Streamlining Variational Inference for Constraint Satisfaction Problems

TL;DR

This paper introduces a novel branching strategy for constraint satisfaction problems that improves upon survey propagation by using streamlining constraints, leading to better solver performance on random k-SAT instances.

Contribution

It proposes a generalization of survey propagation with streamlining constraints, enhancing the efficiency of solving constraint satisfaction problems.

Findings

Streamlined solvers outperform decimation-based solvers on random k-SAT.

Performance gap to theoretical limits is reduced by 16.3% on average.

Method is effective across multiple problem sizes and k-values.

Abstract

Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and are used to inform branching decisions during search; however, marginal estimates obtained via survey propagation are approximate and can be self-contradictory. We introduce a more general branching strategy based on streamlining constraints, which sidestep hard assignments to variables. We show that streamlined solvers consistently outperform decimation-based solvers on random k-SAT instances for several problem sizes, shrinking the gap between empirical performance and theoretical limits of satisfiability by 16.3% on average for k=3,4,5,6.