A fast coset-translation algorithm for computing the cycle structure of Comer relation algebras over $\mathbb{Z}/p\mathbb{Z}$

TL;DR

This paper introduces an improved algorithm for determining the cycle structure of Comer relation algebras over _p, significantly reducing the computational complexity from quadratic to linear time.

Contribution

The paper presents a novel, faster algorithm for computing the cycle structure of Comer relation algebras over _p, enhancing efficiency over previous methods.

Findings

Reduced time complexity from (p)^2 to (p).

Efficient cycle structure checking for Comer relation algebras.

Applicable to large prime p in algebraic computations.

Abstract

Proper relation algebras can be constructed using $\mathbb{Z}/p\mathbb{Z}$ as a base set using a method due to Comer. The cycle structure of such an algebra must, in general, be determined \emph{a posteriori}, normally with the aid of a computer. In this paper, we give an improved algorithm for checking the cycle structure that reduces the time complexity from $\mathcal{O}(p^2)$ to $\mathcal{O}(p)$.