Spanning Trees in Random Satisfiability Problems

TL;DR

This paper establishes a link between random K-satisfiability solutions and spanning trees in factor graphs, introducing a modified survey propagation algorithm to identify satisfiable spanning trees and analyze their organization.

Contribution

It presents a novel correspondence between satisfiability solutions and spanning trees, along with a modified algorithm to find and study satisfiable spanning trees.

Findings

A new method to identify satisfiable spanning trees in factor graphs.

Insights into the organization of satisfiable spanning trees.

Enhanced understanding of solution space structure in random K-satisfiability.

Abstract

Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning trees in the associated factor graph. We introduce a modified survey propagation algorithm which returns null edges of the factor graph and helps us to find satisfiable spanning trees. This allows us to study organization of satisfiable spanning trees in the space spanned by spanning trees.