lemon-0.x: src/work/jacint/preflow_push_max_flow.h@629b9ca9184b (annotated)

jacint@78	1	/*
jacint@78	2	preflow_push_max_flow_h
jacint@78	3	by jacint.
jacint@78	4	Runs a preflow push algorithm with the modification,
jacint@78	5	that we do not push on Nodes with level at least n.
jacint@78	6	Moreover, if a level gets empty, we.set all Nodes above that
jacint@78	7	level to level n. Hence, in the end, we arrive at a maximum preflow
jacint@78	8	with value of a max flow value. An empty level gives a minimum cut.
jacint@78	9
jacint@78	10	Member functions:
jacint@78	11
jacint@78	12	void run() : runs the algorithm
jacint@78	13
jacint@78	14	The following functions should be used after run() was already run.
jacint@78	15
jacint@78	16	T maxflow() : returns the value of a maximum flow
jacint@78	17
jacint@78	18	NodeMap<Graph, bool> mincut(): returns a
jacint@78	19	characteristic vector of a minimum cut.
jacint@78	20	*/
jacint@78	21
jacint@78	22	#ifndef PREFLOW_PUSH_MAX_FLOW_H
jacint@78	23	#define PREFLOW_PUSH_MAX_FLOW_H
jacint@78	24
jacint@78	25	#include <algorithm>
jacint@78	26	#include <vector>
jacint@78	27	#include <stack>
jacint@78	28
jacint@78	29	#include <list_graph.hh>
jacint@78	30	#include <reverse_bfs.h>
jacint@78	31
jacint@78	32
jacint@78	33	namespace marci {
jacint@78	34
jacint@78	35	template <typename Graph, typename T>
jacint@78	36	class preflow_push_max_flow {
jacint@78	37
jacint@78	38	typedef typename Graph::NodeIt NodeIt;
jacint@78	39	typedef typename Graph::EachNodeIt EachNodeIt;
jacint@78	40	typedef typename Graph::OutEdgeIt OutEdgeIt;
jacint@78	41	typedef typename Graph::InEdgeIt InEdgeIt;
jacint@78	42
jacint@78	43	Graph& G;
jacint@78	44	NodeIt s;
jacint@78	45	NodeIt t;
jacint@78	46	typename Graph::EdgeMap<T>& capacity;
jacint@78	47	T value;
jacint@78	48	typename Graph::NodeMap<bool> mincutvector;
jacint@78	49
jacint@78	50
jacint@78	51
jacint@78	52	public:
jacint@78	53
jacint@78	54	preflow_push_max_flow(Graph& _G, NodeIt _s, NodeIt _t, typename Graph::EdgeMap<T>& _capacity) : G(_G), s(_s), t(_t), capacity(_capacity), mincutvector(_G, false) { }
jacint@78	55
jacint@78	56
jacint@78	57	/*
jacint@78	58	The run() function runs a modified version of the highest label preflow-push, which only
jacint@78	59	finds a maximum preflow, hence giving the value of a maximum flow.
jacint@78	60	*/
jacint@78	61	void run() {
jacint@78	62
jacint@78	63	typename Graph::EdgeMap<T> flow(G, 0); //the flow value, 0 everywhere
jacint@78	64	typename Graph::NodeMap<int> level(G); //level of Node
jacint@78	65	typename Graph::NodeMap<T> excess(G); //excess of Node
jacint@78	66
jacint@78	67	int n=G.nodeNum(); //number of Nodes
jacint@78	68	int b=n-2;
jacint@78	69	/b is a bound on the highest level of an active Node. In the beginning it is at most n-2./
jacint@78	70
jacint@78	71	std::vector<int> numb(n); //The number of Nodes on level i < n.
jacint@78	72
jacint@78	73	std::vector<std::stack<NodeIt> > stack(2*n-1); //Stack of the active Nodes in level i.
jacint@78	74
jacint@78	75
jacint@78	76
jacint@78	77	/Reverse_bfs from t, to find the starting level./
jacint@78	78
jacint@78	79	reverse_bfs<Graph> bfs(G, t);
jacint@78	80	bfs.run();
jacint@78	81	for(EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v)
jacint@78	82	{
jacint@78	83	int dist=bfs.dist(v);
jacint@78	84	level.set(v, dist);
jacint@78	85	++numb[dist];
jacint@78	86	}
jacint@78	87
jacint@78	88	/The level of s is fixed to n/
jacint@78	89	level.set(s,n);
jacint@78	90
jacint@78	91
jacint@78	92	/* Starting flow. It is everywhere 0 at the moment. */
jacint@78	93
jacint@78	94	for(OutEdgeIt i=G.template first<OutEdgeIt>(s); i.valid(); ++i)
jacint@78	95	{
jacint@78	96	NodeIt w=G.head(i);
jacint@78	97	flow.set(i, capacity.get(i));
jacint@78	98	stack[bfs.dist(w)].push(w);
jacint@78	99	excess.set(w, capacity.get(i));
jacint@78	100	}
jacint@78	101
jacint@78	102
jacint@78	103	/*
jacint@78	104	End of preprocessing
jacint@78	105	*/
jacint@78	106
jacint@78	107
jacint@78	108
jacint@78	109
jacint@78	110	/*
jacint@78	111	Push/relabel on the highest level active Nodes.
jacint@78	112	*/
jacint@78	113
jacint@78	114	/While there exists an active Node./
jacint@78	115	while (b) {
jacint@78	116
jacint@78	117	/We decrease the bound if there is no active Node of level b./
jacint@78	118	if (stack[b].empty()) {
jacint@78	119	--b;
jacint@78	120	} else {
jacint@78	121
jacint@78	122	NodeIt w=stack[b].top(); //w is the highest label active Node.
jacint@78	123	stack[b].pop(); //We delete w from the stack.
jacint@78	124
jacint@78	125	int newlevel=2*n-2; //In newlevel we maintain the next level of w.
jacint@78	126
jacint@78	127	for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) {
jacint@78	128	NodeIt v=G.head(e);
jacint@78	129	/e is the Edge wv./
jacint@78	130
jacint@78	131	if (flow.get(e)<capacity.get(e)) {
jacint@78	132	/e is an Edge of the residual graph /
jacint@78	133
jacint@78	134	if(level.get(w)==level.get(v)+1) {
jacint@78	135	/Push is allowed now/
jacint@78	136
jacint@78	137	if (capacity.get(e)-flow.get(e) > excess.get(w)) {
jacint@78	138	/A nonsaturating push./
jacint@78	139
jacint@78	140	if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
jacint@78	141	/v becomes active./
jacint@78	142
jacint@78	143	flow.set(e, flow.get(e)+excess.get(w));
jacint@78	144	excess.set(v, excess.get(v)+excess.get(w));
jacint@78	145	excess.set(w,0);
jacint@78	146	//std::cout << w << " " << v <<" elore elen nonsat pump " << std::endl;
jacint@78	147	break;
jacint@78	148	} else {
jacint@78	149	/A saturating push./
jacint@78	150
jacint@78	151	if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
jacint@78	152	/v becomes active./
jacint@78	153
jacint@78	154	excess.set(v, excess.get(v)+capacity.get(e)-flow.get(e));
jacint@78	155	excess.set(w, excess.get(w)-capacity.get(e)+flow.get(e));
jacint@78	156	flow.set(e, capacity.get(e));
jacint@78	157	//std::cout << w <<" " << v <<" elore elen sat pump " << std::endl;
jacint@78	158	if (excess.get(w)==0) break;
jacint@78	159	/If w is not active any more, then we go on to the next Node./
jacint@78	160
jacint@78	161	} // if (capacity.get(e)-flow.get(e) > excess.get(w))
jacint@78	162	} // if (level.get(w)==level.get(v)+1)
jacint@78	163
jacint@78	164	else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
jacint@78	165
jacint@78	166	} //if (flow.get(e)<capacity.get(e))
jacint@78	167
jacint@78	168	} //for(OutEdgeIt e=G.first_OutEdge(w); e.valid(); ++e)
jacint@78	169
jacint@78	170
jacint@78	171
jacint@78	172	for(InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) {
jacint@78	173	NodeIt v=G.tail(e);
jacint@78	174	/e is the Edge vw./
jacint@78	175
jacint@78	176	if (excess.get(w)==0) break;
jacint@78	177	/It may happen, that w became inactive in the first 'for' cycle./
jacint@78	178
jacint@78	179	if(flow.get(e)>0) {
jacint@78	180	/e is an Edge of the residual graph /
jacint@78	181
jacint@78	182	if(level.get(w)==level.get(v)+1) {
jacint@78	183	/Push is allowed now/
jacint@78	184
jacint@78	185	if (flow.get(e) > excess.get(w)) {
jacint@78	186	/A nonsaturating push./
jacint@78	187
jacint@78	188	if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
jacint@78	189	/v becomes active./
jacint@78	190
jacint@78	191	flow.set(e, flow.get(e)-excess.get(w));
jacint@78	192	excess.set(v, excess.get(v)+excess.get(w));
jacint@78	193	excess.set(w,0);
jacint@78	194	//std::cout << v << " " << w << " vissza elen nonsat pump " << std::endl;
jacint@78	195	break;
jacint@78	196	} else {
jacint@78	197	/A saturating push./
jacint@78	198
jacint@78	199	if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
jacint@78	200	/v becomes active./
jacint@78	201
jacint@78	202	flow.set(e,0);
jacint@78	203	excess.set(v, excess.get(v)+flow.get(e));
jacint@78	204	excess.set(w, excess.get(w)-flow.get(e));
jacint@78	205	//std::cout << v <<" " << w << " vissza elen sat pump " << std::endl;
jacint@78	206	if (excess.get(w)==0) { break;}
jacint@78	207	} //if (flow.get(e) > excess.get(v))
jacint@78	208	} //if(level.get(w)==level.get(v)+1)
jacint@78	209
jacint@78	210	else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
jacint@78	211	//std::cout << "Leveldecrease of Node " << w << " to " << newlevel << std::endl;
jacint@78	212
jacint@78	213	} //if (flow.get(e)>0)
jacint@78	214
jacint@78	215	} //for in-Edge
jacint@78	216
jacint@78	217
jacint@78	218
jacint@78	219
jacint@78	220	/*
jacint@78	221	Relabel
jacint@78	222	*/
jacint@78	223	if (excess.get(w)>0) {
jacint@78	224	/Now newlevel <= n/
jacint@78	225
jacint@78	226	int l=level.get(w); //l is the old level of w.
jacint@78	227	--numb[l];
jacint@78	228
jacint@78	229	if (newlevel == n) {
jacint@78	230	level.set(w,n);
jacint@78	231
jacint@78	232	} else {
jacint@78	233
jacint@78	234	if (numb[l]) {
jacint@78	235	/If the level of w remains nonempty./
jacint@78	236
jacint@78	237	level.set(w,++newlevel);
jacint@78	238	++numb[newlevel];
jacint@78	239	stack[newlevel].push(w);
jacint@78	240	b=newlevel;
jacint@78	241	} else {
jacint@78	242	/If the level of w gets empty./
jacint@78	243
jacint@78	244	for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) {
jacint@78	245	if (level.get(v) >= l ) {
jacint@78	246	level.set(v,n);
jacint@78	247	}
jacint@78	248	}
jacint@78	249
jacint@78	250	for (int i=l+1 ; i!=n ; ++i) numb[i]=0;
jacint@78	251	} //if (numb[l])
jacint@78	252
jacint@78	253	} // if (newlevel = n)
jacint@78	254
jacint@78	255	} // if (excess.get(w)>0)
jacint@78	256
jacint@78	257
jacint@78	258	} //else
jacint@78	259
jacint@78	260	} //while(b)
jacint@78	261
jacint@78	262	value=excess.get(t);
jacint@78	263	/Max flow value./
jacint@78	264
jacint@78	265
jacint@78	266
jacint@78	267	/*
jacint@78	268	We find an empty level, e. The Nodes above this level give
jacint@78	269	a minimum cut.
jacint@78	270	*/
jacint@78	271
jacint@78	272	int e=1;
jacint@78	273
jacint@78	274	while(e) {
jacint@78	275	if(numb[e]) ++e;
jacint@78	276	else break;
jacint@78	277	}
jacint@78	278	for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) {
jacint@78	279	if (level.get(v) > e) mincutvector.set(v, true);
jacint@78	280	}
jacint@78	281
jacint@78	282
jacint@78	283	} // void run()
jacint@78	284
jacint@78	285
jacint@78	286
jacint@78	287	/*
jacint@78	288	Returns the maximum value of a flow.
jacint@78	289	*/
jacint@78	290
jacint@78	291	T maxflow() {
jacint@78	292	return value;
jacint@78	293	}
jacint@78	294
jacint@78	295
jacint@78	296
jacint@78	297	/*
jacint@78	298	Returns a minimum cut.
jacint@78	299	*/
jacint@78	300
jacint@78	301	typename Graph::NodeMap<bool> mincut() {
jacint@78	302	return mincutvector;
jacint@78	303	}
jacint@78	304
jacint@78	305
jacint@78	306	};
jacint@78	307	}//namespace marci
jacint@78	308	#endif
jacint@78	309
jacint@78	310
jacint@78	311
jacint@78	312
jacint@78	313

author	alpar
	Mon, 16 Feb 2004 16:27:49 +0000
changeset 80	629b9ca9184b
child 83	efafe79a88d3
permissions	-rw-r--r--