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edgedisjoint - CMSC 451 Edge-Disjoint Paths Slides By Carl...

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CMSC 451: Edge-Disjoint Paths Slides By: Carl Kingsford Department of Computer Science University of Maryland, College Park Based on Section 7.6 of Algorithm Design by Kleinberg & Tardos.
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Edge-disjoint Paths Suppose you want to send k large files from s to t but never have two files use the same network link (to avoid congestion on the links). Leads naturally to the Edge-Disjoint Paths problem: k Edge-disjoint Paths Given directed graph G , and two nodes s and t , find k paths from s to t such that no two paths share an edge.
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Again a Reduction! Given an instance of k-Edge-Disjoint Paths , Create an instance of Maximum Network Flow . The maximum flow will used to find the k edge disjoint paths. What is the maximum flow in the graph? Are there k edge-disjoint paths?
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Paths = Flow There is a nice correspondence between paths and flows in unit capacity networks. Suppose we had k edge-disjoint s - t paths. We could sent 1 unit of flow along each path without violating the capacity constraints.
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