# hw3(6) - CS 473G Combinatorial Algorithms Fall 2005...

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CS 473G: Combinatorial Algorithms, Fall 2005 Homework 3 Due Tuesday, October 18, 2005, at midnight Name: Net ID: Alias: Name: Net ID: Alias: Name: Net ID: Alias: Starting with Homework 1, homeworks may be done in teams of up to three people. Each team turns in just one solution, and every member of a team gets the same grade. Neatly print your name(s), NetID(s), and the alias(es) you used for Homework 0 in the boxes above. Staple this sheet to the top of your homework. 1. Consider the following greedy approximation algorithm to ﬁnd a vertex cover in a graph: GreedyVertexCover ( G ): C while G has at least one edge v vertex in G with maximum degree G G \ v C C v return C In class we proved that the approximation ratio of this algorithm is O (log n ); your task is to prove a matching lower bound. Speciﬁcally, prove that for any integer n , there is a graph G with n vertices such that GreedyVertexCover ( G ) returns a vertex cover that is Ω(log n ) times larger than optimal. 2. Prove that for

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hw3(6) - CS 473G Combinatorial Algorithms Fall 2005...

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