Analysing Survey Propagation Guided Decimationon Random Formulas

Let ~ Φ be a uniformly distributed random k-SAT formula with n variables and m clauses. For clauses/variables ratio m/n ≤ rk-SAT ∼ 2 ln 2 the formula ~ Φ is satisfiable with high probability. However, no efficient algorithm is known to provably find a satisfying assignment beyond m/n ∼ 2k ln(k)/k with a non-vanishing probability. Non-rigorous statistical mechanics work on k-CNF led to the development of a new efficient “message passing algorithm” called Survey Propagation Guided Decimation [Mézard et al., Science 2002]. Experiments conducted for k = 3, 4, 5 suggest that the algorithm finds satisfying assignments close to rk-SAT. However, in the present paper we prove that the basic version of Survey Propagation Guided Decimation fails to solve random k-SAT formulas efficiently already for m/n = 2(1 + εk) ln(k)/k with limk→∞ εk = 0 almost a factor k below rk-SAT. 1998 ACM Subject Classification G.2.1 Combinatorics