Testing Quasiperiodicity

TL;DR

This paper presents an efficient method to determine if a string has a cover, which is a shorter string that overlaps with all parts of the original, and discusses its potential for streaming implementation.

Contribution

It introduces a new efficient testing algorithm for string covers and extends it to streaming contexts, advancing pattern matching techniques.

Findings

Efficient cover testing algorithm developed

Algorithm can be adapted for streaming data

Enhances understanding of quasiperiodic string structures

Abstract

A cover (or quasiperiod) of a string $S$ is a shorter string $C$ such that every position of $S$ is contained in some occurrence of $C$ as a substring. The notion of covers was introduced by Apostolico and Ehrenfeucht over 30 years ago [Theor. Comput. Sci. 1993] and it has received significant attention from the combinatorial pattern matching community. In this note, we show how to efficiently test whether $S$ admits a cover. Our tester can also be translated into a streaming algorithm.