Chapter

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

Volume 4110 of the series Lecture Notes in Computer Science pp 339-350

Complete Convergence of Message Passing Algorithms for Some Satisfiability Problems

  • Uriel FeigeAffiliated withCarnegie Mellon UniversityMicorosoft Research and The Weizmann Institute
  • , Elchanan MosselAffiliated withCarnegie Mellon UniversityU.C. Berkeley
  • , Dan VilenchikAffiliated withCarnegie Mellon UniversityTel Aviv University

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Abstract

Experimental results show that certain message passing algorithms, namely, survey propagation, are very effective in finding satisfying assignments in random satisfiable 3CNF formulas. In this paper we make a modest step towards providing rigorous analysis that proves the effectiveness of message passing algorithms for random 3SAT. We analyze the performance of Warning Propagation, a popular message passing algorithm that is simpler than survey propagation. We show that for 3CNF formulas generated under the planted assignment distribution, running warning propagation in the standard way works when the clause-to-variable ratio is a sufficiently large constant. We are not aware of previous rigorous analysis of message passing algorithms for satisfiability instances, though such analysis was performed for decoding of Low Density Parity Check (LDPC) Codes. We discuss some of the differences between results for the LDPC setting and our results.