Inferring strings from full abelian periods

Makoto Nishida, Tomohiro I, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

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

2 Citations (Scopus)

Abstract

Strings u, v are said to be Abelian equivalent if u is a permutation of the characters appearing in v. A string w is said to have a full Abelian period p if w = w1 …wk, where all wi’s are of length p each and are all Abelian equivalent. This paper studies reverse-engineering problems on full Abelian periods. Given a positive integer n and a set D of divisors of n, we show how to compute in O(n) time the lexicographically smallest string of length n which has all elements of D as its full Abelian periods and has the minimum number of full Abelian periods not in D. Moreover, we give an algorithm to enumerate all such strings in amortized constant time per output after O(n)-time preprocessing. Also, we show how to enumerate the strings which have all elements of D as its full Abelian periods in amortized constant time per output after O(n)-time preprocessing.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 26th International Symposium, ISAAC 2015, Proceedings
EditorsKhaled Elbassioni, Kazuhisa Makino
PublisherSpringer Verlag
Pages768-779
Number of pages12
ISBN (Print)9783662489703
DOIs
Publication statusPublished - Jan 1 2015
Event26th International Symposium on Algorithms and Computation, ISAAC 2015 - Nagoya, Japan
Duration: Dec 9 2015Dec 11 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9472
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other26th International Symposium on Algorithms and Computation, ISAAC 2015
CountryJapan
CityNagoya
Period12/9/1512/11/15

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Nishida, M., I, T., Inenaga, S., Bannai, H., & Takeda, M. (2015). Inferring strings from full abelian periods. In K. Elbassioni, & K. Makino (Eds.), Algorithms and Computation - 26th International Symposium, ISAAC 2015, Proceedings (pp. 768-779). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9472). Springer Verlag. https://doi.org/10.1007/978-3-662-48971-0_64