Randomized Algorithms 2013 A Lecture 11 – Importance Sampling , and the Local Lemma ∗
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چکیده
Problem definition: The input is a DNF formula f with m clauses C1, . . . , Cm over n variables x1, . . . , xn, i.e. f = ∨i=1Ci where each Ci is the conjunction of literals like x2 ∧ x̄5 ∧ xn. The goal is the estimate the number of Boolean assignments that satisfy f . Theorem 1 [Karp and Luby, 1983]: Let S ⊂ {0, 1}n be the set of satisfying assignments. Then |S| can be estimated within factor 1 + ε in time that is polynomial in m+ n+ 1/ε.
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تاریخ انتشار 2013