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Homework 4 - W08/CS5592 Homework Four Design and Analysis...

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W08/CS5592 Homework Four Design and Analysis of Algorithms Due: Monday, March 31, 2008, in class There are four 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 tree (or forest) edges: 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 An independent set of a graph G = (V, E) is a subset V’ V of vertices such that each edge in E is incident on at most one vertex in V’. The independent-set problem is to find a maximum-size independent set in G. This is a difficult problem for general graph G. We will discuss in Chapter 34. However it is not difficult if G is a tree.
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