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Information, Physics, and Computation$
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Marc Mézard and Andrea Montanari

Print publication date: 2009

Print ISBN-13: 9780198570837

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780198570837.001.0001

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Random K-satisfiability

Random K-satisfiability

(p.467) 20 Random K-satisfiability
Information, Physics, and Computation

Marc Mézard

Andrea Montanari

Oxford University Press

This chapter studies an ensemble of random satisfiability problems, ‘random K-satisfiability’ (K-SAT). Applying the 1RSB cavity method, it first derives the phase diagram in the limit of large N, in particular the location of the SAT-UNSAT threshold. Within the SAT phase, the chapter focuses on the intermediate clustered phase close, and computes the number of clusters to leading exponential order in N. The application of survey propagation to this problem is then described. Combined with a simple decimation procedure, the chapter provides an efficient method for finding satisfiable assignments in the clustered phase. The whole chapter is based on heuristic arguments. There is not yet any rigorous proof of the results presented, neither concerning the phase diagram, nor the convergence properties of message passing algorithms and their use in decimation procedures.

Keywords:   satisfiability, K-SAT, random, phase transition, threshold, cluster, survey propagation, decimation

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