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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.
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