ford-fulkerson | 易学教程

What is node-disjoint paths?

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问题 I need explanation about what exactly node-disjoint paths? and How to determine maximum number of node-disjoint path between two nodes Source(s) and Sink(t) in a directed graph. Can anyone explain with graphically. 回答1: A path is sequence of vertices: s, v_1, .., v_m, t . Two paths s, v_1, .., v_m, t and s, u_1, ..., u_k, t are called node-disjoint if v_i != u_j for any valid i and j . We can reduce this problem to finding the maximum number of edge-disjoint paths by splitting each vertex

Update Maximum Flow After Adding an Edge

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问题 Consider we have a network flow and using Edmond-Karp algorithm, we already have the maximum flow on the network. Now, if we add an arbitrary edge (with certain capacity) to the network, what is the best way to update the maximum flow? I was thinking about updating the residual network regarding the new edge and again look for augmenting path until we find new max flow, but I am not sure if it works or if it is the best way! 回答1: After doing maxflow you know the amount of content each edge

Update Maximum Flow After Adding an Edge

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Consider we have a network flow and using Edmond-Karp algorithm, we already have the maximum flow on the network. Now, if we add an arbitrary edge (with certain capacity) to the network, what is the best way to update the maximum flow? I was thinking about updating the residual network regarding the new edge and again look for augmenting path until we find new max flow, but I am not sure if it works or if it is the best way! After doing maxflow you know the amount of content each edge flowed. So, when the cost of an edge changed you can do the following things : Suppose, the content flowed by

Maximum flow - Ford-Fulkerson: Undirected graph

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问题 I am trying to solve the maxium flow problem for a graph using Ford–Fulkerson algorithm. The algorithm is only described with a directed graph. What about when the graph is undirected? What I have done to mimic an undirected graph is to use two directed edges between a pair of vertices. What confuses me is: Should each of these edges then have a residual edge or is the "opposite" directed edge the residual edge? I have assumed the last but my algorithm seems to go in an infinite loop. I hope

Maximum flow - Ford-Fulkerson: Undirected graph

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I am trying to solve the maxium flow problem for a graph using Ford–Fulkerson algorithm. The algorithm is only described with a directed graph. What about when the graph is undirected? What I have done to mimic an undirected graph is to use two directed edges between a pair of vertices. What confuses me is: Should each of these edges then have a residual edge or is the "opposite" directed edge the residual edge? I have assumed the last but my algorithm seems to go in an infinite loop. I hope any of you can give me some help. Below is my own implementation. I am using DFS in find. import sys