Almost optimal searching of maximal subrepetitions in a word

TL;DR

This paper introduces an efficient algorithm for finding all maximal $$-subrepetitions in a word, achieving near-optimal time complexity close to the theoretical lower bound.

Contribution

The paper presents the first algorithm capable of finding all maximal $$-subrepetitions in a word within near-optimal time bounds.

Findings

Algorithm runs in $O(rac{n}{}\lograc{1}{})$ time

Achieves near-optimal performance close to the lower bound

Effectively identifies all maximal $$-subrepetitions in linear time for fixed $$

Abstract

For $0<\delta <1$ a $\delta$-subrepetition in a word is a factor which exponent is less than~2 but is not less than $1+\delta$ (the exponent of the factor is the ratio of the factor length to its minimal period). The $\delta$-subrepetition is maximal if it cannot be extended to the left or to the right by at least one letter with preserving its minimal period. In the paper we propose an algorithm for searching all maximal $\delta$-subrepetitions in a word of length~$n$ in $O(\frac{n}{\delta}\log\frac{1}{\delta})$ time (the lower bound for this time is $\Omega (\frac{n}{\delta})$).