## Abstract

In this paper we analyze the performance of Warning Propagation, a popular

message passing algorithm. We show that for 3CNF formulas drawn from a certain distribution over random satisfiable 3CNF formulas, commonly referred to as the planted-assignment distribution, running Warning Propagation in the standard way (run message passing until convergence, simplify the formula according to the resulting assignment, and satisfy the remaining subformula, if necessary, using a simple “off the shelf” heuristic) works when the clause-variable ratio is a sufficiently large constant. We are not aware of previous rigorous analysis showing the effectiveness of message passing algorithms for satisfiability instances.

message passing algorithm. We show that for 3CNF formulas drawn from a certain distribution over random satisfiable 3CNF formulas, commonly referred to as the planted-assignment distribution, running Warning Propagation in the standard way (run message passing until convergence, simplify the formula according to the resulting assignment, and satisfy the remaining subformula, if necessary, using a simple “off the shelf” heuristic) works when the clause-variable ratio is a sufficiently large constant. We are not aware of previous rigorous analysis showing the effectiveness of message passing algorithms for satisfiability instances.

Original language | English GB |
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Pages (from-to) | 617-651 |

Number of pages | 35 |

Journal | Theory of Computing |

Volume | 9 |

Issue number | 1 |

State | Published - 2013 |