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Unformatted text preview: CSIS 0250B Design and Analysis of Algorithms Assignment 4 Sampled Solution 1. As matching M of G with n- 1 edges are given, we have 1 vertex on each side of the bipartite graph that are not matched. We construct a directed graph G from G . For each edge e ( u,v ) ∈ E- M , we create a directed edge e ( u,v ) on G . For each edge e ( u,v ) ∈ M , we create a directed edge e ( v,u ). WLOG, let the unmatched vertex on the left hand side be s and the one on the right hand side be t . We apply BFS/DFS on G starting with the vertex s and find a path from s to t . If such path exists, we conclude that there exists a perfect matching; otherwise we conclude there does not exist one. Correctness We try to augment the matching like the Maximum Flow Algo- rithm does. The G is in fact a reconstruct of the residual network we would use to solve the bipartite problem on G . If there exists a perfect matching, we should be able to find an augmenting path that increases the current flow by 1, i.e. thebe able to find an augmenting path that increases the current flow by 1, i....
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This note was uploaded on 03/01/2010 for the course CS 1234 taught by Professor Chan during the Spring '10 term at University of the Bío-Bío.
- Spring '10