Midterm1 - factor 1/4. If you believe that your analysis is...

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CS 7250, Approximation Algorithms Midterm 1 Tue, March 1, 2011 Due NOON , Fri, March 4, 2011 Problem 1 Maximum directed cut is the following problem: Given a directed graph G ( V,E ) with non-negative edge costs, find a subset S V so as to maximize the total cost of edges out of S , i.e., cost( { u v : u S and v ¯ S } ). (a) Give a polynomial time algorithm achieving approximation guarantee factor 1/4. If your algorithm is randomized, then the guarantee factor should be, in expectation. (b) Give a greedy deterministic polynomial time algorithm achieving approximation guarantee
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Unformatted text preview: factor 1/4. If you believe that your analysis is tight, give a tight example. Note: If your answer in part (a) was a greedy deterministic algorithm, then you only need to anwer if and why your analysis is tight. Problem 2 Use the method of conditional expectations to derandomize the 1-1 /e factor algorithm for MAX-SAT in paragraph 16.3, pages 133-135, of Vaziranis book....
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