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Finding Periods in Cartesian Tree Matching

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Combinatorial Algorithms (IWOCA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11638))

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Abstract

In Cartesian tree matching, two strings match if the Cartesian trees of the strings are the same. In this paper we define full, initial, and general periods in Cartesian tree matching, and present an O(n) time algorithm for finding all full periods, an \(O(n \log \log n)\) time algorithm for finding all initial periods, and an \(O(n \log n)\) time algorithm for finding all general periods of a string of length n.

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Acknowledgements

M. Bataa, S.G. Park and K. Park were supported by Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No. 2018-0-00551, Framework of Practical Algorithms for NP-hard Graph Problems). A. Amir and G.M. Landau were partially supported by the Israel Science Foundation grant 571/14, and Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF).

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Authors and Affiliations

  1. Seoul National University, Seoul, South Korea

    Magsarjav Bataa, Sung Gwan Park & Kunsoo Park

  2. Bar-Ilan University, Ramat Gan, Israel

    Amihood Amir

  3. University of Haifa, Haifa, Israel

    Gad M. Landau

Authors
  1. Magsarjav Bataa
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  2. Sung Gwan Park
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  3. Amihood Amir
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  4. Gad M. Landau
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  5. Kunsoo Park
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Corresponding author

Correspondence to Kunsoo Park .

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Editors and Affiliations

  1. Arizona State University, Tempe, AZ, USA

    Charles J. Colbourn

  2. University of Pisa, Pisa, Italy

    Roberto Grossi

  3. University of Pisa, Pisa, Italy

    Nadia Pisanti

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Bataa, M., Park, S.G., Amir, A., Landau, G.M., Park, K. (2019). Finding Periods in Cartesian Tree Matching. In: Colbourn, C., Grossi, R., Pisanti, N. (eds) Combinatorial Algorithms. IWOCA 2019. Lecture Notes in Computer Science(), vol 11638. Springer, Cham. https://doi.org/10.1007/978-3-030-25005-8_7

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  • DOI: https://doi.org/10.1007/978-3-030-25005-8_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-25004-1

  • Online ISBN: 978-3-030-25005-8

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