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Unformatted text preview: Fall 2011 CMSC 351: Homework 9 Clyde Kruskal Due at the start of class Wednesday, November 16, 2011. Problem 1. The square of a directed graph G = ( V,E ) is the graph G 2 = ( V,E 2 ) such that ( x,y ) ∈ E 2 if and only if for some z ∈ V , both ( x,z ) ∈ E and ( z,y ) ∈ E . That is, G 2 contains an edge between x and y whenever G contains a path with exactly two edges between x and y . (a) Describe an efficient algorithm for computing G 2 from G using the adjacency matrix representation of G . Analyze its efficiency. (b) Describe an efficient algorithm for computing G 2 from G using the adjacency list representation of G . Analyze its efficiency. Problem 2. Assume that a list of vertices represents a directed (not necessarily simple) cycle where the last vertex of the array has an edge to the first vertex. Assume you have two cycles in a (directed) graph G = ( V,E ), represented by two arrays A and B , where the two cyces do not share any edges but do intersect (at at least one...
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This note was uploaded on 01/13/2012 for the course CMSC 351 taught by Professor Staff during the Fall '11 term at University of Louisville.
- Fall '11