source(e); |
|
1007 } |
|
1008 } |
|
1009 |
|
1010 status=AFTER_FAST_AUGMENTING; |
|
1011 return _augment; |
|
1012 } |
|
1013 |
|
1014 |
|
1015 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
1016 template<typename MutableGraph> |
|
1017 bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow() |
|
1018 { |
|
1019 typedef MutableGraph MG; |
|
1020 bool _augment=false; |
|
1021 |
|
1022 ResGW res_graph(*g, *capacity, *flow); |
|
1023 |
|
1024 //bfs for distances on the residual graph |
|
1025 //ReachedMap level(res_graph); |
|
1026 FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
|
1027 BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
|
1028 bfs.pushAndSetReached(s); |
|
1029 typename ResGW::template NodeMap<int> |
|
1030 dist(res_graph); //filled up with 0's |
|
1031 |
|
1032 //F will contain the physical copy of the residual graph |
|
1033 //with the set of edges which are on shortest paths |
|
1034 MG F; |
|
1035 typename ResGW::template NodeMap<typename MG::Node> |
|
1036 res_graph_to_F(res_graph); |
|
1037 { |
|
1038 typename ResGW::NodeIt n; |
|
1039 for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) { |
|
1040 res_graph_to_F.set(n, F.addNode()); |
|
1041 } |
|
1042 } |
|
1043 |
|
1044 typename MG::Node sF=res_graph_to_F[s]; |
|
1045 typename MG::Node tF=res_graph_to_F[t]; |
|
1046 typename MG::template EdgeMap<ResGWEdge> original_edge(F); |
|
1047 typename MG::template EdgeMap<Num> residual_capacity(F); |
|
1048 |
|
1049 while ( !bfs.finished() ) { |
|
1050 ResGWOutEdgeIt e=bfs; |
|
1051 if (res_graph.valid(e)) { |
|
1052 if (bfs.isBNodeNewlyReached()) { |
|
1053 dist.set(res_graph.target(e), dist[res_graph.source(e)]+1); |
|
1054 typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.source(e)], |
|
1055 res_graph_to_F[res_graph.target(e)]); |
|
1056 original_edge.update(); |
|
1057 original_edge.set(f, e); |
|
1058 residual_capacity.update(); |
|
1059 residual_capacity.set(f, res_graph.resCap(e)); |
|
1060 } else { |
|
1061 if (dist[res_graph.target(e)]==(dist[res_graph.source(e)]+1)) { |
|
1062 typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.source(e)], |
|
1063 res_graph_to_F[res_graph.target(e)]); |
|
1064 original_edge.update(); |
|
1065 original_edge.set(f, e); |
|
1066 residual_capacity.update(); |
|
1067 residual_capacity.set(f, res_graph.resCap(e)); |
|
1068 } |
|
1069 } |
|
1070 } |
|
1071 ++bfs; |
|
1072 } //computing distances from s in the residual graph |
|
1073 |
|
1074 bool __augment=true; |
|
1075 |
|
1076 while (__augment) { |
|
1077 __augment=false; |
|
1078 //computing blocking flow with dfs |
|
1079 DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F); |
|
1080 typename MG::template NodeMap<typename MG::Edge> pred(F); |
|
1081 pred.set(sF, INVALID); |
|
1082 //invalid iterators for sources |
|
1083 |
|
1084 typename MG::template NodeMap<Num> free(F); |
|
1085 |
|
1086 dfs.pushAndSetReached(sF); |
|
1087 while (!dfs.finished()) { |
|
1088 ++dfs; |
|
1089 if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) { |
|
1090 if (dfs.isBNodeNewlyReached()) { |
|
1091 typename MG::Node v=F.aNode(dfs); |
|
1092 typename MG::Node w=F.bNode(dfs); |
|
1093 pred.set(w, dfs); |
|
1094 if (F.valid(pred[v])) { |
|
1095 free.set(w, std::min(free[v], residual_capacity[dfs])); |
|
1096 } else { |
|
1097 free.set(w, residual_capacity[dfs]); |
|
1098 } |
|
1099 if (w==tF) { |
|
1100 __augment=true; |
|
1101 _augment=true; |
|
1102 break; |
|
1103 } |
|
1104 |
|
1105 } else { |
|
1106 F.erase(/*typename MG::OutEdgeIt*/(dfs)); |
|
1107 } |
|
1108 } |
|
1109 } |
|
1110 |
|
1111 if (__augment) { |
|
1112 typename MG::Node n=tF; |
|
1113 Num augment_value=free[tF]; |
|
1114 while (F.valid(pred[n])) { |
|
1115 typename MG::Edge e=pred[n]; |
|
1116 res_graph.augment(original_edge[e], augment_value); |
|
1117 n=F.source(e); |
|
1118 if (residual_capacity[e]==augment_value) |
|
1119 F.erase(e); |
|
1120 else |
|
1121 residual_capacity.set(e, residual_capacity[e]-augment_value); |
|
1122 } |
|
1123 } |
|
1124 |
|
1125 } |
|
1126 |
|
1127 status=AFTER_AUGMENTING; |
|
1128 return _augment; |
|
1129 } |
|
1130 |
|
1131 |
|
1132 |
|
1133 |
|
1134 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
1135 bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2() |
|
1136 { |
|
1137 bool _augment=false; |
|
1138 |
|
1139 ResGW res_graph(*g, *capacity, *flow); |
|
1140 |
|
1141 //ReachedMap level(res_graph); |
|
1142 FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
|
1143 BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
|
1144 |
|
1145 bfs.pushAndSetReached(s); |
|
1146 DistanceMap<ResGW> dist(res_graph); |
|
1147 while ( !bfs.finished() ) { |
|
1148 ResGWOutEdgeIt e=bfs; |
|
1149 if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
|
1150 dist.set(res_graph.target(e), dist[res_graph.source(e)]+1); |
|
1151 } |
|
1152 ++bfs; |
|
1153 } //computing distances from s in the residual graph |
|
1154 |
|
1155 //Subgraph containing the edges on some shortest paths |
|
1156 ConstMap<typename ResGW::Node, bool> true_map(true); |
|
1157 typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, |
|
1158 DistanceMap<ResGW> > FilterResGW; |
|
1159 FilterResGW filter_res_graph(res_graph, true_map, dist); |
|
1160 |
|
1161 //Subgraph, which is able to delete edges which are already |
|
1162 //met by the dfs |
|
1163 typename FilterResGW::template NodeMap<typename FilterResGW::OutEdgeIt> |
|
1164 first_out_edges(filter_res_graph); |
|
1165 typename FilterResGW::NodeIt v; |
|
1166 for(filter_res_graph.first(v); filter_res_graph.valid(v); |
|
1167 filter_res_graph.next(v)) |
|
1168 { |
|
1169 typename FilterResGW::OutEdgeIt e; |
|
1170 filter_res_graph.first(e, v); |
|
1171 first_out_edges.set(v, e); |
|
1172 } |
|
1173 typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW:: |
|
1174 template NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW; |
|
1175 ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges); |
|
1176 |
|
1177 bool __augment=true; |
|
1178 |
|
1179 while (__augment) { |
|
1180 |
|
1181 __augment=false; |
|
1182 //computing blocking flow with dfs |
|
1183 DfsIterator< ErasingResGW, |
|
1184 typename ErasingResGW::template NodeMap<bool> > |
|
1185 dfs(erasing_res_graph); |
|
1186 typename ErasingResGW:: |
|
1187 template NodeMap<typename ErasingResGW::OutEdgeIt> |
|
1188 pred(erasing_res_graph); |
|
1189 pred.set(s, INVALID); |
|
1190 //invalid iterators for sources |
|
1191 |
|
1192 typename ErasingResGW::template NodeMap<Num> |
|
1193 free1(erasing_res_graph); |
|
1194 |
|
1195 dfs.pushAndSetReached |
|
1196 ///\bug lemon 0.2 |
|
1197 (typename ErasingResGW::Node |
|
1198 (typename FilterResGW::Node |
|
1199 (typename ResGW::Node(s) |
|
1200 ) |
|
1201 ) |
|
1202 ); |
|
1203 while (!dfs.finished()) { |
|
1204 ++dfs; |
|
1205 if (erasing_res_graph.valid(typename ErasingResGW::OutEdgeIt(dfs))) |
|
1206 { |
|
1207 if (dfs.isBNodeNewlyReached()) { |
|
1208 |
|
1209 typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs); |
|
1210 typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs); |
|
1211 |
|
1212 pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs)); |
|
1213 if (erasing_res_graph.valid(pred[v])) { |
|
1214 free1.set |
|
1215 (w, std::min(free1[v], res_graph.resCap |
|
1216 (typename ErasingResGW::OutEdgeIt(dfs)))); |
|
1217 } else { |
|
1218 free1.set |
|
1219 (w, res_graph.resCap |
|
1220 (typename ErasingResGW::OutEdgeIt(dfs))); |
|
1221 } |
|
1222 |
|
1223 if (w==t) { |
|
1224 __augment=true; |
|
1225 _augment=true; |
|
1226 break; |
|
1227 } |
|
1228 } else { |
|
1229 erasing_res_graph.erase(dfs); |
|
1230 } |
|
1231 } |
|
1232 } |
|
1233 |
|
1234 if (__augment) { |
|
1235 typename ErasingResGW::Node |
|
1236 n=typename FilterResGW::Node(typename ResGW::Node(t)); |
|
1237 // typename ResGW::NodeMap<Num> a(res_graph); |
|
1238 // typename ResGW::Node b; |
|
1239 // Num j=a[b]; |
|
1240 // typename FilterResGW::NodeMap<Num> a1(filter_res_graph); |
|
1241 // typename FilterResGW::Node b1; |
|
1242 // Num j1=a1[b1]; |
|
1243 // typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph); |
|
1244 // typename ErasingResGW::Node b2; |
|
1245 // Num j2=a2[b2]; |
|
1246 Num augment_value=free1[n]; |
|
1247 while (erasing_res_graph.valid(pred[n])) { |
|
1248 typename ErasingResGW::OutEdgeIt e=pred[n]; |
|
1249 res_graph.augment(e, augment_value); |
|
1250 n=erasing_res_graph.source(e); |
|
1251 if (res_graph.resCap(e)==0) |
|
1252 erasing_res_graph.erase(e); |
|
1253 } |
|
1254 } |
|
1255 |
|
1256 } //while (__augment) |
|
1257 |
|
1258 status=AFTER_AUGMENTING; |
|
1259 return _augment; |
|
1260 } |
|
1261 |
|
1262 |
|
1263 } //namespace lemon |
|
1264 |
|
1265 #endif //LEMON_MAX_FLOW_H |
|
1266 |
|
1267 |
|
1268 |
|
1269 |
|