Computing abelian string regularities based on RLE

Shiho Sugimoto, Naoki Noda, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

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

3 Citations (Scopus)


Two strings x and y are said to be Abelian equivalent if x is a permutation of y, or vice versa. If a string z satisfies z = xy with x and y being Abelian equivalent, then z is said to be an Abelian square. If a string w can be factorized into a sequence v1, …, vs of strings such that v1, …, vs-1 are all Abelian equivalent and vs is a substring of a permutation of v1, then w is said to have a regular Abelian period (p, t) where p = |v1| and t = |vs|. If a substring w1[i.i+l-1] of a string w1 and a substring w2[j.j + l - 1] of another string w2 are Abelian equivalent, then the substrings are said to be a common Abelian factor of w1 and w2 and if the length l is the maximum of such then the substrings are said to be a longest common Abelian factor of w1 and w2. We propose efficient algorithms which compute these Abelian regularities using the run length encoding (RLE) of strings. For a given string w of length n whose RLE is of size m, we propose algorithms which compute all Abelian squares occurring in w in O(mn) time, and all regular Abelian periods of w in O(mn) time. For two given strings w1 and w2 of total length n and of total RLE size m, we propose an algorithm which computes all longest common Abelian factors in O(m2n) time.

Original languageEnglish
Title of host publicationCombinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers
EditorsWilliam F. Smyth, Ljiljana Brankovic, Joe Ryan
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783319788241
Publication statusPublished - 2018
Event28th International Workshop on Combinational Algorithms, IWOCA 2017 - Newcastle, NSW, Australia
Duration: Jul 17 2017Jul 21 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10765 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other28th International Workshop on Combinational Algorithms, IWOCA 2017
CityNewcastle, NSW

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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