  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.
