Survey-propagation decimation through distributed local computations

Abstract

We discuss the implementation of two distributed solvers of the random K-SATproblem, based on some development of the recently introduced survey propagation(SP) algorithm. The first solver, called the ‘SP diffusion algorithm’, diffuses asdynamical information the maximum bias over the system, so that variable nodescan decide to freeze in a self-organized way, each variable making its decisionon the basis of purely local information. The second solver, called the ‘SPreinforcement algorithm’, makes use of time-dependent external forcing messageson each variable, which are adapted in time in such a way that the algorithmapproaches its estimated closest solution. Both methods allow us to find a solution ofthe random 3-SAT problem in a range of parameters comparable with the bestpreviously described serialized solvers. The simulated time of convergence towards asolution (if these solvers were implemented on a fully parallel device) grows aslog(N).