hbs6bis - (b) Describe and analyze a faster algorithm. 3....

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CS 473 HBS 6.5 Spring 2009 CS 473: Undergraduate Algorithms, Spring 2009 HBS 6.5 1. (a) Describe and analyze and algorithm to find the second smallest spanning tree of a given graph G , that is, the spanning tree of G with smallest total weight except for the minimum spanning tree. ? (b) Describe and analyze an efficient algorithm to compute, given a weighted undirected graph G and an integer k , the k smallest spanning trees of G . 2. A looped tree is a weighted, directed graph built from a binary tree by adding an edge from every leaf back to the root. Every edge has a non-negative weight. 5 8 17 0 1 23 9 14 42 4 16 7 (a) How much time would Dijkstra’s algorithm require to compute the shortest path between two vertices u and v in a looped tree with n nodes?
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Unformatted text preview: (b) Describe and analyze a faster algorithm. 3. Consider a path between two vertices s and t in an undirected weighted graph G . The bottleneck length of this path is the maximum weight of any edge in the path. The bottleneck distance between s and t is the minimum bottleneck length of any path from s to t . (If there are no paths from s to t , the bottleneck distance between s and t is .) s t 1 11 7 12 8 5 10 9 2 3 6 4 The bottleneck distance between s and t is 5. Describe and analyze an algorithm to compute the bottleneck distance between every pair of vertices in an arbitrary undirected weighted graph. Assume that no two edges have the same weight. 1...
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