Minimizing energy below the glass thresholds

TL;DR

This paper investigates the effectiveness of a simple backtrack decimation strategy combined with Survey Propagation in minimizing energy in the MAX-K-SAT problem, achieving near-optimal solutions below known thresholds.

Contribution

It demonstrates that a linear-time backtrack decimation approach with Survey Propagation can reach energies below the dynamic threshold, close to the theoretical optimum.

Findings

Backtrack decimation reaches energies below the dynamic threshold.

The approach is computationally efficient, running in linear time.

Results are comparable to the best local search procedures.

Abstract

Focusing on the optimization version of the random K-satisfiability problem, the MAX-K-SAT problem, we study the performance of the finite energy version of the Survey Propagation (SP) algorithm. We show that a simple (linear time) backtrack decimation strategy is sufficient to reach configurations well below the lower bound for the dynamic threshold energy and very close to the analytic prediction for the optimal ground states. A comparative numerical study on one of the most efficient local search procedures is also given.