The MIN SET COVER problem can be solved using the greedyapproximation algorithm described in the textbook (section 35.3)and in the slides. Apply this algorithm to the following instance ofMIN SET COVER:U = {1, 2, 3, …, 8}Collection of subsets:A = {1, 2, 3}B = {2, 3, 4, 5}C = {4, 5, 6}D = {3, 5, 7}E = {7, 8}1. Give a trace of the algorithm on this instance. Note that the algorithm does not specify exactlyhow to break a tie when the numbers of uncovered elements are equal. In the case of morethan
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Show that for any integer n that is a power of 2, there is an instance of the set cover problem (Section 5.4) with the following properties: i. There are n elements in the base set. ii. The optimal cover uses just two sets. iii. The greedy algorithm picks at least logn sets. Thus the approximation ratio we derived in the chapter is tight. | Numerade
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