A Recursive Method for Enumeration of Costas Arrays

TL;DR

This paper introduces a recursive algorithm for efficiently enumerating all Costas arrays of a given size, significantly reducing computational effort compared to exhaustive search while maintaining completeness.

Contribution

The paper presents a novel recursive approach for Costas array enumeration that improves efficiency and is suitable for parallel implementation, advancing computational methods in combinatorial design.

Findings

The recursive method reduces computational complexity compared to exhaustive search.

The algorithm can find all Costas arrays of a specified size.

The approach is validated through theoretical analysis and numerical experiments.

Abstract

In this paper, we propose a recursive method for finding Costas arrays that relies on a particular formation of Costas arrays from similar patterns of smaller size. By using such an idea, the proposed algorithm is able to dramatically reduce the computational burden (when compared to the exhaustive search), and at the same time, still can find all possible Costas arrays of given size. Similar to exhaustive search, the proposed method can be conveniently implemented in parallel computing. The efficiency of the method is discussed based on theoretical and numerical results.