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The search of binary sequences with low auto-correlations (LABS) is adiscrete combinatorial optimization problem contained in the NP-hardcomputational complexity class. We study this problem using Warning Propagation(WP) , a message passing algorithm, and compare the performance of thealgorithm in the original problem and in two different disordered versions. Weshow that in all the cases Warning Propagation converges to low energy minimaof the solution space. Our results highlight the importance of the localstructure of the interaction graph of the variables for the convergence time ofthe algorithm and for the quality of the solutions obtained by WP. While ingeneral the algorithm does not provide the optimal solutions in large systemsit does provide, in polynomial time, solutions that are energetically similarto the optimal ones. Moreover, we designed hybrid models that interpolatebetween the standard LABS problem and the disordered versions of it, andexploit them to improved the convergence time of WP and the quality of thesolutions.

Low Auto-correlation Binary Sequences explored using Warning Propagation