1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/preflow.h Mon May 23 04:48:14 2005 +0000
1.3 @@ -0,0 +1,868 @@
1.4 +/* -*- C++ -*-
1.5 + * lemon/preflow.h - Part of LEMON, a generic C++ optimization library
1.6 + *
1.7 + * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.8 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.9 + *
1.10 + * Permission to use, modify and distribute this software is granted
1.11 + * provided that this copyright notice appears in all copies. For
1.12 + * precise terms see the accompanying LICENSE file.
1.13 + *
1.14 + * This software is provided "AS IS" with no warranty of any kind,
1.15 + * express or implied, and with no claim as to its suitability for any
1.16 + * purpose.
1.17 + *
1.18 + */
1.19 +
1.20 +#ifndef LEMON_PREFLOW_H
1.21 +#define LEMON_PREFLOW_H
1.22 +
1.23 +#include <vector>
1.24 +#include <queue>
1.25 +
1.26 +#include <lemon/invalid.h>
1.27 +#include <lemon/maps.h>
1.28 +#include <lemon/graph_utils.h>
1.29 +
1.30 +/// \file
1.31 +/// \ingroup flowalgs
1.32 +/// Implementation of the preflow algorithm.
1.33 +
1.34 +namespace lemon {
1.35 +
1.36 + /// \addtogroup flowalgs
1.37 + /// @{
1.38 +
1.39 + ///%Preflow algorithms class.
1.40 +
1.41 + ///This class provides an implementation of the \e preflow \e
1.42 + ///algorithm producing a flow of maximum value in a directed
1.43 + ///graph. The preflow algorithms are the fastest known max flow algorithms
1.44 + ///up to now. The \e source node, the \e target node, the \e
1.45 + ///capacity of the edges and the \e starting \e flow value of the
1.46 + ///edges should be passed to the algorithm through the
1.47 + ///constructor. It is possible to change these quantities using the
1.48 + ///functions \ref source, \ref target, \ref capacityMap and \ref
1.49 + ///flowMap.
1.50 + ///
1.51 + ///After running \ref lemon::Preflow::phase1() "phase1()"
1.52 + ///or \ref lemon::Preflow::run() "run()", the maximal flow
1.53 + ///value can be obtained by calling \ref flowValue(). The minimum
1.54 + ///value cut can be written into a <tt>bool</tt> node map by
1.55 + ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes
1.56 + ///the inclusionwise minimum and maximum of the minimum value cuts,
1.57 + ///resp.)
1.58 + ///
1.59 + ///\param Graph The directed graph type the algorithm runs on.
1.60 + ///\param Num The number type of the capacities and the flow values.
1.61 + ///\param CapacityMap The capacity map type.
1.62 + ///\param FlowMap The flow map type.
1.63 + ///
1.64 + ///\author Jacint Szabo
1.65 + ///\todo Second template parameter is superfluous
1.66 + template <typename Graph, typename Num,
1.67 + typename CapacityMap=typename Graph::template EdgeMap<Num>,
1.68 + typename FlowMap=typename Graph::template EdgeMap<Num> >
1.69 + class Preflow {
1.70 + protected:
1.71 + typedef typename Graph::Node Node;
1.72 + typedef typename Graph::NodeIt NodeIt;
1.73 + typedef typename Graph::EdgeIt EdgeIt;
1.74 + typedef typename Graph::OutEdgeIt OutEdgeIt;
1.75 + typedef typename Graph::InEdgeIt InEdgeIt;
1.76 +
1.77 + typedef typename Graph::template NodeMap<Node> NNMap;
1.78 + typedef typename std::vector<Node> VecNode;
1.79 +
1.80 + const Graph* _g;
1.81 + Node _source;
1.82 + Node _target;
1.83 + const CapacityMap* _capacity;
1.84 + FlowMap* _flow;
1.85 + int _node_num; //the number of nodes of G
1.86 +
1.87 + typename Graph::template NodeMap<int> level;
1.88 + typename Graph::template NodeMap<Num> excess;
1.89 +
1.90 + // constants used for heuristics
1.91 + static const int H0=20;
1.92 + static const int H1=1;
1.93 +
1.94 + public:
1.95 +
1.96 + ///Indicates the property of the starting flow map.
1.97 +
1.98 + ///Indicates the property of the starting flow map.
1.99 + ///The meanings are as follows:
1.100 + ///- \c ZERO_FLOW: constant zero flow
1.101 + ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to
1.102 + ///the sum of the out-flows in every node except the \e source and
1.103 + ///the \e target.
1.104 + ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at
1.105 + ///least the sum of the out-flows in every node except the \e source.
1.106 + ///- \c NO_FLOW: indicates an unspecified edge map. \c flow will be
1.107 + ///set to the constant zero flow in the beginning of
1.108 + ///the algorithm in this case.
1.109 + ///
1.110 + enum FlowEnum{
1.111 + NO_FLOW,
1.112 + ZERO_FLOW,
1.113 + GEN_FLOW,
1.114 + PRE_FLOW
1.115 + };
1.116 +
1.117 + ///Indicates the state of the preflow algorithm.
1.118 +
1.119 + ///Indicates the state of the preflow algorithm.
1.120 + ///The meanings are as follows:
1.121 + ///- \c AFTER_NOTHING: before running the algorithm or
1.122 + /// at an unspecified state.
1.123 + ///- \c AFTER_PREFLOW_PHASE_1: right after running \c phase1
1.124 + ///- \c AFTER_PREFLOW_PHASE_2: after running \ref phase2()
1.125 + ///
1.126 + enum StatusEnum {
1.127 + AFTER_NOTHING,
1.128 + AFTER_PREFLOW_PHASE_1,
1.129 + AFTER_PREFLOW_PHASE_2
1.130 + };
1.131 +
1.132 + protected:
1.133 + FlowEnum flow_prop;
1.134 + StatusEnum status; // Do not needle this flag only if necessary.
1.135 +
1.136 + public:
1.137 + ///The constructor of the class.
1.138 +
1.139 + ///The constructor of the class.
1.140 + ///\param _gr The directed graph the algorithm runs on.
1.141 + ///\param _s The source node.
1.142 + ///\param _t The target node.
1.143 + ///\param _cap The capacity of the edges.
1.144 + ///\param _f The flow of the edges.
1.145 + ///Except the graph, all of these parameters can be reset by
1.146 + ///calling \ref source, \ref target, \ref capacityMap and \ref
1.147 + ///flowMap, resp.
1.148 + Preflow(const Graph& _gr, Node _s, Node _t,
1.149 + const CapacityMap& _cap, FlowMap& _f) :
1.150 + _g(&_gr), _source(_s), _target(_t), _capacity(&_cap),
1.151 + _flow(&_f), _node_num(countNodes(_gr)), level(_gr), excess(_gr,0),
1.152 + flow_prop(NO_FLOW), status(AFTER_NOTHING) { }
1.153 +
1.154 +
1.155 +
1.156 + ///Runs the preflow algorithm.
1.157 +
1.158 + ///Runs the preflow algorithm.
1.159 + ///
1.160 + void run() {
1.161 + phase1(flow_prop);
1.162 + phase2();
1.163 + }
1.164 +
1.165 + ///Runs the preflow algorithm.
1.166 +
1.167 + ///Runs the preflow algorithm.
1.168 + ///\pre The starting flow map must be
1.169 + /// - a constant zero flow if \c fp is \c ZERO_FLOW,
1.170 + /// - an arbitrary flow if \c fp is \c GEN_FLOW,
1.171 + /// - an arbitrary preflow if \c fp is \c PRE_FLOW,
1.172 + /// - any map if \c fp is NO_FLOW.
1.173 + ///If the starting flow map is a flow or a preflow then
1.174 + ///the algorithm terminates faster.
1.175 + void run(FlowEnum fp) {
1.176 + flow_prop=fp;
1.177 + run();
1.178 + }
1.179 +
1.180 + ///Runs the first phase of the preflow algorithm.
1.181 +
1.182 + ///The preflow algorithm consists of two phases, this method runs
1.183 + ///the first phase. After the first phase the maximum flow value
1.184 + ///and a minimum value cut can already be computed, although a
1.185 + ///maximum flow is not yet obtained. So after calling this method
1.186 + ///\ref flowValue returns the value of a maximum flow and \ref
1.187 + ///minCut returns a minimum cut.
1.188 + ///\warning \ref minMinCut and \ref maxMinCut do not give minimum
1.189 + ///value cuts unless calling \ref phase2.
1.190 + ///\pre The starting flow must be
1.191 + ///- a constant zero flow if \c fp is \c ZERO_FLOW,
1.192 + ///- an arbitary flow if \c fp is \c GEN_FLOW,
1.193 + ///- an arbitary preflow if \c fp is \c PRE_FLOW,
1.194 + ///- any map if \c fp is NO_FLOW.
1.195 + void phase1(FlowEnum fp)
1.196 + {
1.197 + flow_prop=fp;
1.198 + phase1();
1.199 + }
1.200 +
1.201 +
1.202 + ///Runs the first phase of the preflow algorithm.
1.203 +
1.204 + ///The preflow algorithm consists of two phases, this method runs
1.205 + ///the first phase. After the first phase the maximum flow value
1.206 + ///and a minimum value cut can already be computed, although a
1.207 + ///maximum flow is not yet obtained. So after calling this method
1.208 + ///\ref flowValue returns the value of a maximum flow and \ref
1.209 + ///minCut returns a minimum cut.
1.210 + ///\warning \ref minCut(), \ref minMinCut() and \ref maxMinCut() do not
1.211 + ///give minimum value cuts unless calling \ref phase2().
1.212 + void phase1()
1.213 + {
1.214 + int heur0=(int)(H0*_node_num); //time while running 'bound decrease'
1.215 + int heur1=(int)(H1*_node_num); //time while running 'highest label'
1.216 + int heur=heur1; //starting time interval (#of relabels)
1.217 + int numrelabel=0;
1.218 +
1.219 + bool what_heur=1;
1.220 + //It is 0 in case 'bound decrease' and 1 in case 'highest label'
1.221 +
1.222 + bool end=false;
1.223 + //Needed for 'bound decrease', true means no active
1.224 + //nodes are above bound b.
1.225 +
1.226 + int k=_node_num-2; //bound on the highest level under n containing a node
1.227 + int b=k; //bound on the highest level under n of an active node
1.228 +
1.229 + VecNode first(_node_num, INVALID);
1.230 + NNMap next(*_g, INVALID);
1.231 +
1.232 + NNMap left(*_g, INVALID);
1.233 + NNMap right(*_g, INVALID);
1.234 + VecNode level_list(_node_num,INVALID);
1.235 + //List of the nodes in level i<n, set to n.
1.236 +
1.237 + preflowPreproc(first, next, level_list, left, right);
1.238 +
1.239 + //Push/relabel on the highest level active nodes.
1.240 + while ( true ) {
1.241 + if ( b == 0 ) {
1.242 + if ( !what_heur && !end && k > 0 ) {
1.243 + b=k;
1.244 + end=true;
1.245 + } else break;
1.246 + }
1.247 +
1.248 + if ( first[b]==INVALID ) --b;
1.249 + else {
1.250 + end=false;
1.251 + Node w=first[b];
1.252 + first[b]=next[w];
1.253 + int newlevel=push(w, next, first);
1.254 + if ( excess[w] > 0 ) relabel(w, newlevel, first, next, level_list,
1.255 + left, right, b, k, what_heur);
1.256 +
1.257 + ++numrelabel;
1.258 + if ( numrelabel >= heur ) {
1.259 + numrelabel=0;
1.260 + if ( what_heur ) {
1.261 + what_heur=0;
1.262 + heur=heur0;
1.263 + end=false;
1.264 + } else {
1.265 + what_heur=1;
1.266 + heur=heur1;
1.267 + b=k;
1.268 + }
1.269 + }
1.270 + }
1.271 + }
1.272 + flow_prop=PRE_FLOW;
1.273 + status=AFTER_PREFLOW_PHASE_1;
1.274 + }
1.275 + // Heuristics:
1.276 + // 2 phase
1.277 + // gap
1.278 + // list 'level_list' on the nodes on level i implemented by hand
1.279 + // stack 'active' on the active nodes on level i
1.280 + // runs heuristic 'highest label' for H1*n relabels
1.281 + // runs heuristic 'bound decrease' for H0*n relabels,
1.282 + // starts with 'highest label'
1.283 + // Parameters H0 and H1 are initialized to 20 and 1.
1.284 +
1.285 +
1.286 + ///Runs the second phase of the preflow algorithm.
1.287 +
1.288 + ///The preflow algorithm consists of two phases, this method runs
1.289 + ///the second phase. After calling \ref phase1 and then \ref
1.290 + ///phase2, \ref flow contains a maximum flow, \ref flowValue
1.291 + ///returns the value of a maximum flow, \ref minCut returns a
1.292 + ///minimum cut, while the methods \ref minMinCut and \ref
1.293 + ///maxMinCut return the inclusionwise minimum and maximum cuts of
1.294 + ///minimum value, resp. \pre \ref phase1 must be called before.
1.295 + void phase2()
1.296 + {
1.297 +
1.298 + int k=_node_num-2; //bound on the highest level under n containing a node
1.299 + int b=k; //bound on the highest level under n of an active node
1.300 +
1.301 +
1.302 + VecNode first(_node_num, INVALID);
1.303 + NNMap next(*_g, INVALID);
1.304 + level.set(_source,0);
1.305 + std::queue<Node> bfs_queue;
1.306 + bfs_queue.push(_source);
1.307 +
1.308 + while ( !bfs_queue.empty() ) {
1.309 +
1.310 + Node v=bfs_queue.front();
1.311 + bfs_queue.pop();
1.312 + int l=level[v]+1;
1.313 +
1.314 + for(InEdgeIt e(*_g,v); e!=INVALID; ++e) {
1.315 + if ( (*_capacity)[e] <= (*_flow)[e] ) continue;
1.316 + Node u=_g->source(e);
1.317 + if ( level[u] >= _node_num ) {
1.318 + bfs_queue.push(u);
1.319 + level.set(u, l);
1.320 + if ( excess[u] > 0 ) {
1.321 + next.set(u,first[l]);
1.322 + first[l]=u;
1.323 + }
1.324 + }
1.325 + }
1.326 +
1.327 + for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) {
1.328 + if ( 0 >= (*_flow)[e] ) continue;
1.329 + Node u=_g->target(e);
1.330 + if ( level[u] >= _node_num ) {
1.331 + bfs_queue.push(u);
1.332 + level.set(u, l);
1.333 + if ( excess[u] > 0 ) {
1.334 + next.set(u,first[l]);
1.335 + first[l]=u;
1.336 + }
1.337 + }
1.338 + }
1.339 + }
1.340 + b=_node_num-2;
1.341 +
1.342 + while ( true ) {
1.343 +
1.344 + if ( b == 0 ) break;
1.345 + if ( first[b]==INVALID ) --b;
1.346 + else {
1.347 + Node w=first[b];
1.348 + first[b]=next[w];
1.349 + int newlevel=push(w,next, first);
1.350 +
1.351 + //relabel
1.352 + if ( excess[w] > 0 ) {
1.353 + level.set(w,++newlevel);
1.354 + next.set(w,first[newlevel]);
1.355 + first[newlevel]=w;
1.356 + b=newlevel;
1.357 + }
1.358 + }
1.359 + } // while(true)
1.360 + flow_prop=GEN_FLOW;
1.361 + status=AFTER_PREFLOW_PHASE_2;
1.362 + }
1.363 +
1.364 + /// Returns the value of the maximum flow.
1.365 +
1.366 + /// Returns the value of the maximum flow by returning the excess
1.367 + /// of the target node \c t. This value equals to the value of
1.368 + /// the maximum flow already after running \ref phase1.
1.369 + Num flowValue() const {
1.370 + return excess[_target];
1.371 + }
1.372 +
1.373 +
1.374 + ///Returns a minimum value cut.
1.375 +
1.376 + ///Sets \c M to the characteristic vector of a minimum value
1.377 + ///cut. This method can be called both after running \ref
1.378 + ///phase1 and \ref phase2. It is much faster after
1.379 + ///\ref phase1. \pre M should be a bool-valued node-map. \pre
1.380 + ///If \ref minCut() is called after \ref phase2() then M should
1.381 + ///be initialized to false.
1.382 + template<typename _CutMap>
1.383 + void minCut(_CutMap& M) const {
1.384 + switch ( status ) {
1.385 + case AFTER_PREFLOW_PHASE_1:
1.386 + for(NodeIt v(*_g); v!=INVALID; ++v) {
1.387 + if (level[v] < _node_num) {
1.388 + M.set(v, false);
1.389 + } else {
1.390 + M.set(v, true);
1.391 + }
1.392 + }
1.393 + break;
1.394 + case AFTER_PREFLOW_PHASE_2:
1.395 + minMinCut(M);
1.396 + break;
1.397 + case AFTER_NOTHING:
1.398 + break;
1.399 + }
1.400 + }
1.401 +
1.402 + ///Returns the inclusionwise minimum of the minimum value cuts.
1.403 +
1.404 + ///Sets \c M to the characteristic vector of the minimum value cut
1.405 + ///which is inclusionwise minimum. It is computed by processing a
1.406 + ///bfs from the source node \c s in the residual graph. \pre M
1.407 + ///should be a node map of bools initialized to false. \pre \ref
1.408 + ///phase2 should already be run.
1.409 + template<typename _CutMap>
1.410 + void minMinCut(_CutMap& M) const {
1.411 +
1.412 + std::queue<Node> queue;
1.413 + M.set(_source,true);
1.414 + queue.push(_source);
1.415 +
1.416 + while (!queue.empty()) {
1.417 + Node w=queue.front();
1.418 + queue.pop();
1.419 +
1.420 + for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
1.421 + Node v=_g->target(e);
1.422 + if (!M[v] && (*_flow)[e] < (*_capacity)[e] ) {
1.423 + queue.push(v);
1.424 + M.set(v, true);
1.425 + }
1.426 + }
1.427 +
1.428 + for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
1.429 + Node v=_g->source(e);
1.430 + if (!M[v] && (*_flow)[e] > 0 ) {
1.431 + queue.push(v);
1.432 + M.set(v, true);
1.433 + }
1.434 + }
1.435 + }
1.436 + }
1.437 +
1.438 + ///Returns the inclusionwise maximum of the minimum value cuts.
1.439 +
1.440 + ///Sets \c M to the characteristic vector of the minimum value cut
1.441 + ///which is inclusionwise maximum. It is computed by processing a
1.442 + ///backward bfs from the target node \c t in the residual graph.
1.443 + ///\pre \ref phase2() or run() should already be run.
1.444 + template<typename _CutMap>
1.445 + void maxMinCut(_CutMap& M) const {
1.446 +
1.447 + for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true);
1.448 +
1.449 + std::queue<Node> queue;
1.450 +
1.451 + M.set(_target,false);
1.452 + queue.push(_target);
1.453 +
1.454 + while (!queue.empty()) {
1.455 + Node w=queue.front();
1.456 + queue.pop();
1.457 +
1.458 + for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
1.459 + Node v=_g->source(e);
1.460 + if (M[v] && (*_flow)[e] < (*_capacity)[e] ) {
1.461 + queue.push(v);
1.462 + M.set(v, false);
1.463 + }
1.464 + }
1.465 +
1.466 + for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
1.467 + Node v=_g->target(e);
1.468 + if (M[v] && (*_flow)[e] > 0 ) {
1.469 + queue.push(v);
1.470 + M.set(v, false);
1.471 + }
1.472 + }
1.473 + }
1.474 + }
1.475 +
1.476 + ///Sets the source node to \c _s.
1.477 +
1.478 + ///Sets the source node to \c _s.
1.479 + ///
1.480 + void source(Node _s) {
1.481 + _source=_s;
1.482 + if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW;
1.483 + status=AFTER_NOTHING;
1.484 + }
1.485 +
1.486 + ///Returns the source node.
1.487 +
1.488 + ///Returns the source node.
1.489 + ///
1.490 + Node source() const {
1.491 + return _source;
1.492 + }
1.493 +
1.494 + ///Sets the target node to \c _t.
1.495 +
1.496 + ///Sets the target node to \c _t.
1.497 + ///
1.498 + void target(Node _t) {
1.499 + _target=_t;
1.500 + if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW;
1.501 + status=AFTER_NOTHING;
1.502 + }
1.503 +
1.504 + ///Returns the target node.
1.505 +
1.506 + ///Returns the target node.
1.507 + ///
1.508 + Node target() const {
1.509 + return _target;
1.510 + }
1.511 +
1.512 + /// Sets the edge map of the capacities to _cap.
1.513 +
1.514 + /// Sets the edge map of the capacities to _cap.
1.515 + ///
1.516 + void capacityMap(const CapacityMap& _cap) {
1.517 + _capacity=&_cap;
1.518 + status=AFTER_NOTHING;
1.519 + }
1.520 + /// Returns a reference to capacity map.
1.521 +
1.522 + /// Returns a reference to capacity map.
1.523 + ///
1.524 + const CapacityMap &capacityMap() const {
1.525 + return *_capacity;
1.526 + }
1.527 +
1.528 + /// Sets the edge map of the flows to _flow.
1.529 +
1.530 + /// Sets the edge map of the flows to _flow.
1.531 + ///
1.532 + void flowMap(FlowMap& _f) {
1.533 + _flow=&_f;
1.534 + flow_prop=NO_FLOW;
1.535 + status=AFTER_NOTHING;
1.536 + }
1.537 +
1.538 + /// Returns a reference to flow map.
1.539 +
1.540 + /// Returns a reference to flow map.
1.541 + ///
1.542 + const FlowMap &flowMap() const {
1.543 + return *_flow;
1.544 + }
1.545 +
1.546 + private:
1.547 +
1.548 + int push(Node w, NNMap& next, VecNode& first) {
1.549 +
1.550 + int lev=level[w];
1.551 + Num exc=excess[w];
1.552 + int newlevel=_node_num; //bound on the next level of w
1.553 +
1.554 + for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
1.555 + if ( (*_flow)[e] >= (*_capacity)[e] ) continue;
1.556 + Node v=_g->target(e);
1.557 +
1.558 + if( lev > level[v] ) { //Push is allowed now
1.559 +
1.560 + if ( excess[v]<=0 && v!=_target && v!=_source ) {
1.561 + next.set(v,first[level[v]]);
1.562 + first[level[v]]=v;
1.563 + }
1.564 +
1.565 + Num cap=(*_capacity)[e];
1.566 + Num flo=(*_flow)[e];
1.567 + Num remcap=cap-flo;
1.568 +
1.569 + if ( remcap >= exc ) { //A nonsaturating push.
1.570 +
1.571 + _flow->set(e, flo+exc);
1.572 + excess.set(v, excess[v]+exc);
1.573 + exc=0;
1.574 + break;
1.575 +
1.576 + } else { //A saturating push.
1.577 + _flow->set(e, cap);
1.578 + excess.set(v, excess[v]+remcap);
1.579 + exc-=remcap;
1.580 + }
1.581 + } else if ( newlevel > level[v] ) newlevel = level[v];
1.582 + } //for out edges wv
1.583 +
1.584 + if ( exc > 0 ) {
1.585 + for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
1.586 +
1.587 + if( (*_flow)[e] <= 0 ) continue;
1.588 + Node v=_g->source(e);
1.589 +
1.590 + if( lev > level[v] ) { //Push is allowed now
1.591 +
1.592 + if ( excess[v]<=0 && v!=_target && v!=_source ) {
1.593 + next.set(v,first[level[v]]);
1.594 + first[level[v]]=v;
1.595 + }
1.596 +
1.597 + Num flo=(*_flow)[e];
1.598 +
1.599 + if ( flo >= exc ) { //A nonsaturating push.
1.600 +
1.601 + _flow->set(e, flo-exc);
1.602 + excess.set(v, excess[v]+exc);
1.603 + exc=0;
1.604 + break;
1.605 + } else { //A saturating push.
1.606 +
1.607 + excess.set(v, excess[v]+flo);
1.608 + exc-=flo;
1.609 + _flow->set(e,0);
1.610 + }
1.611 + } else if ( newlevel > level[v] ) newlevel = level[v];
1.612 + } //for in edges vw
1.613 +
1.614 + } // if w still has excess after the out edge for cycle
1.615 +
1.616 + excess.set(w, exc);
1.617 +
1.618 + return newlevel;
1.619 + }
1.620 +
1.621 +
1.622 +
1.623 + void preflowPreproc(VecNode& first, NNMap& next,
1.624 + VecNode& level_list, NNMap& left, NNMap& right)
1.625 + {
1.626 + for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num);
1.627 + std::queue<Node> bfs_queue;
1.628 +
1.629 + if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) {
1.630 + //Reverse_bfs from t in the residual graph,
1.631 + //to find the starting level.
1.632 + level.set(_target,0);
1.633 + bfs_queue.push(_target);
1.634 +
1.635 + while ( !bfs_queue.empty() ) {
1.636 +
1.637 + Node v=bfs_queue.front();
1.638 + bfs_queue.pop();
1.639 + int l=level[v]+1;
1.640 +
1.641 + for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
1.642 + if ( (*_capacity)[e] <= (*_flow)[e] ) continue;
1.643 + Node w=_g->source(e);
1.644 + if ( level[w] == _node_num && w != _source ) {
1.645 + bfs_queue.push(w);
1.646 + Node z=level_list[l];
1.647 + if ( z!=INVALID ) left.set(z,w);
1.648 + right.set(w,z);
1.649 + level_list[l]=w;
1.650 + level.set(w, l);
1.651 + }
1.652 + }
1.653 +
1.654 + for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
1.655 + if ( 0 >= (*_flow)[e] ) continue;
1.656 + Node w=_g->target(e);
1.657 + if ( level[w] == _node_num && w != _source ) {
1.658 + bfs_queue.push(w);
1.659 + Node z=level_list[l];
1.660 + if ( z!=INVALID ) left.set(z,w);
1.661 + right.set(w,z);
1.662 + level_list[l]=w;
1.663 + level.set(w, l);
1.664 + }
1.665 + }
1.666 + } //while
1.667 + } //if
1.668 +
1.669 +
1.670 + switch (flow_prop) {
1.671 + case NO_FLOW:
1.672 + for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0);
1.673 + case ZERO_FLOW:
1.674 + for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
1.675 +
1.676 + //Reverse_bfs from t, to find the starting level.
1.677 + level.set(_target,0);
1.678 + bfs_queue.push(_target);
1.679 +
1.680 + while ( !bfs_queue.empty() ) {
1.681 +
1.682 + Node v=bfs_queue.front();
1.683 + bfs_queue.pop();
1.684 + int l=level[v]+1;
1.685 +
1.686 + for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
1.687 + Node w=_g->source(e);
1.688 + if ( level[w] == _node_num && w != _source ) {
1.689 + bfs_queue.push(w);
1.690 + Node z=level_list[l];
1.691 + if ( z!=INVALID ) left.set(z,w);
1.692 + right.set(w,z);
1.693 + level_list[l]=w;
1.694 + level.set(w, l);
1.695 + }
1.696 + }
1.697 + }
1.698 +
1.699 + //the starting flow
1.700 + for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
1.701 + Num c=(*_capacity)[e];
1.702 + if ( c <= 0 ) continue;
1.703 + Node w=_g->target(e);
1.704 + if ( level[w] < _node_num ) {
1.705 + if ( excess[w] <= 0 && w!=_target ) { //putting into the stack
1.706 + next.set(w,first[level[w]]);
1.707 + first[level[w]]=w;
1.708 + }
1.709 + _flow->set(e, c);
1.710 + excess.set(w, excess[w]+c);
1.711 + }
1.712 + }
1.713 + break;
1.714 +
1.715 + case GEN_FLOW:
1.716 + for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
1.717 + {
1.718 + Num exc=0;
1.719 + for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e];
1.720 + for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e];
1.721 + excess.set(_target,exc);
1.722 + }
1.723 +
1.724 + //the starting flow
1.725 + for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e) {
1.726 + Num rem=(*_capacity)[e]-(*_flow)[e];
1.727 + if ( rem <= 0 ) continue;
1.728 + Node w=_g->target(e);
1.729 + if ( level[w] < _node_num ) {
1.730 + if ( excess[w] <= 0 && w!=_target ) { //putting into the stack
1.731 + next.set(w,first[level[w]]);
1.732 + first[level[w]]=w;
1.733 + }
1.734 + _flow->set(e, (*_capacity)[e]);
1.735 + excess.set(w, excess[w]+rem);
1.736 + }
1.737 + }
1.738 +
1.739 + for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) {
1.740 + if ( (*_flow)[e] <= 0 ) continue;
1.741 + Node w=_g->source(e);
1.742 + if ( level[w] < _node_num ) {
1.743 + if ( excess[w] <= 0 && w!=_target ) {
1.744 + next.set(w,first[level[w]]);
1.745 + first[level[w]]=w;
1.746 + }
1.747 + excess.set(w, excess[w]+(*_flow)[e]);
1.748 + _flow->set(e, 0);
1.749 + }
1.750 + }
1.751 + break;
1.752 +
1.753 + case PRE_FLOW:
1.754 + //the starting flow
1.755 + for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
1.756 + Num rem=(*_capacity)[e]-(*_flow)[e];
1.757 + if ( rem <= 0 ) continue;
1.758 + Node w=_g->target(e);
1.759 + if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]);
1.760 + }
1.761 +
1.762 + for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
1.763 + if ( (*_flow)[e] <= 0 ) continue;
1.764 + Node w=_g->source(e);
1.765 + if ( level[w] < _node_num ) _flow->set(e, 0);
1.766 + }
1.767 +
1.768 + //computing the excess
1.769 + for(NodeIt w(*_g); w!=INVALID; ++w) {
1.770 + Num exc=0;
1.771 + for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e];
1.772 + for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e];
1.773 + excess.set(w,exc);
1.774 +
1.775 + //putting the active nodes into the stack
1.776 + int lev=level[w];
1.777 + if ( exc > 0 && lev < _node_num && Node(w) != _target ) {
1.778 + next.set(w,first[lev]);
1.779 + first[lev]=w;
1.780 + }
1.781 + }
1.782 + break;
1.783 + } //switch
1.784 + } //preflowPreproc
1.785 +
1.786 +
1.787 + void relabel(Node w, int newlevel, VecNode& first, NNMap& next,
1.788 + VecNode& level_list, NNMap& left,
1.789 + NNMap& right, int& b, int& k, bool what_heur )
1.790 + {
1.791 +
1.792 + int lev=level[w];
1.793 +
1.794 + Node right_n=right[w];
1.795 + Node left_n=left[w];
1.796 +
1.797 + //unlacing starts
1.798 + if ( right_n!=INVALID ) {
1.799 + if ( left_n!=INVALID ) {
1.800 + right.set(left_n, right_n);
1.801 + left.set(right_n, left_n);
1.802 + } else {
1.803 + level_list[lev]=right_n;
1.804 + left.set(right_n, INVALID);
1.805 + }
1.806 + } else {
1.807 + if ( left_n!=INVALID ) {
1.808 + right.set(left_n, INVALID);
1.809 + } else {
1.810 + level_list[lev]=INVALID;
1.811 + }
1.812 + }
1.813 + //unlacing ends
1.814 +
1.815 + if ( level_list[lev]==INVALID ) {
1.816 +
1.817 + //gapping starts
1.818 + for (int i=lev; i!=k ; ) {
1.819 + Node v=level_list[++i];
1.820 + while ( v!=INVALID ) {
1.821 + level.set(v,_node_num);
1.822 + v=right[v];
1.823 + }
1.824 + level_list[i]=INVALID;
1.825 + if ( !what_heur ) first[i]=INVALID;
1.826 + }
1.827 +
1.828 + level.set(w,_node_num);
1.829 + b=lev-1;
1.830 + k=b;
1.831 + //gapping ends
1.832 +
1.833 + } else {
1.834 +
1.835 + if ( newlevel == _node_num ) level.set(w,_node_num);
1.836 + else {
1.837 + level.set(w,++newlevel);
1.838 + next.set(w,first[newlevel]);
1.839 + first[newlevel]=w;
1.840 + if ( what_heur ) b=newlevel;
1.841 + if ( k < newlevel ) ++k; //now k=newlevel
1.842 + Node z=level_list[newlevel];
1.843 + if ( z!=INVALID ) left.set(z,w);
1.844 + right.set(w,z);
1.845 + left.set(w,INVALID);
1.846 + level_list[newlevel]=w;
1.847 + }
1.848 + }
1.849 + } //relabel
1.850 +
1.851 + };
1.852 +
1.853 + ///Function type interface for Preflow algorithm.
1.854 +
1.855 + /// \ingroup flowalgs
1.856 + ///Function type interface for Preflow algorithm.
1.857 + ///\sa Preflow
1.858 + template<class GR, class CM, class FM>
1.859 + Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g,
1.860 + typename GR::Node source,
1.861 + typename GR::Node target,
1.862 + const CM &cap,
1.863 + FM &flow
1.864 + )
1.865 + {
1.866 + return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow);
1.867 + }
1.868 +
1.869 +} //namespace lemon
1.870 +
1.871 +#endif //LEMON_PREFLOW_H