K-abelian pattern matching: Revisited, corrected, and extended

Golnaz Badkobeh, Hideo Bannai, Maxime Crochemore, I. Tomohiro, Shunsuke Inenaga, Shiho Sugimoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Two strings of equal length are called k-Abelian equivalent, if they share the same multi-set of factors of length at most k. Ehlers et al. [JDA, 2015] considered the k-Abelian pattern matching problem, where the task is to find all factors in a text T that are k-Abelian equivalent to a pattern P. They claimed a number of algorithmic results for the off-line and on-line versions of the k-Abelian pattern matching problem. In this paper, we first argue that some of the claimed results by Ehlers et al. [JDA, 2015] contain major errors, and then we present a new algorithm that correctly solves the offline version of the problem within the same bounds claimed by Ehlers et al., in O(n + m) time and O(m) space, where n = |T| and m = |P|. We also show how to correct errors in their online algorithm, and errors in their real-time algorithms for a slightly different problem called the extended k-Abelian pattern matching problem.

Original languageEnglish
Title of host publicationProceedings of the Prague Stringology Conference, PSC 2019
EditorsJan Holub, Jan Zdarek
PublisherPrague Stringology Club
Pages29-40
Number of pages12
ISBN (Electronic)9788001066188
Publication statusPublished - 2019
Event23rd Prague Stringology Conference, PSC 2019 - Prague, Czech Republic
Duration: Aug 26 2019Aug 28 2019

Publication series

NameProceedings of the Prague Stringology Conference, PSC 2019

Conference

Conference23rd Prague Stringology Conference, PSC 2019
CountryCzech Republic
CityPrague
Period8/26/198/28/19

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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