hwsol1.2 - Izaksonas-Smith, Evan Problem 1.2 Approximate...

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Unformatted text preview: Izaksonas-Smith, Evan Problem 1.2 Approximate Cuts Problem The max-cut problem is defined as follows. Given an undirected graph G = ( V,E ), a cut is a set of vertices S V . The weight of the cut is the number of edges that cross between S and V \ S , i.e. wt G ( S ) = | E S ( V \ S ) | . The decision problem max-cut is defined by {h G,k i | G = ( V,E ) S V.wt G ( S ) k } , and the search problem is to find a cut with weight max( G ) = max S V wt G ( S ). It is possible to show that max-cut is NP-hard. This question will explore randomized algorithms for the search problem. A randomized algorithm is one that can make independent, unbiased coin flips. The output of the algorithm on any given input is thus a random variable, and we can perform the usual operations on random variables (computing functions, taking expectations and other moments, and so on) on this output. (If you feel a little rusty on probability theory, you can review the materials in Appendix A.2 of the textbook)in Appendix A....
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hwsol1.2 - Izaksonas-Smith, Evan Problem 1.2 Approximate...

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