jacint@109: // -*- C++ -*-
jacint@109: /*
jacint@109: preflow_hl0.h
jacint@109: by jacint.
jacint@109: Heuristics:
jacint@109: 2 phase
jacint@109: gap
jacint@109: list 'level_list' on the nodes on level i implemented by hand
jacint@109: stack 'active' on the active nodes on level i implemented by hand
jacint@109: bound decrease
jacint@109:
jacint@109: The bound decrease heuristic behaves unexpectedly well.
jacint@109:
jacint@109: The constructor runs the algorithm.
jacint@109:
jacint@109: Members:
jacint@109:
jacint@109: T maxFlow() : returns the value of a maximum flow
jacint@109:
jacint@109: T flowOnEdge(EdgeIt e) : for a fixed maximum flow x it returns x(e)
jacint@109:
jacint@109: FlowMap Flow() : returns the fixed maximum flow x
jacint@109:
jacint@109: void minMinCut(CutMap& M) : sets M to the characteristic vector of the
jacint@109: minimum min cut. M should be a map of bools initialized to false.
jacint@109:
jacint@109: void maxMinCut(CutMap& M) : sets M to the characteristic vector of the
jacint@109: maximum min cut. M should be a map of bools initialized to false.
jacint@109:
jacint@109:
jacint@109: void minCut(CutMap& M) : sets M to the characteristic vector of
jacint@109: a min cut. M should be a map of bools initialized to false.
jacint@109:
jacint@109: */
jacint@109:
jacint@109: #ifndef PREFLOW_HL0_H
jacint@109: #define PREFLOW_HL0_H
jacint@109:
jacint@109: #include <vector>
jacint@109: #include <queue>
jacint@109:
jacint@109: #include <time_measure.h> //for test
jacint@109:
jacint@109: namespace hugo {
jacint@109:
jacint@109: template <typename Graph, typename T,
jacint@109: typename FlowMap=typename Graph::EdgeMap<T>,
jacint@109: typename CapMap=typename Graph::EdgeMap<T> >
jacint@109: class preflow_hl0 {
jacint@109:
jacint@109: typedef typename Graph::NodeIt NodeIt;
jacint@109: typedef typename Graph::EdgeIt EdgeIt;
jacint@109: typedef typename Graph::EachNodeIt EachNodeIt;
jacint@109: typedef typename Graph::OutEdgeIt OutEdgeIt;
jacint@109: typedef typename Graph::InEdgeIt InEdgeIt;
jacint@109:
jacint@109: Graph& G;
jacint@109: NodeIt s;
jacint@109: NodeIt t;
jacint@109: FlowMap flow;
jacint@109: CapMap& capacity;
jacint@109: T value;
jacint@109:
jacint@109: public:
jacint@109: double time;
jacint@109:
jacint@109: preflow_hl0(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity ) :
jacint@109: G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity) {
jacint@109:
jacint@109: bool phase=0; //phase 0 is the 1st phase, phase 1 is the 2nd
jacint@109: int n=G.nodeNum();
jacint@109: bool end=false;
jacint@109: /*
jacint@109: 'true' means no active nodes are above bound b.
jacint@109: */
jacint@109: int k=n-2; //bound on the highest level under n containing a node
jacint@109: int b=k; //bound on the highest level under n of an active node
jacint@109: /*
jacint@109: b is a bound on the highest level of the stack.
jacint@109: k is a bound on the highest nonempty level i < n.
jacint@109: */
jacint@109:
jacint@109: typename Graph::NodeMap<int> level(G,n);
jacint@109: typename Graph::NodeMap<T> excess(G);
jacint@109:
jacint@109: std::vector<NodeIt> active(n);
jacint@109: typename Graph::NodeMap<NodeIt> next(G);
jacint@109: //Stack of the active nodes in level i < n.
jacint@109: //We use it in both phases.
jacint@109:
jacint@109: typename Graph::NodeMap<NodeIt> left(G);
jacint@109: typename Graph::NodeMap<NodeIt> right(G);
jacint@109: std::vector<NodeIt> level_list(n);
jacint@109: /*
jacint@109: List of the nodes in level i<n.
jacint@109: */
jacint@109:
jacint@109: /*Reverse_bfs from t, to find the starting level.*/
jacint@109: level.set(t,0);
jacint@109: std::queue<NodeIt> bfs_queue;
jacint@109: bfs_queue.push(t);
jacint@109:
jacint@109: while (!bfs_queue.empty()) {
jacint@109:
jacint@109: NodeIt v=bfs_queue.front();
jacint@109: bfs_queue.pop();
jacint@109: int l=level.get(v)+1;
jacint@109:
jacint@109: for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) {
jacint@109: NodeIt w=G.tail(e);
jacint@109: if ( level.get(w) == n && w != s ) {
jacint@109: bfs_queue.push(w);
jacint@109: NodeIt first=level_list[l];
jacint@109: if ( first != 0 ) left.set(first,w);
jacint@109: right.set(w,first);
jacint@109: level_list[l]=w;
jacint@109: level.set(w, l);
jacint@109: }
jacint@109: }
jacint@109: }
jacint@109:
jacint@109: level.set(s,n);
jacint@109:
jacint@109:
jacint@109: /* Starting flow. It is everywhere 0 at the moment. */
jacint@109: for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e)
jacint@109: {
jacint@109: T c=capacity.get(e);
jacint@109: if ( c == 0 ) continue;
jacint@109: NodeIt w=G.head(e);
jacint@109: if ( level.get(w) < n ) {
jacint@109: if ( excess.get(w) == 0 && w!=t ) {
jacint@109: next.set(w,active[level.get(w)]);
jacint@109: active[level.get(w)]=w;
jacint@109: }
jacint@109: flow.set(e, c);
jacint@109: excess.set(w, excess.get(w)+c);
jacint@109: }
jacint@109: }
jacint@109:
jacint@109: /*
jacint@109: End of preprocessing
jacint@109: */
jacint@109:
jacint@109:
jacint@109:
jacint@109: /*
jacint@109: Push/relabel on the highest level active nodes.
jacint@109: */
jacint@109: while ( true ) {
jacint@109:
jacint@109: if ( b == 0 ) {
jacint@109: if ( phase ) break;
jacint@109:
jacint@109: if ( !end && k > 0 ) {
jacint@109: b=k;
jacint@109: end=true;
jacint@109: } else {
jacint@109: phase=1;
jacint@109: time=currTime();
jacint@109: level.set(s,0);
jacint@109: std::queue<NodeIt> bfs_queue;
jacint@109: bfs_queue.push(s);
jacint@109:
jacint@109: while (!bfs_queue.empty()) {
jacint@109:
jacint@109: NodeIt v=bfs_queue.front();
jacint@109: bfs_queue.pop();
jacint@109: int l=level.get(v)+1;
jacint@109:
jacint@109: for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) {
jacint@109: if ( capacity.get(e) == flow.get(e) ) continue;
jacint@109: NodeIt u=G.tail(e);
jacint@109: if ( level.get(u) >= n ) {
jacint@109: bfs_queue.push(u);
jacint@109: level.set(u, l);
jacint@109: if ( excess.get(u) > 0 ) {
jacint@109: next.set(u,active[l]);
jacint@109: active[l]=u;
jacint@109: }
jacint@109: }
jacint@109: }
jacint@109:
jacint@109: for(OutEdgeIt e=G.template first<OutEdgeIt>(v); e.valid(); ++e) {
jacint@109: if ( 0 == flow.get(e) ) continue;
jacint@109: NodeIt u=G.head(e);
jacint@109: if ( level.get(u) >= n ) {
jacint@109: bfs_queue.push(u);
jacint@109: level.set(u, l);
jacint@109: if ( excess.get(u) > 0 ) {
jacint@109: next.set(u,active[l]);
jacint@109: active[l]=u;
jacint@109: }
jacint@109: }
jacint@109: }
jacint@109: }
jacint@109: b=n-2;
jacint@109: }
jacint@109:
jacint@109: }
jacint@109:
jacint@109:
jacint@109: if ( active[b] == 0 ) --b;
jacint@109: else {
jacint@109: end=false;
jacint@109:
jacint@109: NodeIt w=active[b];
jacint@109: active[b]=next.get(w);
jacint@109: int lev=level.get(w);
jacint@109: T exc=excess.get(w);
jacint@109: int newlevel=n; //bound on the next level of w
jacint@109:
jacint@109: for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) {
jacint@109:
jacint@109: if ( flow.get(e) == capacity.get(e) ) continue;
jacint@109: NodeIt v=G.head(e);
jacint@109: //e=wv
jacint@109:
jacint@109: if( lev > level.get(v) ) {
jacint@109: /*Push is allowed now*/
jacint@109:
jacint@109: if ( excess.get(v)==0 && v!=t && v!=s ) {
jacint@109: int lev_v=level.get(v);
jacint@109: next.set(v,active[lev_v]);
jacint@109: active[lev_v]=v;
jacint@109: }
jacint@109:
jacint@109: T cap=capacity.get(e);
jacint@109: T flo=flow.get(e);
jacint@109: T remcap=cap-flo;
jacint@109:
jacint@109: if ( remcap >= exc ) {
jacint@109: /*A nonsaturating push.*/
jacint@109:
jacint@109: flow.set(e, flo+exc);
jacint@109: excess.set(v, excess.get(v)+exc);
jacint@109: exc=0;
jacint@109: break;
jacint@109:
jacint@109: } else {
jacint@109: /*A saturating push.*/
jacint@109:
jacint@109: flow.set(e, cap);
jacint@109: excess.set(v, excess.get(v)+remcap);
jacint@109: exc-=remcap;
jacint@109: }
jacint@109: } else if ( newlevel > level.get(v) ){
jacint@109: newlevel = level.get(v);
jacint@109: }
jacint@109:
jacint@109: } //for out edges wv
jacint@109:
jacint@109:
jacint@109: if ( exc > 0 ) {
jacint@109: for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) {
jacint@109:
jacint@109: if( flow.get(e) == 0 ) continue;
jacint@109: NodeIt v=G.tail(e);
jacint@109: //e=vw
jacint@109:
jacint@109: if( lev > level.get(v) ) {
jacint@109: /*Push is allowed now*/
jacint@109:
jacint@109: if ( excess.get(v)==0 && v!=t && v!=s ) {
jacint@109: int lev_v=level.get(v);
jacint@109: next.set(v,active[lev_v]);
jacint@109: active[lev_v]=v;
jacint@109: }
jacint@109:
jacint@109: T flo=flow.get(e);
jacint@109:
jacint@109: if ( flo >= exc ) {
jacint@109: /*A nonsaturating push.*/
jacint@109:
jacint@109: flow.set(e, flo-exc);
jacint@109: excess.set(v, excess.get(v)+exc);
jacint@109: exc=0;
jacint@109: break;
jacint@109: } else {
jacint@109: /*A saturating push.*/
jacint@109:
jacint@109: excess.set(v, excess.get(v)+flo);
jacint@109: exc-=flo;
jacint@109: flow.set(e,0);
jacint@109: }
jacint@109: } else if ( newlevel > level.get(v) ) {
jacint@109: newlevel = level.get(v);
jacint@109: }
jacint@109: } //for in edges vw
jacint@109:
jacint@109: } // if w still has excess after the out edge for cycle
jacint@109:
jacint@109: excess.set(w, exc);
jacint@109:
jacint@109: /*
jacint@109: Relabel
jacint@109: */
jacint@109:
jacint@109:
jacint@109: if ( exc > 0 ) {
jacint@109: //now 'lev' is the old level of w
jacint@109:
jacint@109: if ( phase ) {
jacint@109: level.set(w,++newlevel);
jacint@109: next.set(w,active[newlevel]);
jacint@109: active[newlevel]=w;
jacint@109: b=newlevel;
jacint@109: } else {
jacint@109: //unlacing starts
jacint@109: NodeIt right_n=right.get(w);
jacint@109: NodeIt left_n=left.get(w);
jacint@109:
jacint@109: if ( right_n != 0 ) {
jacint@109: if ( left_n != 0 ) {
jacint@109: right.set(left_n, right_n);
jacint@109: left.set(right_n, left_n);
jacint@109: } else {
jacint@109: level_list[lev]=right_n;
jacint@109: left.set(right_n, 0);
jacint@109: }
jacint@109: } else {
jacint@109: if ( left_n != 0 ) {
jacint@109: right.set(left_n, 0);
jacint@109: } else {
jacint@109: level_list[lev]=0;
jacint@109:
jacint@109: }
jacint@109: }
jacint@109: //unlacing ends
jacint@109:
jacint@109: //gapping starts
jacint@109: if ( level_list[lev]==0 ) {
jacint@109:
jacint@109: for (int i=lev; i!=k ; ) {
jacint@109: NodeIt v=level_list[++i];
jacint@109: while ( v != 0 ) {
jacint@109: level.set(v,n);
jacint@109: v=right.get(v);
jacint@109: }
jacint@109: level_list[i]=0;
jacint@109: active[i]=0;
jacint@109: }
jacint@109:
jacint@109: level.set(w,n);
jacint@109: b=lev-1;
jacint@109: k=b;
jacint@109: //gapping ends
jacint@109: } else {
jacint@109:
jacint@109: if ( newlevel == n ) level.set(w,n);
jacint@109: else {
jacint@109: level.set(w,++newlevel);
jacint@109: next.set(w,active[newlevel]);
jacint@109: active[newlevel]=w;
jacint@109: if ( k < newlevel ) ++k;
jacint@109: NodeIt first=level_list[newlevel];
jacint@109: if ( first != 0 ) left.set(first,w);
jacint@109: right.set(w,first);
jacint@109: left.set(w,0);
jacint@109: level_list[newlevel]=w;
jacint@109: }
jacint@109: }
jacint@109:
jacint@109:
jacint@109: } //phase 0
jacint@109:
jacint@109:
jacint@109: } // if ( exc > 0 )
jacint@109:
jacint@109:
jacint@109: } // if stack[b] is nonempty
jacint@109:
jacint@109: } // while(true)
jacint@109:
jacint@109:
jacint@109: value = excess.get(t);
jacint@109: /*Max flow value.*/
jacint@109:
jacint@109: } //void run()
jacint@109:
jacint@109:
jacint@109:
jacint@109:
jacint@109:
jacint@109: /*
jacint@109: Returns the maximum value of a flow.
jacint@109: */
jacint@109:
jacint@109: T maxFlow() {
jacint@109: return value;
jacint@109: }
jacint@109:
jacint@109:
jacint@109:
jacint@109: /*
jacint@109: For the maximum flow x found by the algorithm,
jacint@109: it returns the flow value on edge e, i.e. x(e).
jacint@109: */
jacint@109:
jacint@109: T flowOnEdge(EdgeIt e) {
jacint@109: return flow.get(e);
jacint@109: }
jacint@109:
jacint@109:
jacint@109:
jacint@109: FlowMap Flow() {
jacint@109: return flow;
jacint@109: }
jacint@109:
jacint@109:
jacint@109:
jacint@109: void Flow(FlowMap& _flow ) {
jacint@109: for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v)
jacint@109: _flow.set(v,flow.get(v));
jacint@109: }
jacint@109:
jacint@109:
jacint@109:
jacint@109: /*
jacint@109: Returns the minimum min cut, by a bfs from s in the residual graph.
jacint@109: */
jacint@109:
jacint@109: template<typename _CutMap>
jacint@109: void minMinCut(_CutMap& M) {
jacint@109:
jacint@109: std::queue<NodeIt> queue;
jacint@109:
jacint@109: M.set(s,true);
jacint@109: queue.push(s);
jacint@109:
jacint@109: while (!queue.empty()) {
jacint@109: NodeIt w=queue.front();
jacint@109: queue.pop();
jacint@109:
jacint@109: for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) {
jacint@109: NodeIt v=G.head(e);
jacint@109: if (!M.get(v) && flow.get(e) < capacity.get(e) ) {
jacint@109: queue.push(v);
jacint@109: M.set(v, true);
jacint@109: }
jacint@109: }
jacint@109:
jacint@109: for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) {
jacint@109: NodeIt v=G.tail(e);
jacint@109: if (!M.get(v) && flow.get(e) > 0 ) {
jacint@109: queue.push(v);
jacint@109: M.set(v, true);
jacint@109: }
jacint@109: }
jacint@109: }
jacint@109: }
jacint@109:
jacint@109:
jacint@109:
jacint@109: /*
jacint@109: Returns the maximum min cut, by a reverse bfs
jacint@109: from t in the residual graph.
jacint@109: */
jacint@109:
jacint@109: template<typename _CutMap>
jacint@109: void maxMinCut(_CutMap& M) {
jacint@109:
jacint@109: std::queue<NodeIt> queue;
jacint@109:
jacint@109: M.set(t,true);
jacint@109: queue.push(t);
jacint@109:
jacint@109: while (!queue.empty()) {
jacint@109: NodeIt w=queue.front();
jacint@109: queue.pop();
jacint@109:
jacint@109: for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) {
jacint@109: NodeIt v=G.tail(e);
jacint@109: if (!M.get(v) && flow.get(e) < capacity.get(e) ) {
jacint@109: queue.push(v);
jacint@109: M.set(v, true);
jacint@109: }
jacint@109: }
jacint@109:
jacint@109: for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) {
jacint@109: NodeIt v=G.head(e);
jacint@109: if (!M.get(v) && flow.get(e) > 0 ) {
jacint@109: queue.push(v);
jacint@109: M.set(v, true);
jacint@109: }
jacint@109: }
jacint@109: }
jacint@109:
jacint@109: for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) {
jacint@109: M.set(v, !M.get(v));
jacint@109: }
jacint@109:
jacint@109: }
jacint@109:
jacint@109:
jacint@109:
jacint@109: template<typename _CutMap>
jacint@109: void minCut(_CutMap& M) {
jacint@109: minMinCut(M);
jacint@109: }
jacint@109:
jacint@109: };
jacint@109: }//namespace marci
jacint@109: #endif
jacint@109:
jacint@109:
jacint@109:
jacint@109: