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hw6 - CSE 413 Analysis of Algorithms Fall Semester 2004...

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CSE 413, Analysis of Algorithms Fall Semester, 2004 Assignment 6: Graph Algorithms I Due Date : Nov. 12, 2004 (at the beginning of CSE 413 class) Note : We assume that all input graphs are based on the adjacency list representation (see page 84 of Manber’s book for the adjacency list representation of graphs). 1. Let G =( V,E ) be an undirected graph of n vertices and m edges, such that every edge e of E has a weight w ( e ) 0( w ( e ) is a real number). For any input integer k> 0 and two vertices s and t of G ,a k -edge shortest path in G is de±ned as follows: It is an s -to- t path in G that consists of no more than k edges and that has the minimum total sum of edge weights among all possible s -to- t paths in G with no more than k edges. Design an O ( k ( m + n )) time algorithm based on the dynamic programming technique for computing a k -edge shortest path in G . ( 20 points ) 2. Recall the Hamiltonian cycle problem in Assignment 1 of this class. In this problem, you are asked to solve the
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