/* preflow_push_max_flow_hh by jacint. Runs a preflow push algorithm with the modification, that we do not push on nodes with level at least n. Moreover, if a level gets empty, we put all nodes above that level to level n. Hence, in the end, we arrive at a maximum preflow with value of a max flow value. An empty level gives a minimum cut. 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 node_property_vector mincut(): returns a characteristic vector of a minimum cut. */ #ifndef PREFLOW_PUSH_MAX_FLOW_HH #define PREFLOW_PUSH_MAX_FLOW_HH #include #include #include #include #include #include #include namespace marci { template class preflow_push_max_flow { typedef typename graph_traits::node_iterator node_iterator; typedef typename graph_traits::each_node_iterator each_node_iterator; typedef typename graph_traits::out_edge_iterator out_edge_iterator; typedef typename graph_traits::in_edge_iterator in_edge_iterator; graph_type& G; node_iterator s; node_iterator t; edge_property_vector& capacity; T value; node_property_vector mincutvector; public: preflow_push_max_flow(graph_type& _G, node_iterator _s, node_iterator _t, edge_property_vector& _capacity) : G(_G), s(_s), t(_t), capacity(_capacity), mincutvector(_G, false) { } /* The run() function runs a modified version of the highest label preflow-push, which only finds a maximum preflow, hence giving the value of a maximum flow. */ void run() { edge_property_vector flow(G, 0); //the flow value, 0 everywhere node_property_vector level(G); //level of node node_property_vector excess(G); //excess of node int n=number_of(G.first_node()); //number of nodes int b=n-2; /*b is a bound on the highest level of an active node. In the beginning it is at most n-2.*/ std::vector numb(n); //The number of nodes on level i < n. std::vector > stack(2*n-1); //Stack of the active nodes in level i. /*Reverse_bfs from t, to find the starting level.*/ reverse_bfs bfs(G, t); bfs.run(); for(each_node_iterator v=G.first_node(); v.valid(); ++v) { int dist=bfs.dist(v); level.put(v, dist); ++numb[dist]; } /*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.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 an 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.valid(); ++e) { node_iterator v=G.head(e); /*e is the edge wv.*/ 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 << 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)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.*/ flow.put(e,0); excess.put(v, excess.get(v)+flow.get(e)); excess.put(w, excess.get(w)-flow.get(e)); //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);} //std::cout << "Leveldecrease of node " << w << " to " << newlevel << std::endl; } //if (flow.get(e)>0) } //for in-edge /* Relabel */ if (excess.get(w)>0) { /*Now newlevel <= n*/ int l=level.get(w); //l is the old level of w. --numb[l]; if (newlevel == n) { level.put(w,n); } else { if (numb[l]) { /*If the level of w remains nonempty.*/ level.put(w,++newlevel); ++numb[newlevel]; stack[newlevel].push(w); b=newlevel; } else { /*If the level of w gets empty.*/ for (each_node_iterator v=G.first_node() ; v.valid() ; ++v) { if (level.get(v) >= l ) { level.put(v,n); } } for (int i=l+1 ; i!=n ; ++i) numb[i]=0; } //if (numb[l]) } // if (newlevel = n) } // if (excess.get(w)>0) } //else } //while(b) value=excess.get(t); /*Max flow value.*/ /* We find an empty level, e. The nodes above this level give a minimum cut. */ int e=1; while(e) { if(numb[e]) ++e; else break; } for (each_node_iterator v=G.first_node(); v.valid(); ++v) { if (level.get(v) > e) mincutvector.put(v, true); } } // void run() /* Returns the maximum value of a flow. */ T maxflow() { return value; } /* Returns a minimum cut. */ node_property_vector mincut() { return mincutvector; } }; }//namespace marci #endif