Low-Autocorrelation Binary Sequences: On Improved Merit Factors and Runtime Predictions to Achieve Them

TL;DR

This paper compares three stochastic solvers for the low autocorrelation binary sequence problem, demonstrating that a new approach with self-avoiding walks has superior asymptotic performance and potential for achieving higher merit factors.

Contribution

The paper introduces a novel solver based on self-avoiding walks and provides a rigorous performance comparison, showing its superior asymptotic runtime and potential for better solutions.

Findings

The self-avoiding walk solver outperforms state-of-the-art methods asymptotically.

The solver's runtime scales as 0.000032*1.1504^L with sequence length L.

Potential to reach merit factors closer to the conjectured maximum of 12.3248.

Abstract

The search for binary sequences with a high figure of merit, known as the low autocorrelation binary sequence ($labs$}) problem, represents a formidable computational challenge. To mitigate the computational constraints of the problem, we consider solvers that accept odd values of sequence length $L$ and return solutions for skew-symmetric binary sequences only -- with the consequence that not all best solutions under this constraint will be optimal for each $L$. In order to improve both, the search for best merit factor $and$ the asymptotic runtime performance, we instrumented three stochastic solvers, the first two are state-of-the-art solvers that rely on variants of memetic and tabu search ($lssMAts$ and $lssRRts$), the third solver ($lssOrel$) organizes the search as a sequence of independent contiguous self-avoiding walk segments. By adapting a rigorous statistical methodology to performance testing of all three combinatorial solvers, experiments show that the solver with the best asymptotic average-case performance, $lssOrel\_8 = 0.000032*1.1504^L$, has the best chance of finding solutions that improve, as $L$ increases, figures of merit reported to date. The same methodology can be applied to engineering new $labs$ solvers that may return merit factors even closer to the conjectured asymptotic value of 12.3248.