# Homework 4 - W07/CS592 Homework Four Design and Analysis of...

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W07/CS592 Homework Four Design and Analysis of Algorithms Due: Mar. 20, 2007 There are 5 problems 1 (a) Conduct a DFS for the following graph. Please label each vertex u with the discovery time and the finish time d ( u )/ f ( u ). You should start the traversal from vertex a , and follow the alphabetic order whenever you need to make choices. p e f h a s d g b c k m j (b) List all edges that belong to each of the following sets: The set of back edges: The set of forward edges: The set of cross edges: (c) Identify the strongly connected components and draw the component graph. 1

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2 (a) Given a graph G( V , E ), where every edge has the same weight w (> 0), and two vertices u and v in V , design an O(| V | + | E |) algorithm that finds a shortest path from u to v . (b) Suppose the edge weights are not the same, but have only two possible values. Some edges have weight w (> 0) and the other edges have weight 2 w . Repeat the problem (a). 3
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## This note was uploaded on 04/12/2008 for the course CS 592 taught by Professor Shen during the Winter '05 term at University of Missouri-Kansas City .

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Homework 4 - W07/CS592 Homework Four Design and Analysis of...

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