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Survey propagation: An algorithm for satisfiability
Author(s) -
Braunstein A.,
Mézard M.,
Zecchina R.
Publication year - 2005
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20057
Subject(s) - satisfiability , heuristic , probabilistic logic , belief propagation , boolean satisfiability problem , cluster analysis , algorithm , product (mathematics) , maximum satisfiability problem , computer science , conjunctive normal form , dpll algorithm , order (exchange) , mathematics , discrete mathematics , boolean function , artificial intelligence , decoding methods , geometry , finance , economics , telecommunications , phase locked loop , jitter
We study the satisfiability of randomly generated formulas formed by M clauses of exactly K literals over N Boolean variables. For a given value of N the problem is known to be most difficult when α = M/N is close to the experimental threshold α c separating the region where almost all formulas are SAT from the region where all formulas are UNSAT. Recent results from a statistical physics analysis suggest that the difficulty is related to the existence of a clustering phenomenon of the solutions when α is close to (but smaller than) α c . We introduce a new type of message passing algorithm which allows to find efficiently a satisfying assignment of the variables in this difficult region. This algorithm is iterative and composed of two main parts. The first is a message‐passing procedure which generalizes the usual methods like Sum‐Product or Belief Propagation: It passes messages that may be thought of as surveys over clusters of the ordinary messages. The second part uses the detailed probabilistic information obtained from the surveys in order to fix variables and simplify the problem. Eventually, the simplified problem that remains is solved by a conventional heuristic. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005