We investigate the time-complexity of the All-Pairs Max-Flow problem: Given a graph with n n n nodes and m m m edges, compute for all pairs of nodes the maximum-flow value between them. If Max-Flow (the version with a given source-sink pair s,t s,t ) can be solved in time T...
We study the problem of computing the vitality of edges and vertices with respect to the st-max flow in undirected planar graphs, where the vitality of an edge/vertex is the s/-max flow decrease when the edge/vertex is removed from the graph. This allows us to establish the vulnerability...
Example:mf = maxflow(G,1,10) Data Types:double|char|string algorithm—Maximum flow algorithm 'searchtrees'(default) |'augmentpath'|'pushrelabel' Maximum flow algorithm, specified as one of the entries in the table. Note You can only specify nondefaultalgorithmoptions with a directed graph. ...
In this paper, we describe the recent work by Orlin[1] which gives a strongly-polynomial O(nm)-time algorithm for max flow, where m is the number of edges in our graph and n is the number of nodes. This is the best asymptotic running time that has been attained for the max-flow ...
There are several versions of Menger's Theorem, all can be derived from the Max-Flow-Min-Cut Theorem. Undirected, Vertex Version. LetGbe an undirected graph, and letuandvbe nonadjacent vertices inG. Then, the maximum number of pairwise-internally-disjoint(u,v)-paths inGequals the minimum nu...
Improved Minimum Cuts and Maximum Flows in Undirected Planar Graphs In this paper we study minimum cut and maximum flow problems on planar graphs, both in static and in dynamic settings. First, we present an algorithm that ... GF Italiano,P Sankowski 被引量: 13发表: 2010年 Faster Maxflow ...
mincut_maxflow
(graph[vq][i] && parent[i]==-1) queue[tail++]=i; parent[i]=vq; if(i==t){ found=true; break; } } } return found; } void maxflow(){ int vj,min; fTotal=0; while(reachable(s,t)){ //Gets the minimum possible capacity in edges of the path s to t min=graph[parent[t]...
The max-flow min-cut theorem of Ford and Fulkerson (for undirected networks) may be regarded as a statement about the circuits and cocircuits using some fixed element of the cycle matroid of a graph. We show that, in general, a matroid has this property (in the integer form) if and on...
rGraph[u][v]=graph[u][v]; } intparent[V]; while(bfs(rGraph, s, t, parent)) { intpath_flow=65536; for(v=t;v!=s;v=parent[v]) { u=parent[v]; path_flow=min(path_flow, rGraph[u][v]); } for(v=t;v!=s;v=parent[v]) ...