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International Symposium on Algorithms and Computation

ISAAC 2010: Algorithms and Computation pp 25–36Cite as

Approximate Periodicity

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6506))

Abstract

We consider the question of finding an approximate period in a given string S of length n. Let S′ be a periodic string closest to S under some distance metric. We consider this distance the error of the periodic string, and seek the smallest period that generates a string with this distance to S. In this paper we consider the Hamming and swap distance metrics. In particular, if S is the given string, and S′ is the closest periodic string to S under the Hamming distance, and if that distance is k, we develop an O(nkloglogn) algorithm that constructs the smallest period that defines such a periodic string S′. We call that string the approximate period of S under the Hamming distance. We further develop an O(n 2) algorithm that constructs the approximate period under the swap distance. Finally, we show an O(nlogn) algorithm for finite alphabets, and O(nlog3 n) algorithm for infinite alphabets, that approximates the number of mismatches in the approximate period of the string.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Bar-Ilan University, Ramat-Gan, 52900, Israel

    Amihood Amir & Estrella Eisenberg

  2. Department of Computer Science, Johns Hopkins University, Baltimore, MD, 21218, USA

    Amihood Amir

  3. Department of Software Engineering, Shenkar College, 12 Anna Frank, Ramat-Gan, Israel

    Avivit Levy

  4. CRI, Haifa University, Mount Carmel, Haifa, 31905, Israel

    Avivit Levy

Authors
  1. Amihood Amir
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  2. Estrella Eisenberg
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  3. Avivit Levy
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Editor information

Editors and Affiliations

  1. Department of Computer Science, KAIST, Gwahangno 335, 305-701, Yuseong-gu, Daejeon, Korea

    Otfried Cheong  & Kyung-Yong Chwa  & 

  2. School of Computer Science and Engineering, Seoul National University, 151-742, Seoul, Korea

    Kunsoo Park

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Amir, A., Eisenberg, E., Levy, A. (2010). Approximate Periodicity. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17517-6_5

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  • DOI: https://doi.org/10.1007/978-3-642-17517-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17516-9

  • Online ISBN: 978-3-642-17517-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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