Enhanced string factoring from alphabet orderings

TL;DR

This paper introduces a new greedy algorithm for string factoring based on alphabet orderings, producing efficient Lyndon factorizations and exploring applications of circ-UMFFs.

Contribution

It presents a novel greedy algorithm for Lyndon factorization using alphabet orderings and introduces the Exponent Parikh vector for improved string factoring.

Findings

Efficient Lyndon factorizations with fewer factors.

A modification for handling large numbers of factors.

Discussion of applications and future research directions.

Abstract

In this note we consider the concept of alphabet ordering in the context of string factoring. We propose a greedy-type algorithm which produces Lyndon factorizations with small numbers of factors along with a modification for large numbers of factors. For the technique we introduce the Exponent Parikh vector. Applications and research directions derived from circ-UMFFs are discussed.