maxFlow-capacityex

# maxFlow-capacityex - Engineering Exercises 1 Describe(in...

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Engineering Exercises 2. How would you modify your algorithm in the last 1. Describe (in words) an algorithm for finding k edge- disjoint paths joining a given pair of vertices in a problem to find a set of k vertex-disjoint paths (a set of paths is vertex-disjoint if no vertex appears on more than one path – excepting the initial and final vertices in the path). directed graph. (A set of paths is edge-disjoint if no edge appears in both paths). Let s and t be the given pair of vertices. Treat the graph as a flow network with all edges having capacity 1 Now find We can use the same approach to find vertex-disjoint paths. We first must create a new graph having vertices u 1 , u 2 for each vertex u in the original graph. For each pair u 1 , u 2 , we include an edge (u 1 ,u 2 ) and for each edge (u v) in the original graph we add an edge (u v ) in the a flow network with all edges having capacity 1. Now find a maximum flow in the graph from s to t. If the capacity of

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