Survey propagation: an algorithm for satisfiability

: 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 = M/N is close to the experimental threshold 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 is close to (but smaller than) 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 pro...

• Type: Journal
• Year: 2002
• Where: CORR
• Authors: Alfredo Braunstein, Marc Mézard, Riccardo Zecchina
• Keywords: Clustering Phenomenon, CORR 2002, Education, Formulas, Statistical Physics