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Unformatted text preview: CS180 Winter 2011 Homework 4 Due: February 2 When submitting your homework, please include your name at the top of each page. If you submit multiple pages, please staple them together . We also ask that you do something to indicate which name is your last name on the first page, such as underlining it. Please submit your solutions with the problems solved in the order they are given. 1. Consider the following definitions: A Bottleneck Spanning Tree is a spanning tree T = ( V,E ) built as follows: for any two vertices in G , define the bottleneck path between them to be the maximum cost of an edge traversed; a minimum bottleneck path between two vertices minimizes this value. The bottleneck spanning tree is a spanning tree that, for all vertices u,v V , the minimum bottleneck path is in T . A Lexicographic Spanning Tree is also a spanning tree T = ( V,E ); if we have two Lexicographic Spanning Trees, and want to know which the cheaper is, we look at which has the cheaper most-expensive edge. If these are tied, we check the second most-expensive edge.the cheaper most-expensive edge....
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