Divide and concur: A general approach to constraint satisfaction

TL;DR

The paper introduces a geometric framework for solving complex constraint satisfaction problems, demonstrating competitive performance on benchmarks like 3SAT and sphere packing, and offering an alternative to stochastic methods.

Contribution

It presents a novel, simple geometric approach to constraint satisfaction problems applicable to various domains, with demonstrated effectiveness on benchmark problems.

Findings

Performance comparable to specialized algorithms on 3SAT

Improved solutions in sphere packing problems

Framework offers a competitive alternative to stochastic methods

Abstract

Many difficult computational problems involve the simultaneous satisfaction of multiple constraints which are individually easy to satisfy. Such problems occur in diffractive imaging, protein folding, constrained optimization (e.g., spin glasses), and satisfiability testing. We present a simple geometric framework to express and solve such problems and apply it to two benchmarks. In the first application (3SAT, a boolean satisfaction problem), the resulting method exhibits similar performance scaling as a leading context-specific algorithm (walksat). In the second application (sphere packing), the method allowed us to find improved solutions to some old and well-studied optimization problems. Based upon its simplicity and observed efficiency, we argue that this framework provides a competitive alternative to stochastic methods such as simulated annealing.