Low Auto-correlation Binary Sequences explored using Warning Propagation

TL;DR

This paper investigates the effectiveness of Warning Propagation in solving the NP-hard problem of finding low auto-correlation binary sequences, showing it converges to near-optimal solutions efficiently.

Contribution

It demonstrates the application of Warning Propagation to LABS, compares performance on different models, and introduces hybrid models to improve convergence and solution quality.

Findings

Warning Propagation converges to low energy minima.

Local structure influences convergence and solution quality.

Hybrid models enhance convergence speed and solution quality.

Abstract

The search of binary sequences with low auto-correlations (LABS) is a discrete combinatorial optimization problem contained in the NP-hard computational complexity class. We study this problem using Warning Propagation (WP) , a message passing algorithm, and compare the performance of the algorithm in the original problem and in two different disordered versions. We show that in all the cases Warning Propagation converges to low energy minima of the solution space. Our results highlight the importance of the local structure of the interaction graph of the variables for the convergence time of the algorithm and for the quality of the solutions obtained by WP. While in general the algorithm does not provide the optimal solutions in large systems it does provide, in polynomial time, solutions that are energetically similar to the optimal ones. Moreover, we designed hybrid models that interpolate between the standard LABS problem and the disordered versions of it, and exploit them to improved the convergence time of WP and the quality of the solutions.