Survey-propagation decimation through distributed local computations

TL;DR

This paper introduces two distributed survey-propagation based algorithms for solving random K-SAT problems, achieving solutions efficiently with convergence times growing logarithmically with problem size.

Contribution

It presents novel distributed implementations of survey-propagation decimation algorithms, enabling local decision-making and rapid convergence in solving K-SAT.

Findings

Both algorithms find solutions in parameter ranges comparable to state-of-the-art serialized solvers.

Convergence time scales as log(N), indicating high efficiency for large problems.

Distributed methods can effectively solve K-SAT problems without centralized control.

Abstract

We discuss the implementation of two distributed solvers of the random K-SAT problem, based on some development of the recently introduced survey-propagation (SP) algorithm. The first solver, called the "SP diffusion algorithm", diffuses as dynamical information the maximum bias over the system, so that variable nodes can decide to freeze in a self-organized way, each variable making its decision on the basis of purely local information. The second solver, called the "SP reinforcement algorithm", makes use of time-dependent external forcing messages on each variable, which let the variables get completely polarized in the direction of a solution at the end of a single convergence. Both methods allow us to find a solution of the random 3-SAT problem in a range of parameters comparable with the best previously described serialized solvers. The simulated time of convergence towards a solution (if these solvers were implemented on a distributed device) grows as log(N).