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Finding All Approximate Gapped Palindromes

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Algorithms and Computation (ISAAC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5878))

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Abstract

We study the problem of finding all maximal approximate gapped palindromes in a string. More specifically, given a string S of length n, a parameter q ≥ 0 and a threshold k > 0, the problem is to identify all substrings in S of the form uvw such that (1) the Levenshtein distance between u and w r is at most k, where w r is the reverse of w and (2) v is a string of length q. The best previous work requires O(k 2 n) time. In this paper, we propose an O(kn)-time algorithm for this problem by utilizing an incremental string comparison technique. It turns out that the core technique actually solves a more general incremental string comparison problem that allows the insertion, deletion, and substitution of multiple symbols.

This research was supported in part by NSC grants NSC 95-2221-E-002-126-MY3 and NSC 97-2221-E-002-097-MY3 from the National Science Council, Taiwan.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Engineering,  

    Ping-Hui Hsu, Kuan-Yu Chen & Kun-Mao Chao

  2. Graduate Institute of Biomedical Electronics and Bioinformatics,  

    Kun-Mao Chao

  3. Graduate Institute of Networking and Multimedia, National Taiwan University, Taipei, Taiwan, 106

    Kun-Mao Chao

Authors
  1. Ping-Hui Hsu
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  2. Kuan-Yu Chen
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  3. Kun-Mao Chao
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Editor information

Editors and Affiliations

  1. Dept. of Electrical and Computer Engineering, University of Hawaii, Holmes Hall 483, 2540 Dole Street, 96822, Honolulu, HI, USA

    Yingfei Dong

  2. Department of Computer Science, University of Texas at Dallas, 75083, Dallas, TX, USA

    Ding-Zhu Du

  3. Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Oscar Ibarra

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© 2009 Springer-Verlag Berlin Heidelberg

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Hsu, PH., Chen, KY., Chao, KM. (2009). Finding All Approximate Gapped Palindromes. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_109

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  • DOI: https://doi.org/10.1007/978-3-642-10631-6_109

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10630-9

  • Online ISBN: 978-3-642-10631-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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