jacint javitgatott.
2 #ifndef HUGO_MAX_FLOW_NO_STACK_H
3 #define HUGO_MAX_FLOW_NO_STACK_H
9 #include <hugo/graph_wrapper.h>
10 #include <hugo/invalid.h>
11 #include <hugo/maps.h>
14 /// \brief The same as max_flow.h, but without using stl stack for the active nodes. Only for test.
21 ///Maximum flow algorithms class.
23 ///This class provides various algorithms for finding a flow of
24 ///maximum value in a directed graph. The \e source node, the \e
25 ///target node, the \e capacity of the edges and the \e starting \e
26 ///flow value of the edges should be passed to the algorithm through the
27 ///constructor. It is possible to change these quantities using the
28 ///functions \ref resetSource, \ref resetTarget, \ref resetCap and
29 ///\ref resetFlow. Before any subsequent runs of any algorithm of
30 ///the class \ref resetFlow should be called.
32 ///After running an algorithm of the class, the actual flow value
33 ///can be obtained by calling \ref flowValue(). The minimum
34 ///value cut can be written into a \c node map of \c bools by
35 ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes
36 ///the inclusionwise minimum and maximum of the minimum value
38 ///\param Graph The directed graph type the algorithm runs on.
39 ///\param Num The number type of the capacities and the flow values.
40 ///\param CapMap The capacity map type.
41 ///\param FlowMap The flow map type.
42 ///\author Marton Makai, Jacint Szabo
43 template <typename Graph, typename Num,
44 typename CapMap=typename Graph::template EdgeMap<Num>,
45 typename FlowMap=typename Graph::template EdgeMap<Num> >
48 typedef typename Graph::Node Node;
49 typedef typename Graph::NodeIt NodeIt;
50 typedef typename Graph::EdgeIt EdgeIt;
51 typedef typename Graph::OutEdgeIt OutEdgeIt;
52 typedef typename Graph::InEdgeIt InEdgeIt;
54 // typedef typename std::vector<std::stack<Node> > VecStack;
55 typedef typename std::vector<Node> VecFirst;
56 typedef typename Graph::template NodeMap<Node> NNMap;
57 typedef typename std::vector<Node> VecNode;
62 const CapMap* capacity;
64 int n; //the number of nodes of G
65 typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;
66 //typedef ExpResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;
67 typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;
68 typedef typename ResGW::Edge ResGWEdge;
69 //typedef typename ResGW::template NodeMap<bool> ReachedMap;
70 typedef typename Graph::template NodeMap<int> ReachedMap;
73 //level works as a bool map in augmenting path algorithms and is
74 //used by bfs for storing reached information. In preflow, it
75 //shows the levels of nodes.
78 //excess is needed only in preflow
79 typename Graph::template NodeMap<Num> excess;
81 // constants used for heuristics
82 static const int H0=20;
83 static const int H1=1;
87 ///Indicates the property of the starting flow.
89 ///Indicates the property of the starting flow. The meanings are as follows:
90 ///- \c ZERO_FLOW: constant zero flow
91 ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to
92 ///the sum of the out-flows in every node except the \e source and
94 ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at
95 ///least the sum of the out-flows in every node except the \e source.
96 ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be
97 ///set to the constant zero flow in the beginning of the algorithm in this case.
108 AFTER_FAST_AUGMENTING,
109 AFTER_PRE_FLOW_PHASE_1,
110 AFTER_PRE_FLOW_PHASE_2
113 /// Don not needle this flag only if necessary.
116 // int number_of_augmentations;
119 // template<typename IntMap>
120 // class TrickyReachedMap {
123 // int* number_of_augmentations;
125 // TrickyReachedMap(IntMap& _map, int& _number_of_augmentations) :
126 // map(&_map), number_of_augmentations(&_number_of_augmentations) { }
127 // void set(const Node& n, bool b) {
129 // map->set(n, *number_of_augmentations);
131 // map->set(n, *number_of_augmentations-1);
133 // bool operator[](const Node& n) const {
134 // return (*map)[n]==*number_of_augmentations;
140 ///\todo Document, please.
142 MaxFlow(const Graph& _G, Node _s, Node _t,
143 const CapMap& _capacity, FlowMap& _flow) :
144 g(&_G), s(_s), t(_t), capacity(&_capacity),
145 flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0),
146 status(AFTER_NOTHING) { }
148 ///Runs a maximum flow algorithm.
150 ///Runs a preflow algorithm, which is the fastest maximum flow
151 ///algorithm up-to-date. The default for \c fe is ZERO_FLOW.
152 ///\pre The starting flow must be
153 /// - a constant zero flow if \c fe is \c ZERO_FLOW,
154 /// - an arbitary flow if \c fe is \c GEN_FLOW,
155 /// - an arbitary preflow if \c fe is \c PRE_FLOW,
156 /// - any map if \c fe is NO_FLOW.
157 void run(FlowEnum fe=ZERO_FLOW) {
162 ///Runs a preflow algorithm.
164 ///Runs a preflow algorithm. The preflow algorithms provide the
165 ///fastest way to compute a maximum flow in a directed graph.
166 ///\pre The starting flow must be
167 /// - a constant zero flow if \c fe is \c ZERO_FLOW,
168 /// - an arbitary flow if \c fe is \c GEN_FLOW,
169 /// - an arbitary preflow if \c fe is \c PRE_FLOW,
170 /// - any map if \c fe is NO_FLOW.
172 ///\todo NO_FLOW should be the default flow.
173 void preflow(FlowEnum fe) {
180 // list 'level_list' on the nodes on level i implemented by hand
181 // stack 'active' on the active nodes on level i
182 // runs heuristic 'highest label' for H1*n relabels
183 // runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'
184 // Parameters H0 and H1 are initialized to 20 and 1.
186 ///Runs the first phase of the preflow algorithm.
188 ///The preflow algorithm consists of two phases, this method runs the
189 ///first phase. After the first phase the maximum flow value and a
190 ///minimum value cut can already be computed, though a maximum flow
191 ///is net yet obtained. So after calling this method \ref flowValue
192 ///and \ref actMinCut gives proper results.
193 ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not
194 ///give minimum value cuts unless calling \ref preflowPhase2.
195 ///\pre The starting flow must be
196 /// - a constant zero flow if \c fe is \c ZERO_FLOW,
197 /// - an arbitary flow if \c fe is \c GEN_FLOW,
198 /// - an arbitary preflow if \c fe is \c PRE_FLOW,
199 /// - any map if \c fe is NO_FLOW.
200 void preflowPhase1(FlowEnum fe)
203 int heur0=(int)(H0*n); //time while running 'bound decrease'
204 int heur1=(int)(H1*n); //time while running 'highest label'
205 int heur=heur1; //starting time interval (#of relabels)
209 //It is 0 in case 'bound decrease' and 1 in case 'highest label'
212 //Needed for 'bound decrease', true means no active nodes are above bound
215 int k=n-2; //bound on the highest level under n containing a node
216 int b=k; //bound on the highest level under n of an active node
218 VecFirst first(n, INVALID);
219 NNMap next(*g, INVALID); //maybe INVALID is not needed
221 NNMap left(*g, INVALID);
222 NNMap right(*g, INVALID);
223 VecNode level_list(n,INVALID);
224 //List of the nodes in level i<n, set to n.
227 for(g->first(v); g->valid(v); g->next(v)) level.set(v,n);
228 //setting each node to level n
230 if ( fe == NO_FLOW ) {
232 for(g->first(e); g->valid(e); g->next(e)) flow->set(e,0);
235 switch (fe) { //computing the excess
239 for(g->first(v); g->valid(v); g->next(v)) {
243 for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e];
245 for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f];
249 //putting the active nodes into the stack
251 if ( exc > 0 && lev < n && v != t )
253 next.set(v,first[lev]);
262 for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);
266 for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e];
268 for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f];
276 for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);
281 preflowPreproc(fe, next, first, level_list, left, right);
282 //End of preprocessing
285 //Push/relabel on the highest level active nodes.
288 if ( !what_heur && !end && k > 0 ) {
294 if ( !g->valid(first[b]) ) --b;
299 int newlevel=push(w, next, first);
300 if ( excess[w] > 0 ) relabel(w, newlevel, next, first, level_list,
301 left, right, b, k, what_heur);
304 if ( numrelabel >= heur ) {
319 status=AFTER_PRE_FLOW_PHASE_1;
323 ///Runs the second phase of the preflow algorithm.
325 ///The preflow algorithm consists of two phases, this method runs
326 ///the second phase. After calling \ref preflowPhase1 and then
327 ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut,
328 ///\ref minMinCut and \ref maxMinCut give proper results.
329 ///\pre \ref preflowPhase1 must be called before.
333 int k=n-2; //bound on the highest level under n containing a node
334 int b=k; //bound on the highest level under n of an active node
337 VecFirst first(n, INVALID);
338 NNMap next(*g, INVALID); //maybe INVALID is not needed
340 std::queue<Node> bfs_queue;
343 while (!bfs_queue.empty()) {
345 Node v=bfs_queue.front();
350 for(g->first(e,v); g->valid(e); g->next(e)) {
351 if ( (*capacity)[e] <= (*flow)[e] ) continue;
353 if ( level[u] >= n ) {
356 if ( excess[u] > 0 ) {
357 next.set(u,first[l]);
364 for(g->first(f,v); g->valid(f); g->next(f)) {
365 if ( 0 >= (*flow)[f] ) continue;
367 if ( level[u] >= n ) {
370 if ( excess[u] > 0 ) {
371 next.set(u,first[l]);
383 if ( !g->valid(first[b]) ) --b;
388 int newlevel=push(w,next, first/*active*/);
391 if ( excess[w] > 0 ) {
392 level.set(w,++newlevel);
393 next.set(w,first[newlevel]);
397 } // if stack[b] is nonempty
400 status=AFTER_PRE_FLOW_PHASE_2;
404 /// Returns the maximum value of a flow.
406 /// Returns the maximum value of a flow, by counting the
407 /// over-flow of the target node \ref t.
408 /// It can be called already after running \ref preflowPhase1.
409 Num flowValue() const {
411 for(InEdgeIt e(*g,t);g->valid(e);g->next(e)) a+=(*flow)[e];
412 for(OutEdgeIt e(*g,t);g->valid(e);g->next(e)) a-=(*flow)[e];
414 //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan
416 Num flowValue2() const {
419 // for(InEdgeIt e(*g,t);g->valid(e);g->next(e)) a+=(*flow)[e];
420 // for(OutEdgeIt e(*g,t);g->valid(e);g->next(e)) a-=(*flow)[e];
422 // //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan
426 ///Returns a minimum value cut after calling \ref preflowPhase1.
428 ///After the first phase of the preflow algorithm the maximum flow
429 ///value and a minimum value cut can already be computed. This
430 ///method can be called after running \ref preflowPhase1 for
431 ///obtaining a minimum value cut.
432 /// \warning Gives proper result only right after calling \ref
434 /// \todo We have to make some status variable which shows the
436 /// of the class. This enables us to determine which methods are valid
437 /// for MinCut computation
438 template<typename _CutMap>
439 void actMinCut(_CutMap& M) const {
442 case AFTER_PRE_FLOW_PHASE_1:
443 for(g->first(v); g->valid(v); g->next(v)) {
451 case AFTER_PRE_FLOW_PHASE_2:
453 case AFTER_AUGMENTING:
454 case AFTER_FAST_AUGMENTING:
460 ///Returns the inclusionwise minimum of the minimum value cuts.
462 ///Sets \c M to the characteristic vector of the minimum value cut
463 ///which is inclusionwise minimum. It is computed by processing
464 ///a bfs from the source node \c s in the residual graph.
465 ///\pre M should be a node map of bools initialized to false.
466 ///\pre \c flow must be a maximum flow.
467 template<typename _CutMap>
468 void minMinCut(_CutMap& M) const {
469 std::queue<Node> queue;
474 while (!queue.empty()) {
475 Node w=queue.front();
479 for(g->first(e,w) ; g->valid(e); g->next(e)) {
481 if (!M[v] && (*flow)[e] < (*capacity)[e] ) {
488 for(g->first(f,w) ; g->valid(f); g->next(f)) {
490 if (!M[v] && (*flow)[f] > 0 ) {
498 ///Returns the inclusionwise maximum of the minimum value cuts.
500 ///Sets \c M to the characteristic vector of the minimum value cut
501 ///which is inclusionwise maximum. It is computed by processing a
502 ///backward bfs from the target node \c t in the residual graph.
503 ///\pre M should be a node map of bools initialized to false.
504 ///\pre \c flow must be a maximum flow.
505 template<typename _CutMap>
506 void maxMinCut(_CutMap& M) const {
509 for(g->first(v) ; g->valid(v); g->next(v)) {
513 std::queue<Node> queue;
518 while (!queue.empty()) {
519 Node w=queue.front();
523 for(g->first(e,w) ; g->valid(e); g->next(e)) {
525 if (M[v] && (*flow)[e] < (*capacity)[e] ) {
532 for(g->first(f,w) ; g->valid(f); g->next(f)) {
534 if (M[v] && (*flow)[f] > 0 ) {
542 ///Returns a minimum value cut.
544 ///Sets \c M to the characteristic vector of a minimum value cut.
545 ///\pre M should be a node map of bools initialized to false.
546 ///\pre \c flow must be a maximum flow.
547 template<typename CutMap>
548 void minCut(CutMap& M) const { minMinCut(M); }
550 ///Resets the source node to \c _s.
552 ///Resets the source node to \c _s.
554 void resetSource(Node _s) { s=_s; status=AFTER_NOTHING; }
556 ///Resets the target node to \c _t.
558 ///Resets the target node to \c _t.
560 void resetTarget(Node _t) { t=_t; status=AFTER_NOTHING; }
562 /// Resets the edge map of the capacities to _cap.
564 /// Resets the edge map of the capacities to _cap.
566 void resetCap(const CapMap& _cap)
567 { capacity=&_cap; status=AFTER_NOTHING; }
569 /// Resets the edge map of the flows to _flow.
571 /// Resets the edge map of the flows to _flow.
573 void resetFlow(FlowMap& _flow) { flow=&_flow; status=AFTER_NOTHING; }
578 int push(Node w, NNMap& next, VecFirst& first) {
582 int newlevel=n; //bound on the next level of w
585 for(g->first(e,w); g->valid(e); g->next(e)) {
587 if ( (*flow)[e] >= (*capacity)[e] ) continue;
590 if( lev > level[v] ) { //Push is allowed now
592 if ( excess[v]<=0 && v!=t && v!=s ) {
593 next.set(v,first[level[v]]);
597 Num cap=(*capacity)[e];
601 if ( remcap >= exc ) { //A nonsaturating push.
603 flow->set(e, flo+exc);
604 excess.set(v, excess[v]+exc);
608 } else { //A saturating push.
610 excess.set(v, excess[v]+remcap);
613 } else if ( newlevel > level[v] ) newlevel = level[v];
618 for(g->first(e,w); g->valid(e); g->next(e)) {
620 if( (*flow)[e] <= 0 ) continue;
623 if( lev > level[v] ) { //Push is allowed now
625 if ( excess[v]<=0 && v!=t && v!=s ) {
626 next.set(v,first[level[v]]);
632 if ( flo >= exc ) { //A nonsaturating push.
634 flow->set(e, flo-exc);
635 excess.set(v, excess[v]+exc);
638 } else { //A saturating push.
640 excess.set(v, excess[v]+flo);
644 } else if ( newlevel > level[v] ) newlevel = level[v];
647 } // if w still has excess after the out edge for cycle
655 void preflowPreproc(FlowEnum fe, NNMap& next, VecFirst& first,
656 VecNode& level_list, NNMap& left, NNMap& right)
658 std::queue<Node> bfs_queue;
661 case NO_FLOW: //flow is already set to const zero in this case
664 //Reverse_bfs from t, to find the starting level.
668 while (!bfs_queue.empty()) {
670 Node v=bfs_queue.front();
675 for(g->first(e,v); g->valid(e); g->next(e)) {
677 if ( level[w] == n && w != s ) {
679 Node z=level_list[l];
680 if ( g->valid(z) ) left.set(z,w);
690 for(g->first(e,s); g->valid(e); g->next(e))
692 Num c=(*capacity)[e];
693 if ( c <= 0 ) continue;
695 if ( level[w] < n ) {
696 if ( excess[w] <= 0 && w!=t )
698 next.set(w,first[level[w]]);
702 excess.set(w, excess[w]+c);
711 //Reverse_bfs from t in the residual graph,
712 //to find the starting level.
716 while (!bfs_queue.empty()) {
718 Node v=bfs_queue.front();
723 for(g->first(e,v); g->valid(e); g->next(e)) {
724 if ( (*capacity)[e] <= (*flow)[e] ) continue;
726 if ( level[w] == n && w != s ) {
728 Node z=level_list[l];
729 if ( g->valid(z) ) left.set(z,w);
737 for(g->first(f,v); g->valid(f); g->next(f)) {
738 if ( 0 >= (*flow)[f] ) continue;
740 if ( level[w] == n && w != s ) {
742 Node z=level_list[l];
743 if ( g->valid(z) ) left.set(z,w);
754 for(g->first(e,s); g->valid(e); g->next(e))
756 Num rem=(*capacity)[e]-(*flow)[e];
757 if ( rem <= 0 ) continue;
759 if ( level[w] < n ) {
760 if ( excess[w] <= 0 && w!=t )
762 next.set(w,first[level[w]]);
765 flow->set(e, (*capacity)[e]);
766 excess.set(w, excess[w]+rem);
771 for(g->first(f,s); g->valid(f); g->next(f))
773 if ( (*flow)[f] <= 0 ) continue;
775 if ( level[w] < n ) {
776 if ( excess[w] <= 0 && w!=t )
778 next.set(w,first[level[w]]);
781 excess.set(w, excess[w]+(*flow)[f]);
792 void relabel(Node w, int newlevel, NNMap& next, VecFirst& first,
793 VecNode& level_list, NNMap& left,
794 NNMap& right, int& b, int& k, bool what_heur )
799 Node right_n=right[w];
803 if ( g->valid(right_n) ) {
804 if ( g->valid(left_n) ) {
805 right.set(left_n, right_n);
806 left.set(right_n, left_n);
808 level_list[lev]=right_n;
809 left.set(right_n, INVALID);
812 if ( g->valid(left_n) ) {
813 right.set(left_n, INVALID);
815 level_list[lev]=INVALID;
820 if ( !g->valid(level_list[lev]) ) {
823 for (int i=lev; i!=k ; ) {
824 Node v=level_list[++i];
825 while ( g->valid(v) ) {
829 level_list[i]=INVALID;
830 if ( !what_heur ) first[i]=INVALID;
840 if ( newlevel == n ) level.set(w,n);
842 level.set(w,++newlevel);
843 next.set(w,first[newlevel]);
845 if ( what_heur ) b=newlevel;
846 if ( k < newlevel ) ++k; //now k=newlevel
847 Node z=level_list[newlevel];
848 if ( g->valid(z) ) left.set(z,w);
851 level_list[newlevel]=w;
858 #endif //HUGO_MAX_FLOW_H