Simplifying Random Satisfiability Problem by Removing Frustrating Interactions

TL;DR

This paper introduces a modified survey propagation algorithm to identify minimal satisfiable subproblems in random K-satisfiability problems by removing interactions, aiding in solving the original CSP efficiently.

Contribution

It presents a novel algorithm that can generate minimal satisfiable subproblems from random K-satisfiability instances, preserving satisfiability while reducing complexity.

Findings

Able to construct satisfiable subproblems with fewer interactions

Minimal subproblems directly yield solutions to the original problem

Algorithm controls the number of removed interactions via a tuning parameter

Abstract

How can we remove some interactions in a constraint satisfaction problem (CSP) such that it still remains satisfiable? In this paper we study a modified survey propagation algorithm that enables us to address this question for a prototypical CSP, i.e. random K-satisfiability problem. The average number of removed interactions is controlled by a tuning parameter in the algorithm. If the original problem is satisfiable then we are able to construct satisfiable subproblems ranging from the original one to a minimal one with minimum possible number of interactions. The minimal satisfiable subproblems will provide directly the solutions of the original problem.