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On the maximum satisfiability of random formulas

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3 Author(s)
Achlioptas, D. ; Microsoft Res., Redmond, WA, USA ; Naor, A. ; Peres, Y.

Maximum satisfiability is a canonical NP-complete problem that appears empirically hard for random instances. At the same time, it is rapidly becoming a canonical problem for statistical physics. In both of these realms, evaluating new ideas relies crucially on knowing the maximum number of clauses one can typically satisfy in a random k-CNF formula. In this paper we give asymptotically tight estimates for this quantity. Our result gives very tight bounds for the fraction of satisfiable clauses in a random k-CNF. In particular, for k > 2 it improves upon all previously known such bound.

Published in:

Foundations of Computer Science, 2003. Proceedings. 44th Annual IEEE Symposium on

Date of Conference:

11-14 Oct. 2003