Computing abelian string regularities based on RLE

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

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

1 被引用数 (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.

ホスト出版物のタイトルCombinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers
編集者William F. Smyth, Ljiljana Brankovic, Joe Ryan
出版社Springer Verlag
出版ステータス出版済み - 1 1 2018
イベント28th International Workshop on Combinational Algorithms, IWOCA 2017 - Newcastle, NSW, オーストラリア
継続期間: 7 17 20177 21 2017


名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
10765 LNCS


その他28th International Workshop on Combinational Algorithms, IWOCA 2017
CityNewcastle, NSW

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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