k-Abelian pattern matching: Revisited, corrected, and extended

Badkobeh, Golnaz; Bannai, Hideo; Crochemore, Maxime; I, Tomohiro; Inenaga, shunsuke and Sugimoto, Shiho. 2019. k-Abelian pattern matching: Revisited, corrected, and extended. pp. 29-40. [Article]

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Abstract or Description

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.

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2 June 2019Accepted
29 August 2019Published

Event Location:

Prague, Czech Republic

Date range:

26 – 28 August 2019

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Date Deposited:

30 Jul 2020 13:45

Last Modified:

11 Jun 2021 06:59



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