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# hwk11 - any pair of nodes in the subset(a WISP is an...

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Fall 2011 CMSC 351: Homework 11 Clyde Kruskal Due at the start of class, Wednesday, December 7, 2011. Problem 1. Indicate, for each pair of expressions ( A,B ) in the table below, whether A is O , o ,Ω, ω , or Θ of B . Your answer should be in the form of the table with ”yes” or ”no” written in each box. A B O o Ω ω Θ a. (lg n ) 4 n b. 2 n n 4 c. n n sin n d. 2 n 2 n/ 2 e. lg( n !) lg( n n ) Problem 2. The WEIGHTED INDEPENDENT SET PROBLEM (WISP) is, given a graph G = ( V,E ) with integer weights on the nodes, find a subset of the nodes whose sum of weights is as large as possible such that there is no edge between
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Unformatted text preview: any pair of nodes in the subset. (a) WISP is an optimization problem. De±ne a decision version of WISP. (b) Show that the decision version is in NP . (c) Show that if you could solve the optimization version in polynomial time that you could also solve the decision version in polynomial time. (d) Show that if you could solve the decision version in polynomial time that you could also solve the optimization version in polynomial time. HINT: First ±nd the weight of an optimal independent set. 1...
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