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

1 Citation (Scopus)

Abstract

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
Pages420-431
Number of pages12
ISBN (Print)9783319788241
DOIs
Publication statusPublished - Jan 1 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

Other

Other28th International Workshop on Combinational Algorithms, IWOCA 2017
CountryAustralia
CityNewcastle, NSW
Period7/17/177/21/17

Fingerprint

Run-length Encoding
Strings
Regularity
Computing
Permutation
Efficient Algorithms

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Sugimoto, S., Noda, N., Inenaga, S., Bannai, H., & Takeda, M. (2018). Computing abelian string regularities based on RLE. In W. F. Smyth, L. Brankovic, & J. Ryan (Eds.), Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers (pp. 420-431). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10765 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-78825-8_34

Computing abelian string regularities based on RLE. / Sugimoto, Shiho; Noda, Naoki; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers. ed. / William F. Smyth; Ljiljana Brankovic; Joe Ryan. Springer Verlag, 2018. p. 420-431 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10765 LNCS).

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

Sugimoto, S, Noda, N, Inenaga, S, Bannai, H & Takeda, M 2018, Computing abelian string regularities based on RLE. in WF Smyth, L Brankovic & J Ryan (eds), Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10765 LNCS, Springer Verlag, pp. 420-431, 28th International Workshop on Combinational Algorithms, IWOCA 2017, Newcastle, NSW, Australia, 7/17/17. https://doi.org/10.1007/978-3-319-78825-8_34
Sugimoto S, Noda N, Inenaga S, Bannai H, Takeda M. Computing abelian string regularities based on RLE. In Smyth WF, Brankovic L, Ryan J, editors, Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers. Springer Verlag. 2018. p. 420-431. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-78825-8_34
Sugimoto, Shiho ; Noda, Naoki ; Inenaga, Shunsuke ; Bannai, Hideo ; Takeda, Masayuki. / Computing abelian string regularities based on RLE. Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers. editor / William F. Smyth ; Ljiljana Brankovic ; Joe Ryan. Springer Verlag, 2018. pp. 420-431 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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