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Unformatted text preview: AMS/MBA 546 (Fall, 2010) Estie Arkin Network Flows: Solution sketch to homework set # 2 1). (Text 13.19) Consider the following reverse greedy algorithm: Sort the edges in decreasing order of their weights w e 1 w e 2 w e m . Let G := G For k = 1 to m do: If G \ e k is connected then set G := G \ e k end Prove that at the termination of this algorithm G is a minimum spanning tree. It is easy to see that at the end of the algorithm, G will be a spanning tree: G must be connected (if the original graph was connected) and can contain no cycles, because the first edge of the cycle that is considered would be removed without destroying connectivity (and all edges get considered in turn). Next, we need to show that the spanning tree is a minimum weight spanning tree. This is easy: Consider any cycle in G , call it C . The edges of C are considered in decreasing order of their weight, therefore the first edge among the edges of the cycle to be considered is the one of max weight, and it will be removed....
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This note was uploaded on 01/31/2011 for the course AMS 546 taught by Professor Arkin,e during the Fall '08 term at SUNY Stony Brook.
- Fall '08