Performance of the Survey Propagation-guided decimation algorithm for the random NAE-K-SAT problem

We show that the Survey Propagation guided decimation algorithm fails to find satisfying assignments on random instances of the "Not-All-Equal-K-SAT" problem, well below the satisfiability threshold. Our analysis applies to a broad class of algorithms that may be described as "sequential local algorithms" --such algorithms iteratively set variables based on some local information and/or local randomness, and then recurse on the reduced instance. Survey Propagation guided as well as Belief Propagation guided decimation algorithms, studied widely in the past, fall under this category of algorithms. Our main technical result shows that under fairly mild conditions, sequential local algorithms find satisfying assignments only when the solution space is nicely connected, despite the earlier predictions by statistical physicists. Combined with the knowledge that the solution space tends to cluster well before the satisfiability threshold, our main result follows immediately. This approach of showing that local algorithms work only when the solution space is connected has been applied before in the literature: the novelty of our work is our ability to extend the approach also to sequential local algorithms.