Internal Quasiperiod Queries

TL;DR

This paper introduces a data structure for efficiently answering internal cover queries in strings, providing faster query times for identifying quasiperiods after a comprehensive preprocessing step.

Contribution

It is the first to address internal cover queries and offers a novel data structure with improved query times for covers of string factors.

Findings

Answers shortest cover in O(log n log log n) time

Provides all covers in O(log n (log log n)^2) time

Preprocessing takes O(n log n) time and space

Abstract

Internal pattern matching requires one to answer queries about factors of a given string. Many results are known on answering internal period queries, asking for the periods of a given factor. In this paper we investigate (for the first time) internal queries asking for covers (also known as quasiperiods) of a given factor. We propose a data structure that answers such queries in $O(\log n \log \log n)$ time for the shortest cover and in $O(\log n (\log \log n)^2)$ time for a representation of all the covers, after $O(n \log n)$ time and space preprocessing.