String Cadences

TL;DR

This paper introduces efficient algorithms to detect regular repeating patterns, called cadences, in strings, including anchored cadences, with improved computational complexity.

Contribution

It presents a sub-quadratic algorithm for detecting cadences with at least three occurrences and a nearly linear algorithm for finding all anchored cadences.

Findings

Sub-quadratic algorithm for cadence detection

Nearly linear algorithm for anchored cadences

Efficient pattern detection in strings

Abstract

We say a string has a cadence if a certain character is repeated at regular intervals, possibly with intervening occurrences of that character. We call the cadence anchored if the first interval must be the same length as the others. We give a sub-quadratic algorithm for determining whether a string has any cadence consisting of at least three occurrences of a character, and a nearly linear algorithm for finding all anchored cadences.