alpar@906: /* -*- C++ -*-
alpar@906: *
alpar@1956: * This file is a part of LEMON, a generic C++ optimization library
alpar@1956: *
alpar@1956: * Copyright (C) 2003-2006
alpar@1956: * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@1359: * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@906: *
alpar@906: * Permission to use, modify and distribute this software is granted
alpar@906: * provided that this copyright notice appears in all copies. For
alpar@906: * precise terms see the accompanying LICENSE file.
alpar@906: *
alpar@906: * This software is provided "AS IS" with no warranty of any kind,
alpar@906: * express or implied, and with no claim as to its suitability for any
alpar@906: * purpose.
alpar@906: *
alpar@906: */
alpar@906:
alpar@921: #ifndef LEMON_PREFLOW_H
alpar@921: #define LEMON_PREFLOW_H
jacint@836:
jacint@836: #include <vector>
jacint@836: #include <queue>
jacint@836:
jacint@1762: #include <lemon/error.h>
deba@1993: #include <lemon/bits/invalid.h>
alpar@1835: #include <lemon/tolerance.h>
alpar@921: #include <lemon/maps.h>
klao@977: #include <lemon/graph_utils.h>
jacint@836:
jacint@836: /// \file
jacint@836: /// \ingroup flowalgs
deba@1742: /// \brief Implementation of the preflow algorithm.
jacint@836:
alpar@921: namespace lemon {
jacint@836:
deba@1792: ///\ingroup flowalgs
deba@1792: ///\brief %Preflow algorithms class.
deba@1792: ///
jacint@836: ///This class provides an implementation of the \e preflow \e
jacint@836: ///algorithm producing a flow of maximum value in a directed
jacint@2024: ///graph. The preflow algorithms are the fastest known max flow algorithms.
jacint@2024: ///The \e source node, the \e target node, the \e
jacint@836: ///capacity of the edges and the \e starting \e flow value of the
jacint@836: ///edges should be passed to the algorithm through the
jacint@836: ///constructor. It is possible to change these quantities using the
zsuzska@1285: ///functions \ref source, \ref target, \ref capacityMap and \ref
zsuzska@1285: ///flowMap.
jacint@836: ///
alpar@921: ///After running \ref lemon::Preflow::phase1() "phase1()"
alpar@921: ///or \ref lemon::Preflow::run() "run()", the maximal flow
jacint@836: ///value can be obtained by calling \ref flowValue(). The minimum
alpar@851: ///value cut can be written into a <tt>bool</tt> node map by
alpar@851: ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes
jacint@836: ///the inclusionwise minimum and maximum of the minimum value cuts,
jacint@836: ///resp.)
jacint@836: ///
jacint@836: ///\param Graph The directed graph type the algorithm runs on.
jacint@836: ///\param Num The number type of the capacities and the flow values.
alpar@1222: ///\param CapacityMap The capacity map type.
jacint@836: ///\param FlowMap The flow map type.
jacint@2024: ///\param Tolerance The tolerance type.
jacint@836: ///
jacint@836: ///\author Jacint Szabo
alpar@1227: ///\todo Second template parameter is superfluous
jacint@836: template <typename Graph, typename Num,
alpar@1222: typename CapacityMap=typename Graph::template EdgeMap<Num>,
alpar@1835: typename FlowMap=typename Graph::template EdgeMap<Num>,
deba@2019: typename Tolerance=Tolerance<Num> >
jacint@836: class Preflow {
jacint@836: protected:
jacint@836: typedef typename Graph::Node Node;
jacint@836: typedef typename Graph::NodeIt NodeIt;
jacint@836: typedef typename Graph::EdgeIt EdgeIt;
jacint@836: typedef typename Graph::OutEdgeIt OutEdgeIt;
jacint@836: typedef typename Graph::InEdgeIt InEdgeIt;
jacint@836:
jacint@836: typedef typename Graph::template NodeMap<Node> NNMap;
jacint@836: typedef typename std::vector<Node> VecNode;
jacint@836:
alpar@1222: const Graph* _g;
alpar@1222: Node _source;
alpar@1222: Node _target;
alpar@1222: const CapacityMap* _capacity;
alpar@1222: FlowMap* _flow;
alpar@1835:
deba@2019: Tolerance _surely;
alpar@1835:
alpar@1222: int _node_num; //the number of nodes of G
jacint@836:
jacint@836: typename Graph::template NodeMap<int> level;
jacint@836: typename Graph::template NodeMap<Num> excess;
jacint@836:
jacint@836: // constants used for heuristics
jacint@836: static const int H0=20;
jacint@836: static const int H1=1;
jacint@836:
jacint@1762: public:
jacint@1762:
jacint@1762: ///\ref Exception for the case when s=t.
jacint@1762:
jacint@1762: ///\ref Exception for the case when the source equals the target.
jacint@1762: class InvalidArgument : public lemon::LogicError {
jacint@836: public:
jacint@1762: virtual const char* exceptionName() const {
jacint@1762: return "lemon::Preflow::InvalidArgument";
jacint@1762: }
jacint@1762: };
jacint@1762:
jacint@1762:
jacint@836: ///Indicates the property of the starting flow map.
jacint@1762:
alpar@1222: ///Indicates the property of the starting flow map.
jacint@836: ///
jacint@836: enum FlowEnum{
alpar@1898: ///indicates an unspecified edge map. \c flow will be
alpar@1898: ///set to the constant zero flow in the beginning of
alpar@1898: ///the algorithm in this case.
jacint@836: NO_FLOW,
alpar@1898: ///constant zero flow
jacint@836: ZERO_FLOW,
alpar@1898: ///any flow, i.e. the sum of the in-flows equals to
alpar@1898: ///the sum of the out-flows in every node except the \c source and
alpar@1898: ///the \c target.
jacint@836: GEN_FLOW,
alpar@1898: ///any preflow, i.e. the sum of the in-flows is at
alpar@1898: ///least the sum of the out-flows in every node except the \c source.
jacint@836: PRE_FLOW
jacint@836: };
jacint@836:
jacint@836: ///Indicates the state of the preflow algorithm.
jacint@836:
alpar@1222: ///Indicates the state of the preflow algorithm.
jacint@836: ///
jacint@836: enum StatusEnum {
alpar@1898: ///before running the algorithm or
alpar@1898: ///at an unspecified state.
jacint@836: AFTER_NOTHING,
alpar@1898: ///right after running \ref phase1()
jacint@836: AFTER_PREFLOW_PHASE_1,
alpar@1898: ///after running \ref phase2()
jacint@836: AFTER_PREFLOW_PHASE_2
jacint@836: };
jacint@836:
jacint@1762: protected:
jacint@1762: FlowEnum flow_prop;
jacint@836: StatusEnum status; // Do not needle this flag only if necessary.
jacint@836:
jacint@836: public:
jacint@836: ///The constructor of the class.
jacint@836:
jacint@836: ///The constructor of the class.
zsuzska@1285: ///\param _gr The directed graph the algorithm runs on.
jacint@836: ///\param _s The source node.
jacint@836: ///\param _t The target node.
alpar@1222: ///\param _cap The capacity of the edges.
alpar@1222: ///\param _f The flow of the edges.
alpar@1953: ///\param tol Tolerance class.
jacint@836: ///Except the graph, all of these parameters can be reset by
zsuzska@1285: ///calling \ref source, \ref target, \ref capacityMap and \ref
zsuzska@1285: ///flowMap, resp.
deba@2033: Preflow(const Graph& _gr, Node _s, Node _t,
deba@2033: const CapacityMap& _cap, FlowMap& _f,
deba@2033: const Tolerance &_sr=Tolerance()) :
alpar@1222: _g(&_gr), _source(_s), _target(_t), _capacity(&_cap),
deba@2019: _flow(&_f), _surely(_sr),
alpar@1835: _node_num(countNodes(_gr)), level(_gr), excess(_gr,0),
jacint@1762: flow_prop(NO_FLOW), status(AFTER_NOTHING) {
jacint@1762: if ( _source==_target )
jacint@1762: throw InvalidArgument();
deba@2033: }
jacint@1762:
alpar@1898: ///Give a reference to the tolerance handler class
jacint@836:
alpar@1898: ///Give a reference to the tolerance handler class
alpar@1898: ///\sa Tolerance
deba@2019: Tolerance &tolerance() { return _surely; }
alpar@1898:
jacint@836: ///Runs the preflow algorithm.
jacint@836:
alpar@851: ///Runs the preflow algorithm.
alpar@851: ///
jacint@836: void run() {
jacint@836: phase1(flow_prop);
jacint@836: phase2();
jacint@836: }
jacint@836:
jacint@836: ///Runs the preflow algorithm.
jacint@836:
jacint@836: ///Runs the preflow algorithm.
jacint@836: ///\pre The starting flow map must be
jacint@836: /// - a constant zero flow if \c fp is \c ZERO_FLOW,
jacint@836: /// - an arbitrary flow if \c fp is \c GEN_FLOW,
jacint@836: /// - an arbitrary preflow if \c fp is \c PRE_FLOW,
jacint@836: /// - any map if \c fp is NO_FLOW.
jacint@836: ///If the starting flow map is a flow or a preflow then
jacint@836: ///the algorithm terminates faster.
jacint@836: void run(FlowEnum fp) {
jacint@836: flow_prop=fp;
jacint@836: run();
jacint@836: }
jacint@836:
jacint@836: ///Runs the first phase of the preflow algorithm.
jacint@836:
jacint@920: ///The preflow algorithm consists of two phases, this method runs
jacint@920: ///the first phase. After the first phase the maximum flow value
zsuzska@1285: ///and a minimum value cut can already be computed, although a
jacint@920: ///maximum flow is not yet obtained. So after calling this method
jacint@920: ///\ref flowValue returns the value of a maximum flow and \ref
jacint@920: ///minCut returns a minimum cut.
jacint@920: ///\warning \ref minMinCut and \ref maxMinCut do not give minimum
jacint@920: ///value cuts unless calling \ref phase2.
jacint@920: ///\pre The starting flow must be
jacint@920: ///- a constant zero flow if \c fp is \c ZERO_FLOW,
jacint@920: ///- an arbitary flow if \c fp is \c GEN_FLOW,
jacint@920: ///- an arbitary preflow if \c fp is \c PRE_FLOW,
jacint@920: ///- any map if \c fp is NO_FLOW.
jacint@836: void phase1(FlowEnum fp)
jacint@836: {
jacint@836: flow_prop=fp;
jacint@836: phase1();
jacint@836: }
jacint@836:
jacint@836:
jacint@836: ///Runs the first phase of the preflow algorithm.
jacint@836:
jacint@920: ///The preflow algorithm consists of two phases, this method runs
jacint@920: ///the first phase. After the first phase the maximum flow value
zsuzska@1285: ///and a minimum value cut can already be computed, although a
jacint@920: ///maximum flow is not yet obtained. So after calling this method
jacint@920: ///\ref flowValue returns the value of a maximum flow and \ref
jacint@920: ///minCut returns a minimum cut.
deba@1786: ///\warning \ref minMinCut() and \ref maxMinCut() do not
alpar@911: ///give minimum value cuts unless calling \ref phase2().
jacint@836: void phase1()
jacint@836: {
alpar@1222: int heur0=(int)(H0*_node_num); //time while running 'bound decrease'
alpar@1222: int heur1=(int)(H1*_node_num); //time while running 'highest label'
jacint@836: int heur=heur1; //starting time interval (#of relabels)
jacint@836: int numrelabel=0;
jacint@836:
jacint@836: bool what_heur=1;
jacint@836: //It is 0 in case 'bound decrease' and 1 in case 'highest label'
jacint@836:
jacint@836: bool end=false;
jacint@836: //Needed for 'bound decrease', true means no active
jacint@836: //nodes are above bound b.
jacint@836:
alpar@1222: int k=_node_num-2; //bound on the highest level under n containing a node
jacint@2024: int b=k; //bound on the highest level under n containing an active node
jacint@836:
alpar@1222: VecNode first(_node_num, INVALID);
alpar@1222: NNMap next(*_g, INVALID);
jacint@836:
alpar@1222: NNMap left(*_g, INVALID);
alpar@1222: NNMap right(*_g, INVALID);
alpar@1222: VecNode level_list(_node_num,INVALID);
jacint@836: //List of the nodes in level i<n, set to n.
jacint@836:
jacint@836: preflowPreproc(first, next, level_list, left, right);
jacint@836:
jacint@836: //Push/relabel on the highest level active nodes.
jacint@836: while ( true ) {
jacint@836: if ( b == 0 ) {
jacint@836: if ( !what_heur && !end && k > 0 ) {
jacint@836: b=k;
jacint@836: end=true;
jacint@836: } else break;
jacint@836: }
jacint@836:
jacint@836: if ( first[b]==INVALID ) --b;
jacint@836: else {
jacint@836: end=false;
jacint@836: Node w=first[b];
jacint@836: first[b]=next[w];
jacint@836: int newlevel=push(w, next, first);
jacint@2024: if ( _surely.positive(excess[w]) ) relabel(w, newlevel, first, next, level_list,
jacint@836: left, right, b, k, what_heur);
jacint@836:
jacint@836: ++numrelabel;
jacint@836: if ( numrelabel >= heur ) {
jacint@836: numrelabel=0;
jacint@836: if ( what_heur ) {
jacint@836: what_heur=0;
jacint@836: heur=heur0;
jacint@836: end=false;
jacint@836: } else {
jacint@836: what_heur=1;
jacint@836: heur=heur1;
jacint@836: b=k;
jacint@836: }
jacint@836: }
jacint@836: }
jacint@836: }
jacint@836: flow_prop=PRE_FLOW;
jacint@836: status=AFTER_PREFLOW_PHASE_1;
jacint@836: }
jacint@836: // Heuristics:
jacint@836: // 2 phase
jacint@836: // gap
jacint@836: // list 'level_list' on the nodes on level i implemented by hand
jacint@836: // stack 'active' on the active nodes on level i
jacint@836: // runs heuristic 'highest label' for H1*n relabels
alpar@1222: // runs heuristic 'bound decrease' for H0*n relabels,
alpar@1222: // starts with 'highest label'
jacint@836: // Parameters H0 and H1 are initialized to 20 and 1.
jacint@836:
jacint@836:
jacint@836: ///Runs the second phase of the preflow algorithm.
jacint@836:
jacint@836: ///The preflow algorithm consists of two phases, this method runs
alpar@1631: ///the second phase. After calling \ref phase1() and then
alpar@1631: ///\ref phase2(),
alpar@1631: /// \ref flowMap() return a maximum flow, \ref flowValue
jacint@920: ///returns the value of a maximum flow, \ref minCut returns a
jacint@920: ///minimum cut, while the methods \ref minMinCut and \ref
jacint@920: ///maxMinCut return the inclusionwise minimum and maximum cuts of
jacint@920: ///minimum value, resp. \pre \ref phase1 must be called before.
jacint@836: void phase2()
jacint@836: {
jacint@836:
alpar@1222: int k=_node_num-2; //bound on the highest level under n containing a node
jacint@836: int b=k; //bound on the highest level under n of an active node
jacint@836:
jacint@836:
alpar@1222: VecNode first(_node_num, INVALID);
alpar@1222: NNMap next(*_g, INVALID);
alpar@1222: level.set(_source,0);
jacint@836: std::queue<Node> bfs_queue;
alpar@1222: bfs_queue.push(_source);
jacint@836:
jacint@836: while ( !bfs_queue.empty() ) {
jacint@836:
jacint@836: Node v=bfs_queue.front();
jacint@836: bfs_queue.pop();
jacint@836: int l=level[v]+1;
jacint@836:
alpar@1222: for(InEdgeIt e(*_g,v); e!=INVALID; ++e) {
jacint@2024: if ( !_surely.less((*_flow)[e], (*_capacity)[e]) ) continue;
alpar@1222: Node u=_g->source(e);
alpar@1222: if ( level[u] >= _node_num ) {
jacint@836: bfs_queue.push(u);
jacint@836: level.set(u, l);
jacint@2024: if ( _surely.positive(excess[u]) ) {
jacint@836: next.set(u,first[l]);
jacint@836: first[l]=u;
jacint@836: }
jacint@836: }
jacint@836: }
jacint@836:
alpar@1222: for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) {
jacint@2024: if ( !_surely.positive((*_flow)[e]) ) continue;
alpar@1222: Node u=_g->target(e);
alpar@1222: if ( level[u] >= _node_num ) {
jacint@836: bfs_queue.push(u);
jacint@836: level.set(u, l);
jacint@2024: if ( _surely.positive(excess[u]) ) {
jacint@836: next.set(u,first[l]);
jacint@836: first[l]=u;
jacint@836: }
jacint@836: }
jacint@836: }
jacint@836: }
alpar@1222: b=_node_num-2;
jacint@836:
jacint@836: while ( true ) {
jacint@836:
jacint@836: if ( b == 0 ) break;
jacint@836: if ( first[b]==INVALID ) --b;
jacint@836: else {
jacint@836: Node w=first[b];
jacint@836: first[b]=next[w];
jacint@836: int newlevel=push(w,next, first);
jacint@836:
jacint@836: //relabel
jacint@2024: if ( _surely.positive(excess[w]) ) {
jacint@836: level.set(w,++newlevel);
jacint@836: next.set(w,first[newlevel]);
jacint@836: first[newlevel]=w;
jacint@836: b=newlevel;
jacint@836: }
jacint@836: }
jacint@836: } // while(true)
jacint@836: flow_prop=GEN_FLOW;
jacint@836: status=AFTER_PREFLOW_PHASE_2;
jacint@836: }
jacint@836:
jacint@836: /// Returns the value of the maximum flow.
jacint@836:
jacint@836: /// Returns the value of the maximum flow by returning the excess
alpar@911: /// of the target node \c t. This value equals to the value of
jacint@836: /// the maximum flow already after running \ref phase1.
jacint@836: Num flowValue() const {
alpar@1222: return excess[_target];
jacint@836: }
jacint@836:
jacint@836:
jacint@836: ///Returns a minimum value cut.
jacint@836:
jacint@836: ///Sets \c M to the characteristic vector of a minimum value
jacint@836: ///cut. This method can be called both after running \ref
jacint@836: ///phase1 and \ref phase2. It is much faster after
marci@849: ///\ref phase1. \pre M should be a bool-valued node-map. \pre
alpar@911: ///If \ref minCut() is called after \ref phase2() then M should
jacint@836: ///be initialized to false.
jacint@836: template<typename _CutMap>
jacint@836: void minCut(_CutMap& M) const {
jacint@836: switch ( status ) {
jacint@836: case AFTER_PREFLOW_PHASE_1:
alpar@1222: for(NodeIt v(*_g); v!=INVALID; ++v) {
alpar@1222: if (level[v] < _node_num) {
jacint@836: M.set(v, false);
jacint@836: } else {
jacint@836: M.set(v, true);
jacint@836: }
jacint@836: }
jacint@836: break;
jacint@836: case AFTER_PREFLOW_PHASE_2:
jacint@836: minMinCut(M);
jacint@836: break;
jacint@836: case AFTER_NOTHING:
jacint@836: break;
jacint@836: }
jacint@836: }
jacint@836:
jacint@836: ///Returns the inclusionwise minimum of the minimum value cuts.
jacint@836:
jacint@836: ///Sets \c M to the characteristic vector of the minimum value cut
jacint@836: ///which is inclusionwise minimum. It is computed by processing a
jacint@836: ///bfs from the source node \c s in the residual graph. \pre M
jacint@836: ///should be a node map of bools initialized to false. \pre \ref
jacint@836: ///phase2 should already be run.
jacint@836: template<typename _CutMap>
jacint@836: void minMinCut(_CutMap& M) const {
jacint@836:
jacint@836: std::queue<Node> queue;
alpar@1222: M.set(_source,true);
alpar@1227: queue.push(_source);
jacint@836:
jacint@836: while (!queue.empty()) {
jacint@836: Node w=queue.front();
jacint@836: queue.pop();
jacint@836:
alpar@1222: for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
alpar@1222: Node v=_g->target(e);
jacint@2024: if (!M[v] && _surely.less((*_flow)[e] , (*_capacity)[e]) ) {
jacint@836: queue.push(v);
jacint@836: M.set(v, true);
jacint@836: }
jacint@836: }
jacint@836:
alpar@1222: for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
alpar@1222: Node v=_g->source(e);
jacint@2024: if (!M[v] && _surely.positive((*_flow)[e]) ) {
jacint@836: queue.push(v);
jacint@836: M.set(v, true);
jacint@836: }
jacint@836: }
jacint@836: }
jacint@836: }
jacint@836:
jacint@836: ///Returns the inclusionwise maximum of the minimum value cuts.
jacint@836:
jacint@836: ///Sets \c M to the characteristic vector of the minimum value cut
jacint@836: ///which is inclusionwise maximum. It is computed by processing a
jacint@836: ///backward bfs from the target node \c t in the residual graph.
alpar@911: ///\pre \ref phase2() or run() should already be run.
jacint@836: template<typename _CutMap>
jacint@836: void maxMinCut(_CutMap& M) const {
jacint@836:
alpar@1222: for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true);
jacint@836:
jacint@836: std::queue<Node> queue;
jacint@836:
alpar@1222: M.set(_target,false);
alpar@1222: queue.push(_target);
jacint@836:
jacint@836: while (!queue.empty()) {
jacint@836: Node w=queue.front();
jacint@836: queue.pop();
jacint@836:
alpar@1222: for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
alpar@1222: Node v=_g->source(e);
jacint@2024: if (M[v] && _surely.less((*_flow)[e], (*_capacity)[e]) ) {
jacint@836: queue.push(v);
jacint@836: M.set(v, false);
jacint@836: }
jacint@836: }
jacint@836:
alpar@1222: for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
alpar@1222: Node v=_g->target(e);
jacint@2024: if (M[v] && _surely.positive((*_flow)[e]) ) {
jacint@836: queue.push(v);
jacint@836: M.set(v, false);
jacint@836: }
jacint@836: }
jacint@836: }
jacint@836: }
jacint@836:
jacint@836: ///Sets the source node to \c _s.
jacint@836:
jacint@836: ///Sets the source node to \c _s.
jacint@836: ///
alpar@1222: void source(Node _s) {
alpar@1222: _source=_s;
jacint@836: if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW;
jacint@836: status=AFTER_NOTHING;
jacint@836: }
jacint@836:
alpar@1222: ///Returns the source node.
alpar@1222:
alpar@1222: ///Returns the source node.
alpar@1222: ///
alpar@1222: Node source() const {
alpar@1222: return _source;
alpar@1222: }
alpar@1222:
jacint@836: ///Sets the target node to \c _t.
jacint@836:
jacint@836: ///Sets the target node to \c _t.
jacint@836: ///
alpar@1222: void target(Node _t) {
alpar@1222: _target=_t;
jacint@836: if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW;
jacint@836: status=AFTER_NOTHING;
jacint@836: }
jacint@836:
alpar@1222: ///Returns the target node.
alpar@1222:
alpar@1222: ///Returns the target node.
alpar@1222: ///
alpar@1222: Node target() const {
alpar@1222: return _target;
alpar@1222: }
alpar@1222:
jacint@836: /// Sets the edge map of the capacities to _cap.
jacint@836:
jacint@836: /// Sets the edge map of the capacities to _cap.
jacint@836: ///
alpar@1222: void capacityMap(const CapacityMap& _cap) {
alpar@1222: _capacity=&_cap;
jacint@836: status=AFTER_NOTHING;
jacint@836: }
zsuzska@1285: /// Returns a reference to capacity map.
alpar@1222:
zsuzska@1285: /// Returns a reference to capacity map.
alpar@1222: ///
alpar@1222: const CapacityMap &capacityMap() const {
alpar@1222: return *_capacity;
alpar@1222: }
jacint@836:
jacint@836: /// Sets the edge map of the flows to _flow.
jacint@836:
jacint@836: /// Sets the edge map of the flows to _flow.
jacint@836: ///
alpar@1222: void flowMap(FlowMap& _f) {
alpar@1222: _flow=&_f;
jacint@836: flow_prop=NO_FLOW;
jacint@836: status=AFTER_NOTHING;
jacint@836: }
alpar@1222:
zsuzska@1285: /// Returns a reference to flow map.
jacint@836:
zsuzska@1285: /// Returns a reference to flow map.
alpar@1222: ///
alpar@1222: const FlowMap &flowMap() const {
alpar@1222: return *_flow;
alpar@1222: }
jacint@836:
jacint@836: private:
jacint@836:
jacint@836: int push(Node w, NNMap& next, VecNode& first) {
jacint@836:
jacint@836: int lev=level[w];
jacint@836: Num exc=excess[w];
alpar@1222: int newlevel=_node_num; //bound on the next level of w
jacint@836:
alpar@1222: for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
jacint@2024: if ( !_surely.less((*_flow)[e], (*_capacity)[e]) ) continue;
alpar@1222: Node v=_g->target(e);
jacint@2024:
jacint@836: if( lev > level[v] ) { //Push is allowed now
jacint@836:
jacint@2024: if ( !_surely.positive(excess[v]) && v!=_target && v!=_source ) {
jacint@836: next.set(v,first[level[v]]);
jacint@836: first[level[v]]=v;
jacint@836: }
jacint@836:
alpar@1222: Num cap=(*_capacity)[e];
alpar@1222: Num flo=(*_flow)[e];
jacint@836: Num remcap=cap-flo;
jacint@836:
jacint@2024: if ( ! _surely.less(remcap, exc) ) { //A nonsaturating push.
jacint@836:
alpar@1222: _flow->set(e, flo+exc);
jacint@836: excess.set(v, excess[v]+exc);
jacint@836: exc=0;
jacint@836: break;
jacint@836:
jacint@836: } else { //A saturating push.
alpar@1222: _flow->set(e, cap);
jacint@836: excess.set(v, excess[v]+remcap);
jacint@836: exc-=remcap;
jacint@836: }
jacint@836: } else if ( newlevel > level[v] ) newlevel = level[v];
jacint@836: } //for out edges wv
jacint@836:
jacint@2024: if ( _surely.positive(exc) ) {
alpar@1222: for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
jacint@836:
jacint@2024: if ( !_surely.positive((*_flow)[e]) ) continue;
alpar@1222: Node v=_g->source(e);
jacint@2024:
jacint@836: if( lev > level[v] ) { //Push is allowed now
jacint@836:
jacint@2024: if ( !_surely.positive(excess[v]) && v!=_target && v!=_source ) {
jacint@836: next.set(v,first[level[v]]);
jacint@836: first[level[v]]=v;
jacint@836: }
jacint@836:
alpar@1222: Num flo=(*_flow)[e];
jacint@836:
jacint@2024: if ( !_surely.less(flo, exc) ) { //A nonsaturating push.
jacint@836:
alpar@1222: _flow->set(e, flo-exc);
jacint@836: excess.set(v, excess[v]+exc);
jacint@836: exc=0;
jacint@836: break;
jacint@836: } else { //A saturating push.
jacint@836:
jacint@836: excess.set(v, excess[v]+flo);
jacint@836: exc-=flo;
alpar@1222: _flow->set(e,0);
jacint@836: }
jacint@836: } else if ( newlevel > level[v] ) newlevel = level[v];
jacint@836: } //for in edges vw
jacint@836:
jacint@836: } // if w still has excess after the out edge for cycle
jacint@836:
jacint@836: excess.set(w, exc);
jacint@836:
jacint@836: return newlevel;
jacint@836: }
jacint@836:
jacint@836:
jacint@836:
jacint@836: void preflowPreproc(VecNode& first, NNMap& next,
jacint@836: VecNode& level_list, NNMap& left, NNMap& right)
jacint@836: {
alpar@1222: for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num);
jacint@836: std::queue<Node> bfs_queue;
jacint@836:
jacint@836: if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) {
jacint@836: //Reverse_bfs from t in the residual graph,
jacint@836: //to find the starting level.
alpar@1222: level.set(_target,0);
alpar@1222: bfs_queue.push(_target);
jacint@836:
jacint@836: while ( !bfs_queue.empty() ) {
jacint@836:
jacint@836: Node v=bfs_queue.front();
jacint@836: bfs_queue.pop();
jacint@836: int l=level[v]+1;
jacint@836:
alpar@1222: for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
jacint@2024: if ( !_surely.less((*_flow)[e],(*_capacity)[e]) ) continue;
alpar@1222: Node w=_g->source(e);
alpar@1222: if ( level[w] == _node_num && w != _source ) {
jacint@836: bfs_queue.push(w);
jacint@836: Node z=level_list[l];
jacint@836: if ( z!=INVALID ) left.set(z,w);
jacint@836: right.set(w,z);
jacint@836: level_list[l]=w;
jacint@836: level.set(w, l);
jacint@836: }
jacint@836: }
jacint@836:
alpar@1222: for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
jacint@2024: if ( !_surely.positive((*_flow)[e]) ) continue;
alpar@1222: Node w=_g->target(e);
alpar@1222: if ( level[w] == _node_num && w != _source ) {
jacint@836: bfs_queue.push(w);
jacint@836: Node z=level_list[l];
jacint@836: if ( z!=INVALID ) left.set(z,w);
jacint@836: right.set(w,z);
jacint@836: level_list[l]=w;
jacint@836: level.set(w, l);
jacint@836: }
jacint@836: }
jacint@836: } //while
jacint@836: } //if
jacint@836:
jacint@836:
jacint@836: switch (flow_prop) {
jacint@836: case NO_FLOW:
alpar@1222: for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0);
jacint@836: case ZERO_FLOW:
alpar@1222: for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
jacint@836:
jacint@836: //Reverse_bfs from t, to find the starting level.
alpar@1222: level.set(_target,0);
alpar@1222: bfs_queue.push(_target);
jacint@836:
jacint@836: while ( !bfs_queue.empty() ) {
jacint@836:
jacint@836: Node v=bfs_queue.front();
jacint@836: bfs_queue.pop();
jacint@836: int l=level[v]+1;
jacint@836:
alpar@1222: for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
alpar@1222: Node w=_g->source(e);
alpar@1222: if ( level[w] == _node_num && w != _source ) {
jacint@836: bfs_queue.push(w);
jacint@836: Node z=level_list[l];
jacint@836: if ( z!=INVALID ) left.set(z,w);
jacint@836: right.set(w,z);
jacint@836: level_list[l]=w;
jacint@836: level.set(w, l);
jacint@836: }
jacint@836: }
jacint@836: }
jacint@836:
jacint@836: //the starting flow
alpar@1222: for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
alpar@1222: Num c=(*_capacity)[e];
jacint@2024: if ( !_surely.positive(c) ) continue;
alpar@1222: Node w=_g->target(e);
alpar@1222: if ( level[w] < _node_num ) {
jacint@2024: if ( !_surely.positive(excess[w]) && w!=_target ) { //putting into the stack
jacint@836: next.set(w,first[level[w]]);
jacint@836: first[level[w]]=w;
jacint@836: }
alpar@1222: _flow->set(e, c);
jacint@836: excess.set(w, excess[w]+c);
jacint@836: }
jacint@836: }
jacint@836: break;
jacint@836:
jacint@836: case GEN_FLOW:
alpar@1222: for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
jacint@836: {
jacint@836: Num exc=0;
alpar@1222: for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e];
alpar@1222: for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e];
alpar@1222: excess.set(_target,exc);
jacint@836: }
jacint@836:
jacint@836: //the starting flow
alpar@1222: for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e) {
alpar@1222: Num rem=(*_capacity)[e]-(*_flow)[e];
jacint@2024: if ( !_surely.positive(rem) ) continue;
alpar@1222: Node w=_g->target(e);
alpar@1222: if ( level[w] < _node_num ) {
jacint@2024: if ( !_surely.positive(excess[w]) && w!=_target ) { //putting into the stack
jacint@836: next.set(w,first[level[w]]);
jacint@836: first[level[w]]=w;
jacint@836: }
alpar@1222: _flow->set(e, (*_capacity)[e]);
jacint@836: excess.set(w, excess[w]+rem);
jacint@836: }
jacint@836: }
jacint@836:
alpar@1222: for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) {
jacint@2024: if ( !_surely.positive((*_flow)[e]) ) continue;
alpar@1222: Node w=_g->source(e);
alpar@1222: if ( level[w] < _node_num ) {
jacint@2024: if ( !_surely.positive(excess[w]) && w!=_target ) {
jacint@836: next.set(w,first[level[w]]);
jacint@836: first[level[w]]=w;
jacint@836: }
alpar@1222: excess.set(w, excess[w]+(*_flow)[e]);
alpar@1222: _flow->set(e, 0);
jacint@836: }
jacint@836: }
jacint@836: break;
jacint@836:
jacint@836: case PRE_FLOW:
jacint@836: //the starting flow
alpar@1222: for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
alpar@1222: Num rem=(*_capacity)[e]-(*_flow)[e];
jacint@2024: if ( !_surely.positive(rem) ) continue;
alpar@1222: Node w=_g->target(e);
alpar@1222: if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]);
jacint@836: }
jacint@836:
alpar@1222: for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
jacint@2024: if ( !_surely.positive((*_flow)[e]) ) continue;
alpar@1222: Node w=_g->source(e);
alpar@1222: if ( level[w] < _node_num ) _flow->set(e, 0);
jacint@836: }
jacint@836:
jacint@836: //computing the excess
alpar@1222: for(NodeIt w(*_g); w!=INVALID; ++w) {
jacint@836: Num exc=0;
alpar@1222: for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e];
alpar@1222: for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e];
jacint@836: excess.set(w,exc);
jacint@836:
jacint@836: //putting the active nodes into the stack
jacint@836: int lev=level[w];
jacint@2024: if ( _surely.positive(exc) && lev < _node_num && Node(w) != _target ) {
jacint@836: next.set(w,first[lev]);
jacint@836: first[lev]=w;
jacint@836: }
jacint@836: }
jacint@836: break;
jacint@836: } //switch
jacint@836: } //preflowPreproc
jacint@836:
jacint@836:
jacint@836: void relabel(Node w, int newlevel, VecNode& first, NNMap& next,
jacint@836: VecNode& level_list, NNMap& left,
jacint@836: NNMap& right, int& b, int& k, bool what_heur )
jacint@836: {
jacint@836:
jacint@836: int lev=level[w];
jacint@836:
jacint@836: Node right_n=right[w];
jacint@836: Node left_n=left[w];
jacint@836:
jacint@836: //unlacing starts
jacint@836: if ( right_n!=INVALID ) {
jacint@836: if ( left_n!=INVALID ) {
jacint@836: right.set(left_n, right_n);
jacint@836: left.set(right_n, left_n);
jacint@836: } else {
jacint@836: level_list[lev]=right_n;
jacint@836: left.set(right_n, INVALID);
jacint@836: }
jacint@836: } else {
jacint@836: if ( left_n!=INVALID ) {
jacint@836: right.set(left_n, INVALID);
jacint@836: } else {
jacint@836: level_list[lev]=INVALID;
jacint@836: }
jacint@836: }
jacint@836: //unlacing ends
jacint@836:
jacint@836: if ( level_list[lev]==INVALID ) {
jacint@836:
jacint@836: //gapping starts
jacint@836: for (int i=lev; i!=k ; ) {
jacint@836: Node v=level_list[++i];
jacint@836: while ( v!=INVALID ) {
alpar@1222: level.set(v,_node_num);
jacint@836: v=right[v];
jacint@836: }
jacint@836: level_list[i]=INVALID;
jacint@836: if ( !what_heur ) first[i]=INVALID;
jacint@836: }
jacint@836:
alpar@1222: level.set(w,_node_num);
jacint@836: b=lev-1;
jacint@836: k=b;
jacint@836: //gapping ends
jacint@836:
jacint@836: } else {
jacint@836:
alpar@1222: if ( newlevel == _node_num ) level.set(w,_node_num);
jacint@836: else {
jacint@836: level.set(w,++newlevel);
jacint@836: next.set(w,first[newlevel]);
jacint@836: first[newlevel]=w;
jacint@836: if ( what_heur ) b=newlevel;
jacint@836: if ( k < newlevel ) ++k; //now k=newlevel
jacint@836: Node z=level_list[newlevel];
jacint@836: if ( z!=INVALID ) left.set(z,w);
jacint@836: right.set(w,z);
jacint@836: left.set(w,INVALID);
jacint@836: level_list[newlevel]=w;
jacint@836: }
jacint@836: }
jacint@836: } //relabel
jacint@836:
jacint@836: };
alpar@1227:
deba@1792: ///\ingroup flowalgs
deba@1792: ///\brief Function type interface for Preflow algorithm.
deba@1792: ///
alpar@1227: ///Function type interface for Preflow algorithm.
alpar@1227: ///\sa Preflow
alpar@1227: template<class GR, class CM, class FM>
alpar@1227: Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g,
alpar@1227: typename GR::Node source,
alpar@1227: typename GR::Node target,
alpar@1227: const CM &cap,
alpar@1227: FM &flow
alpar@1227: )
alpar@1227: {
alpar@1227: return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow);
alpar@1227: }
alpar@1227:
alpar@921: } //namespace lemon
jacint@836:
alpar@921: #endif //LEMON_PREFLOW_H