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International Symposium on Algorithms and Computation

ISAAC 2015: Algorithms and Computation pp 768–779Cite as

Inferring Strings from Full Abelian Periods

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9472))

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 \(w = w_1 \cdots w_k\), where all \(w_i\)’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.

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Author information

Authors and Affiliations

  1. Department of Informatics, Kyushu University, Fukuoka, Japan

    Makoto Nishida, Shunsuke Inenaga, Hideo Bannai & Masayuki Takeda

  2. Department of Computer Science, TU Dortmund, Dortmund, Germany

    Tomohiro I.

Authors
  1. Makoto Nishida
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  2. Tomohiro I.
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  3. Shunsuke Inenaga
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  4. Hideo Bannai
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  5. Masayuki Takeda
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Corresponding author

Correspondence to Tomohiro I. .

Editor information

Editors and Affiliations

  1. Masdar Institute, Abu Dhabi, United Arab Emirates

    Khaled Elbassioni

  2. Kyoto University, Kyoto, Japan

    Kazuhisa Makino

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Nishida, M., I., T., Inenaga, S., Bannai, H., Takeda, M. (2015). Inferring Strings from Full Abelian Periods. In: Elbassioni, K., Makino, K. (eds) Algorithms and Computation. ISAAC 2015. Lecture Notes in Computer Science(), vol 9472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48971-0_64

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  • DOI: https://doi.org/10.1007/978-3-662-48971-0_64

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48970-3

  • Online ISBN: 978-3-662-48971-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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