Com S 633: Randomness in Computation Lecture 12 Scribe: Aaron Sterling Summary: Com S 633: Randomness in Computation Lecture 12 Scribe: Aaron Sterling Today's Topic: Randomized Rounding Algorithm for MAX-SAT Problem Statement: Given a CNF-formula  = c 1 ^ c 2 ^    ^ c m , nd an assignment that satis es the maximum number of clauses. Exact solution of this problem is known to be NP-hard. We will improve on the randomized approximation algorithm of Lecture 2 by using the Randomized Rounding technique introduced in the previous lecture. 1 A randomized algorithm for MAX-SAT MAX-SAT is a generalization of the MAX-3CNF problem that we discussed in Lecture 2. In MAX-3CNF, each formula  is a conjunction of clauses c i , such that each c i is a disjunction of three literals, x i 1 ; x i 2 ; x i 3 , where either x i j or :x i j appears in c i . In the case of MAX-SAT, each c i is a disjunction of nitely many literals (or their negations), but the number of literals in each clause may vary. Collections: Computer Technologies and Information Sciences