# HG changeset patch
# User jacint
# Date 1074633755 0
# Node ID bf088f14b87a35bbd293fc506b1757206d5548af
# Parent 3151a1026db98969f471dbb84f5a59c7e10dfc69
A max flow algorithm
diff -r 3151a1026db9 -r bf088f14b87a src/work/preflow_push_hl.hh
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/work/preflow_push_hl.hh Tue Jan 20 21:22:35 2004 +0000
@@ -0,0 +1,320 @@
+/*
+preflow_push_hl.hh
+by jacint.
+Runs the highest label variant of the preflow push algorithm with
+running time O(n^2\sqrt(m)).
+
+Member functions:
+
+void run() : runs the algorithm
+
+ The following functions should be used after run() was already run.
+
+T maxflow() : returns the value of a maximum flow
+
+T flowonedge(edge_iterator e) : for a fixed maximum flow x it returns x(e)
+
+edge_property_vector<graph_type, T> allflow() : returns the fixed maximum flow x
+
+node_property_vector<graph_type, bool> mincut() : returns a
+ characteristic vector of a minimum cut. (An empty level
+ in the algorithm gives a minimum cut.)
+*/
+
+#ifndef PREFLOW_PUSH_HL_HH
+#define PREFLOW_PUSH_HL_HH
+
+#include <algorithm>
+#include <vector>
+#include <stack>
+
+#include <marci_graph_traits.hh>
+#include <marci_property_vector.hh>
+#include <reverse_bfs.hh>
+
+namespace marci {
+
+ template <typename graph_type, typename T>
+ class preflow_push_hl {
+
+ typedef typename graph_traits<graph_type>::node_iterator node_iterator;
+ typedef typename graph_traits<graph_type>::edge_iterator edge_iterator;
+ typedef typename graph_traits<graph_type>::each_node_iterator each_node_iterator;
+ typedef typename graph_traits<graph_type>::out_edge_iterator out_edge_iterator;
+ typedef typename graph_traits<graph_type>::in_edge_iterator in_edge_iterator;
+ typedef typename graph_traits<graph_type>::each_edge_iterator each_edge_iterator;
+
+
+ graph_type& G;
+ node_iterator s;
+ node_iterator t;
+ edge_property_vector<graph_type, T> flow;
+ edge_property_vector<graph_type, T>& capacity;
+ T value;
+ node_property_vector<graph_type, bool> mincutvector;
+
+
+ public:
+
+ preflow_push_hl(graph_type& _G, node_iterator _s, node_iterator _t, edge_property_vector<graph_type, T>& _capacity) : G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), mincutvector(_G, true) { }
+
+
+
+
+ /*
+ The run() function runs the highest label preflow-push,
+ running time: O(n^2\sqrt(m))
+ */
+ void run() {
+
+ node_property_vector<graph_type, int> level(G); //level of node
+ node_property_vector<graph_type, T> excess(G); //excess of node
+
+ int n=number_of(G.first_node()); //number of nodes
+ int b=n;
+ /*b is a bound on the highest level of an active node. In the beginning it is at most n-2.*/
+
+ std::vector<std::stack<node_iterator> > stack(2*n-1); //Stack of the active nodes in level i.
+
+
+
+
+ /*Reverse_bfs from t, to find the starting level.*/
+
+ reverse_bfs<list_graph> bfs(G, t);
+ bfs.run();
+ for(each_node_iterator v=G.first_node(); v.is_valid(); ++v) {
+ level.put(v, bfs.dist(v));
+ //std::cout << "the level of " << v << " is " << bfs.dist(v);
+ }
+
+ /*The level of s is fixed to n*/
+ level.put(s,n);
+
+
+
+
+
+ /* Starting flow. It is everywhere 0 at the moment. */
+
+ for(out_edge_iterator i=G.first_out_edge(s); i.is_valid(); ++i)
+ {
+ node_iterator w=G.head(i);
+ flow.put(i, capacity.get(i));
+ stack[bfs.dist(w)].push(w);
+ excess.put(w, capacity.get(i));
+ }
+
+
+ /*
+ End of preprocessing
+ */
+
+
+
+ /*
+ Push/relabel on the highest level active nodes.
+ */
+
+ /*While there exists active node.*/
+ while (b) {
+
+ /*We decrease the bound if there is no active node of level b.*/
+ if (stack[b].empty()) {
+ --b;
+ } else {
+
+ node_iterator w=stack[b].top(); //w is the highest label active node.
+ stack[b].pop(); //We delete w from the stack.
+
+ int newlevel=2*n-2; //In newlevel we maintain the next level of w.
+
+ for(out_edge_iterator e=G.first_out_edge(w); e.is_valid(); ++e) {
+ node_iterator v=G.head(e);
+ /*e is the edge wv.*/
+
+ if (flow.get(e)<capacity.get(e)) {
+ /*e is an edge of the residual graph */
+
+ if(level.get(w)==level.get(v)+1) {
+ /*Push is allowed now*/
+
+ if (capacity.get(e)-flow.get(e) > excess.get(w)) {
+ /*A nonsaturating push.*/
+
+ if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
+ /*v becomes active.*/
+
+ flow.put(e, flow.get(e)+excess.get(w));
+ excess.put(v, excess.get(v)+excess.get(w));
+ excess.put(w,0);
+ //std::cout << w << " " << v <<" elore elen nonsat pump " << std::endl;
+ break;
+ } else {
+ /*A saturating push.*/
+
+ if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
+ /*v becomes active.*/
+
+ excess.put(v, excess.get(v)+capacity.get(e)-flow.get(e));
+ excess.put(w, excess.get(w)-capacity.get(e)+flow.get(e));
+ flow.put(e, capacity.get(e));
+ //std::cout << w<<" " <<v<<" elore elen sat pump " << std::endl;
+ if (excess.get(w)==0) break;
+ /*If w is not active any more, then we go on to the next node.*/
+
+ } // if (capacity.get(e)-flow.get(e) > excess.get(w))
+ } // if(level.get(w)==level.get(v)+1)
+
+ else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
+
+ } //if (flow.get(e)<capacity.get(e))
+
+ } //for(out_edge_iterator e=G.first_out_edge(w); e.is_valid(); ++e)
+
+
+
+ for(in_edge_iterator e=G.first_in_edge(w); e.is_valid(); ++e) {
+ node_iterator v=G.tail(e);
+ /*e is the edge vw.*/
+
+ if (excess.get(w)==0) break;
+ /*It may happen, that w became inactive in the first for cycle.*/
+ if(flow.get(e)>0) {
+ /*e is an edge of the residual graph */
+
+ if(level.get(w)==level.get(v)+1) {
+ /*Push is allowed now*/
+
+ if (flow.get(e) > excess.get(w)) {
+ /*A nonsaturating push.*/
+
+ if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
+ /*v becomes active.*/
+
+ flow.put(e, flow.get(e)-excess.get(w));
+ excess.put(v, excess.get(v)+excess.get(w));
+ excess.put(w,0);
+ //std::cout << v << " " << w << " vissza elen nonsat pump " << std::endl;
+ break;
+ } else {
+ /*A saturating push.*/
+
+ if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
+ /*v becomes active.*/
+
+ excess.put(v, excess.get(v)+flow.get(e));
+ excess.put(w, excess.get(w)-flow.get(e));
+ flow.put(e,0);
+ //std::cout << v <<" " << w << " vissza elen sat pump " << std::endl;
+ if (excess.get(w)==0) { break;}
+ } //if (flow.get(e) > excess.get(v))
+ } //if(level.get(w)==level.get(v)+1)
+
+ else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
+
+
+ } //if (flow.get(e)>0)
+
+ } //for
+
+
+ if (excess.get(w)>0) {
+ level.put(w,++newlevel);
+ stack[newlevel].push(w);
+ b=newlevel;
+ //std::cout << "The new level of " << w << " is "<< newlevel <<std::endl;
+ }
+
+
+ } //else
+
+ } //while(b)
+
+ value = excess.get(t);
+ /*Max flow value.*/
+
+
+
+
+ } //void run()
+
+
+
+
+
+ /*
+ Returns the maximum value of a flow.
+ */
+
+ T maxflow() {
+ return value;
+ }
+
+
+
+ /*
+ For the maximum flow x found by the algorithm, it returns the flow value on edge e, i.e. x(e).
+ */
+
+ T flowonedge(edge_iterator e) {
+ return flow.get(e);
+ }
+
+
+
+ /*
+ Returns the maximum flow x found by the algorithm.
+ */
+
+ edge_property_vector<graph_type, T> allflow() {
+ return flow;
+ }
+
+
+
+ /*
+ Returns a minimum cut by using a reverse bfs from t in the residual graph.
+ */
+
+ node_property_vector<graph_type, bool> mincut() {
+
+ std::queue<node_iterator> queue;
+
+ mincutvector.put(t,false);
+ queue.push(t);
+
+ while (!queue.empty()) {
+ node_iterator w=queue.front();
+ queue.pop();
+
+ for(in_edge_iterator e=G.first_in_edge(w) ; e.is_valid(); ++e) {
+ node_iterator v=G.tail(e);
+ if (mincutvector.get(v) && flow.get(e) < capacity.get(e) ) {
+ queue.push(v);
+ mincutvector.put(v, false);
+ }
+ } // for
+
+ for(out_edge_iterator e=G.first_out_edge(w) ; e.is_valid(); ++e) {
+ node_iterator v=G.head(e);
+ if (mincutvector.get(v) && flow.get(e) > 0 ) {
+ queue.push(v);
+ mincutvector.put(v, false);
+ }
+ } // for
+
+ }
+
+ return mincutvector;
+
+ }
+
+
+ };
+}//namespace marci
+#endif
+
+
+
+