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# hw10 - CS 473 Homework 10(practice only Spring 2010 This...

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CS 473 Homework 10 (practice only) Spring 2010 This homework is practice only. However, there will be at least one NP-hardness problem on the final exam, so working through this homework is strongly recommended. Stu- dents / groups are welcome to submit solutions for feedback (but not credit) in class on May 4, after which we will publish official solutions. 1. Recall that 3SAT asks whether a given boolean formula in conjunctive normal form, with exactly three literals in each clause, is satisfiable. In class we proved that 3SAT is NP-complete, using a reduction from C IRCUIT SAT. Now consider the related problem 2SAT : Given a boolean formula in conjunctive normal form, with exactly two literals in each clause, is the formula satisfiable? For example, the following boolean formula is a valid input to 2SAT: ( x y ) ( y z ) ( x z ) ( w y ) . Either prove that 2SAT is NP-hard or describe a polynomial-time algorithm to solve it. [Hint: Recall that ( x y ) ( x y ) , and build a graph.] 2. Let G = ( V , E ) be a graph. A
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