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Unformatted text preview: CS 473: Algorithms, Fall 2010 HBS 11 1. Consider an instance of the satisfiability problem specified by clauses C 1 ,C 2 ,...,C k over a set of boolean variables x 1 ,x 2 ,...,x n . We say that the instance is monotone if each term in each clause consists of a nonnegated variable i.e. each term is equal to x i , for some i , rather than x i . They could be easily satisfied by setting each variable to 1. For example, suppose we have three clauses ( x 1 x 2 ) , ( x 1 x 3 ) , ( x 3 x 2 ). These could be satisfied by setting all three variables to 1, or by setting x 1 and x 2 to 1 and x 3 to 0. Given a monotone instance of satisfiability, together with a number k , the problem Monotone Satisfiability asks whether there is a satisfying assignment for the instance in which at most k variables are set to 1. Give a polynomial time reduction from set cover to monotone satisfiability and prove that it is correct....
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This note was uploaded on 01/22/2011 for the course CS 473 taught by Professor Chekuri,c during the Fall '08 term at University of Illinois, Urbana Champaign.
- Fall '08