1 | // -*- C++ -*- |
---|
2 | /* |
---|
3 | preflow.h |
---|
4 | by jacint. |
---|
5 | Heuristics: |
---|
6 | 2 phase |
---|
7 | gap |
---|
8 | list 'level_list' on the nodes on level i implemented by hand |
---|
9 | stack 'active' on the active nodes on level i implemented by hand |
---|
10 | runs heuristic 'highest label' for H1*n relabels |
---|
11 | runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
---|
12 | |
---|
13 | Parameters H0 and H1 are initialized to 20 and 10. |
---|
14 | |
---|
15 | The best preflow I could ever write. |
---|
16 | |
---|
17 | The constructor runs the algorithm. |
---|
18 | |
---|
19 | Members: |
---|
20 | |
---|
21 | T maxFlow() : returns the value of a maximum flow |
---|
22 | |
---|
23 | T flowOnEdge(EdgeIt e) : for a fixed maximum flow x it returns x(e) |
---|
24 | |
---|
25 | FlowMap Flow() : returns the fixed maximum flow x |
---|
26 | |
---|
27 | void minMinCut(CutMap& M) : sets M to the characteristic vector of the |
---|
28 | minimum min cut. M should be a map of bools initialized to false. |
---|
29 | |
---|
30 | void maxMinCut(CutMap& M) : sets M to the characteristic vector of the |
---|
31 | maximum min cut. M should be a map of bools initialized to false. |
---|
32 | |
---|
33 | void minCut(CutMap& M) : sets M to the characteristic vector of |
---|
34 | a min cut. M should be a map of bools initialized to false. |
---|
35 | |
---|
36 | */ |
---|
37 | |
---|
38 | #ifndef PREFLOW_H |
---|
39 | #define PREFLOW_H |
---|
40 | |
---|
41 | #define H0 20 |
---|
42 | #define H1 1 |
---|
43 | |
---|
44 | #include <vector> |
---|
45 | #include <queue> |
---|
46 | |
---|
47 | #include <time_measure.h> |
---|
48 | |
---|
49 | namespace hugo { |
---|
50 | |
---|
51 | template <typename Graph, typename T, |
---|
52 | typename FlowMap=typename Graph::EdgeMap<T>, |
---|
53 | typename CapMap=typename Graph::EdgeMap<T> > |
---|
54 | class preflow { |
---|
55 | |
---|
56 | typedef typename Graph::NodeIt NodeIt; |
---|
57 | typedef typename Graph::EdgeIt EdgeIt; |
---|
58 | typedef typename Graph::EachNodeIt EachNodeIt; |
---|
59 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
60 | typedef typename Graph::InEdgeIt InEdgeIt; |
---|
61 | |
---|
62 | Graph& G; |
---|
63 | NodeIt s; |
---|
64 | NodeIt t; |
---|
65 | FlowMap flow; |
---|
66 | CapMap& capacity; |
---|
67 | T value; |
---|
68 | |
---|
69 | public: |
---|
70 | double time; |
---|
71 | preflow(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity ) : |
---|
72 | G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity) |
---|
73 | { |
---|
74 | |
---|
75 | bool phase=0; //phase 0 is the 1st phase, phase 1 is the 2nd |
---|
76 | int n=G.nodeNum(); |
---|
77 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
---|
78 | int heur1=(int)(H1*n); //time while running 'highest label' |
---|
79 | int heur=heur1; //starting time interval (#of relabels) |
---|
80 | bool what_heur=1; |
---|
81 | /* |
---|
82 | what_heur is 0 in case 'bound decrease' |
---|
83 | and 1 in case 'highest label' |
---|
84 | */ |
---|
85 | bool end=false; |
---|
86 | /* |
---|
87 | Needed for 'bound decrease', 'true' |
---|
88 | means no active nodes are above bound b. |
---|
89 | */ |
---|
90 | int relabel=0; |
---|
91 | int k=n-2; //bound on the highest level under n containing a node |
---|
92 | int b=k; //bound on the highest level under n of an active node |
---|
93 | |
---|
94 | typename Graph::NodeMap<int> level(G,n); |
---|
95 | typename Graph::NodeMap<T> excess(G); |
---|
96 | |
---|
97 | std::vector<NodeIt> active(n); |
---|
98 | typename Graph::NodeMap<NodeIt> next(G); |
---|
99 | //Stack of the active nodes in level i < n. |
---|
100 | //We use it in both phases. |
---|
101 | |
---|
102 | typename Graph::NodeMap<NodeIt> left(G); |
---|
103 | typename Graph::NodeMap<NodeIt> right(G); |
---|
104 | std::vector<NodeIt> level_list(n); |
---|
105 | /* |
---|
106 | List of the nodes in level i<n. |
---|
107 | */ |
---|
108 | |
---|
109 | /*Reverse_bfs from t, to find the starting level.*/ |
---|
110 | level.set(t,0); |
---|
111 | std::queue<NodeIt> bfs_queue; |
---|
112 | bfs_queue.push(t); |
---|
113 | |
---|
114 | while (!bfs_queue.empty()) { |
---|
115 | |
---|
116 | NodeIt v=bfs_queue.front(); |
---|
117 | bfs_queue.pop(); |
---|
118 | int l=level.get(v)+1; |
---|
119 | |
---|
120 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
---|
121 | NodeIt w=G.tail(e); |
---|
122 | if ( level.get(w) == n && w != s ) { |
---|
123 | bfs_queue.push(w); |
---|
124 | NodeIt first=level_list[l]; |
---|
125 | if ( first != 0 ) left.set(first,w); |
---|
126 | right.set(w,first); |
---|
127 | level_list[l]=w; |
---|
128 | level.set(w, l); |
---|
129 | } |
---|
130 | } |
---|
131 | } |
---|
132 | |
---|
133 | level.set(s,n); |
---|
134 | |
---|
135 | |
---|
136 | /* Starting flow. It is everywhere 0 at the moment. */ |
---|
137 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
---|
138 | { |
---|
139 | T c=capacity.get(e); |
---|
140 | if ( c == 0 ) continue; |
---|
141 | NodeIt w=G.head(e); |
---|
142 | if ( level.get(w) < n ) { |
---|
143 | if ( excess.get(w) == 0 && w!=t ) { |
---|
144 | next.set(w,active[level.get(w)]); |
---|
145 | active[level.get(w)]=w; |
---|
146 | } |
---|
147 | flow.set(e, c); |
---|
148 | excess.set(w, excess.get(w)+c); |
---|
149 | } |
---|
150 | } |
---|
151 | |
---|
152 | /* |
---|
153 | End of preprocessing |
---|
154 | */ |
---|
155 | |
---|
156 | |
---|
157 | |
---|
158 | /* |
---|
159 | Push/relabel on the highest level active nodes. |
---|
160 | */ |
---|
161 | while ( true ) { |
---|
162 | |
---|
163 | if ( b == 0 ) { |
---|
164 | if ( phase ) break; |
---|
165 | |
---|
166 | if ( !what_heur && !end && k > 0 ) { |
---|
167 | b=k; |
---|
168 | end=true; |
---|
169 | } else { |
---|
170 | phase=1; |
---|
171 | time=currTime(); |
---|
172 | level.set(s,0); |
---|
173 | std::queue<NodeIt> bfs_queue; |
---|
174 | bfs_queue.push(s); |
---|
175 | |
---|
176 | while (!bfs_queue.empty()) { |
---|
177 | |
---|
178 | NodeIt v=bfs_queue.front(); |
---|
179 | bfs_queue.pop(); |
---|
180 | int l=level.get(v)+1; |
---|
181 | |
---|
182 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
---|
183 | if ( capacity.get(e) == flow.get(e) ) continue; |
---|
184 | NodeIt u=G.tail(e); |
---|
185 | if ( level.get(u) >= n ) { |
---|
186 | bfs_queue.push(u); |
---|
187 | level.set(u, l); |
---|
188 | if ( excess.get(u) > 0 ) { |
---|
189 | next.set(u,active[l]); |
---|
190 | active[l]=u; |
---|
191 | } |
---|
192 | } |
---|
193 | } |
---|
194 | |
---|
195 | for(OutEdgeIt e=G.template first<OutEdgeIt>(v); e.valid(); ++e) { |
---|
196 | if ( 0 == flow.get(e) ) continue; |
---|
197 | NodeIt u=G.head(e); |
---|
198 | if ( level.get(u) >= n ) { |
---|
199 | bfs_queue.push(u); |
---|
200 | level.set(u, l); |
---|
201 | if ( excess.get(u) > 0 ) { |
---|
202 | next.set(u,active[l]); |
---|
203 | active[l]=u; |
---|
204 | } |
---|
205 | } |
---|
206 | } |
---|
207 | } |
---|
208 | b=n-2; |
---|
209 | } |
---|
210 | |
---|
211 | } |
---|
212 | |
---|
213 | |
---|
214 | if ( active[b] == 0 ) --b; |
---|
215 | else { |
---|
216 | end=false; |
---|
217 | |
---|
218 | NodeIt w=active[b]; |
---|
219 | active[b]=next.get(w); |
---|
220 | int lev=level.get(w); |
---|
221 | T exc=excess.get(w); |
---|
222 | int newlevel=n; //bound on the next level of w |
---|
223 | |
---|
224 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
---|
225 | |
---|
226 | if ( flow.get(e) == capacity.get(e) ) continue; |
---|
227 | NodeIt v=G.head(e); |
---|
228 | //e=wv |
---|
229 | |
---|
230 | if( lev > level.get(v) ) { |
---|
231 | /*Push is allowed now*/ |
---|
232 | |
---|
233 | if ( excess.get(v)==0 && v!=t && v!=s ) { |
---|
234 | int lev_v=level.get(v); |
---|
235 | next.set(v,active[lev_v]); |
---|
236 | active[lev_v]=v; |
---|
237 | } |
---|
238 | |
---|
239 | T cap=capacity.get(e); |
---|
240 | T flo=flow.get(e); |
---|
241 | T remcap=cap-flo; |
---|
242 | |
---|
243 | if ( remcap >= exc ) { |
---|
244 | /*A nonsaturating push.*/ |
---|
245 | |
---|
246 | flow.set(e, flo+exc); |
---|
247 | excess.set(v, excess.get(v)+exc); |
---|
248 | exc=0; |
---|
249 | break; |
---|
250 | |
---|
251 | } else { |
---|
252 | /*A saturating push.*/ |
---|
253 | |
---|
254 | flow.set(e, cap); |
---|
255 | excess.set(v, excess.get(v)+remcap); |
---|
256 | exc-=remcap; |
---|
257 | } |
---|
258 | } else if ( newlevel > level.get(v) ){ |
---|
259 | newlevel = level.get(v); |
---|
260 | } |
---|
261 | |
---|
262 | } //for out edges wv |
---|
263 | |
---|
264 | |
---|
265 | if ( exc > 0 ) { |
---|
266 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
---|
267 | |
---|
268 | if( flow.get(e) == 0 ) continue; |
---|
269 | NodeIt v=G.tail(e); |
---|
270 | //e=vw |
---|
271 | |
---|
272 | if( lev > level.get(v) ) { |
---|
273 | /*Push is allowed now*/ |
---|
274 | |
---|
275 | if ( excess.get(v)==0 && v!=t && v!=s ) { |
---|
276 | int lev_v=level.get(v); |
---|
277 | next.set(v,active[lev_v]); |
---|
278 | active[lev_v]=v; |
---|
279 | } |
---|
280 | |
---|
281 | T flo=flow.get(e); |
---|
282 | |
---|
283 | if ( flo >= exc ) { |
---|
284 | /*A nonsaturating push.*/ |
---|
285 | |
---|
286 | flow.set(e, flo-exc); |
---|
287 | excess.set(v, excess.get(v)+exc); |
---|
288 | exc=0; |
---|
289 | break; |
---|
290 | } else { |
---|
291 | /*A saturating push.*/ |
---|
292 | |
---|
293 | excess.set(v, excess.get(v)+flo); |
---|
294 | exc-=flo; |
---|
295 | flow.set(e,0); |
---|
296 | } |
---|
297 | } else if ( newlevel > level.get(v) ) { |
---|
298 | newlevel = level.get(v); |
---|
299 | } |
---|
300 | } //for in edges vw |
---|
301 | |
---|
302 | } // if w still has excess after the out edge for cycle |
---|
303 | |
---|
304 | excess.set(w, exc); |
---|
305 | |
---|
306 | /* |
---|
307 | Relabel |
---|
308 | */ |
---|
309 | |
---|
310 | |
---|
311 | if ( exc > 0 ) { |
---|
312 | //now 'lev' is the old level of w |
---|
313 | |
---|
314 | if ( phase ) { |
---|
315 | level.set(w,++newlevel); |
---|
316 | next.set(w,active[newlevel]); |
---|
317 | active[newlevel]=w; |
---|
318 | b=newlevel; |
---|
319 | } else { |
---|
320 | //unlacing starts |
---|
321 | NodeIt right_n=right.get(w); |
---|
322 | NodeIt left_n=left.get(w); |
---|
323 | |
---|
324 | if ( right_n != 0 ) { |
---|
325 | if ( left_n != 0 ) { |
---|
326 | right.set(left_n, right_n); |
---|
327 | left.set(right_n, left_n); |
---|
328 | } else { |
---|
329 | level_list[lev]=right_n; |
---|
330 | left.set(right_n, 0); |
---|
331 | } |
---|
332 | } else { |
---|
333 | if ( left_n != 0 ) { |
---|
334 | right.set(left_n, 0); |
---|
335 | } else { |
---|
336 | level_list[lev]=0; |
---|
337 | |
---|
338 | } |
---|
339 | } |
---|
340 | //unlacing ends |
---|
341 | |
---|
342 | //gapping starts |
---|
343 | if ( level_list[lev]==0 ) { |
---|
344 | |
---|
345 | for (int i=lev; i!=k ; ) { |
---|
346 | NodeIt v=level_list[++i]; |
---|
347 | while ( v != 0 ) { |
---|
348 | level.set(v,n); |
---|
349 | v=right.get(v); |
---|
350 | } |
---|
351 | level_list[i]=0; |
---|
352 | if ( !what_heur ) active[i]=0; |
---|
353 | } |
---|
354 | |
---|
355 | level.set(w,n); |
---|
356 | b=lev-1; |
---|
357 | k=b; |
---|
358 | //gapping ends |
---|
359 | } else { |
---|
360 | |
---|
361 | if ( newlevel == n ) level.set(w,n); |
---|
362 | else { |
---|
363 | level.set(w,++newlevel); |
---|
364 | next.set(w,active[newlevel]); |
---|
365 | active[newlevel]=w; |
---|
366 | if ( what_heur ) b=newlevel; |
---|
367 | if ( k < newlevel ) ++k; |
---|
368 | NodeIt first=level_list[newlevel]; |
---|
369 | if ( first != 0 ) left.set(first,w); |
---|
370 | right.set(w,first); |
---|
371 | left.set(w,0); |
---|
372 | level_list[newlevel]=w; |
---|
373 | } |
---|
374 | } |
---|
375 | |
---|
376 | |
---|
377 | ++relabel; |
---|
378 | if ( relabel >= heur ) { |
---|
379 | relabel=0; |
---|
380 | if ( what_heur ) { |
---|
381 | what_heur=0; |
---|
382 | heur=heur0; |
---|
383 | end=false; |
---|
384 | } else { |
---|
385 | what_heur=1; |
---|
386 | heur=heur1; |
---|
387 | b=k; |
---|
388 | } |
---|
389 | } |
---|
390 | } //phase 0 |
---|
391 | |
---|
392 | |
---|
393 | } // if ( exc > 0 ) |
---|
394 | |
---|
395 | |
---|
396 | } // if stack[b] is nonempty |
---|
397 | |
---|
398 | } // while(true) |
---|
399 | |
---|
400 | |
---|
401 | value = excess.get(t); |
---|
402 | /*Max flow value.*/ |
---|
403 | |
---|
404 | } //void run() |
---|
405 | |
---|
406 | |
---|
407 | |
---|
408 | |
---|
409 | |
---|
410 | /* |
---|
411 | Returns the maximum value of a flow. |
---|
412 | */ |
---|
413 | |
---|
414 | T maxFlow() { |
---|
415 | return value; |
---|
416 | } |
---|
417 | |
---|
418 | |
---|
419 | |
---|
420 | /* |
---|
421 | For the maximum flow x found by the algorithm, |
---|
422 | it returns the flow value on edge e, i.e. x(e). |
---|
423 | */ |
---|
424 | |
---|
425 | T flowOnEdge(EdgeIt e) { |
---|
426 | return flow.get(e); |
---|
427 | } |
---|
428 | |
---|
429 | |
---|
430 | |
---|
431 | FlowMap Flow() { |
---|
432 | return flow; |
---|
433 | } |
---|
434 | |
---|
435 | |
---|
436 | |
---|
437 | void Flow(FlowMap& _flow ) { |
---|
438 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) |
---|
439 | _flow.set(v,flow.get(v)); |
---|
440 | } |
---|
441 | |
---|
442 | |
---|
443 | |
---|
444 | /* |
---|
445 | Returns the minimum min cut, by a bfs from s in the residual graph. |
---|
446 | */ |
---|
447 | |
---|
448 | template<typename _CutMap> |
---|
449 | void minMinCut(_CutMap& M) { |
---|
450 | |
---|
451 | std::queue<NodeIt> queue; |
---|
452 | |
---|
453 | M.set(s,true); |
---|
454 | queue.push(s); |
---|
455 | |
---|
456 | while (!queue.empty()) { |
---|
457 | NodeIt w=queue.front(); |
---|
458 | queue.pop(); |
---|
459 | |
---|
460 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
---|
461 | NodeIt v=G.head(e); |
---|
462 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
---|
463 | queue.push(v); |
---|
464 | M.set(v, true); |
---|
465 | } |
---|
466 | } |
---|
467 | |
---|
468 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
---|
469 | NodeIt v=G.tail(e); |
---|
470 | if (!M.get(v) && flow.get(e) > 0 ) { |
---|
471 | queue.push(v); |
---|
472 | M.set(v, true); |
---|
473 | } |
---|
474 | } |
---|
475 | } |
---|
476 | } |
---|
477 | |
---|
478 | |
---|
479 | |
---|
480 | /* |
---|
481 | Returns the maximum min cut, by a reverse bfs |
---|
482 | from t in the residual graph. |
---|
483 | */ |
---|
484 | |
---|
485 | template<typename _CutMap> |
---|
486 | void maxMinCut(_CutMap& M) { |
---|
487 | |
---|
488 | std::queue<NodeIt> queue; |
---|
489 | |
---|
490 | M.set(t,true); |
---|
491 | queue.push(t); |
---|
492 | |
---|
493 | while (!queue.empty()) { |
---|
494 | NodeIt w=queue.front(); |
---|
495 | queue.pop(); |
---|
496 | |
---|
497 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
---|
498 | NodeIt v=G.tail(e); |
---|
499 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
---|
500 | queue.push(v); |
---|
501 | M.set(v, true); |
---|
502 | } |
---|
503 | } |
---|
504 | |
---|
505 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
---|
506 | NodeIt v=G.head(e); |
---|
507 | if (!M.get(v) && flow.get(e) > 0 ) { |
---|
508 | queue.push(v); |
---|
509 | M.set(v, true); |
---|
510 | } |
---|
511 | } |
---|
512 | } |
---|
513 | |
---|
514 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) { |
---|
515 | M.set(v, !M.get(v)); |
---|
516 | } |
---|
517 | |
---|
518 | } |
---|
519 | |
---|
520 | |
---|
521 | |
---|
522 | template<typename CutMap> |
---|
523 | void minCut(CutMap& M) { |
---|
524 | minMinCut(M); |
---|
525 | } |
---|
526 | |
---|
527 | |
---|
528 | }; |
---|
529 | }//namespace marci |
---|
530 | #endif |
---|
531 | |
---|
532 | |
---|
533 | |
---|
534 | |
---|