Complexity of several constraint satisfaction problems using the heuristic, classical, algorithm, WalkSAT

TL;DR

This paper investigates the computational complexity of various constraint satisfaction problems when solved with the WalkSAT heuristic, revealing exponential growth in complexity and surprising difficulty in some polynomial-time solvable cases.

Contribution

It provides the first detailed analysis of WalkSAT's performance across multiple CSP models, highlighting unexpected challenges in polynomial-time solvable problems.

Findings

Complexity increases exponentially with problem size N.

WalkSAT struggles most with models that have polynomial-time algorithms.

All studied models exhibit exponential complexity at large sizes.

Abstract

We determine the complexity of several constraint satisfaction problems using the heuristic algorithm, WalkSAT. At large sizes N, the complexity increases exponentially with N in all cases. Perhaps surprisingly, out of all the models studied, the hardest for WalkSAT is the one for which there is a polynomial time algorithm.