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Optimal Discovery of Subword Associations in Strings

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Discovery Science (DS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3245))

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Abstract

Given a textstring x of n symbols and an integer constant d, we consider the problem of finding, for any pair (y,z) of subwords of x the number of times that y and z occur in tandem (i.e., with no intermediate occurrence of either one of them) within a distance of d symbols of x. Although in principle there might be n 4 distinct subword pairs in x, we show that it suffices to consider a family of only n 2 such pairs, with the property that for any neglected pair (y′,z′), there is a corresponding pair (y,z) contained in our family and such that: (i) y′ is a prefix of y and z′ is a prefix of z, and (ii) the tandem index of (y′,z′) equals that of (y,z). We show that an algorithm for the construction of the table of all such tandem indices can be built to run in optimal O(n 2 ) time and space.

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Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria dell’ Informazione, Università di Padova, Padova, Italy

    Alberto Apostolico

  2. Department of Computer Sciences, Purdue University, Computer Sciences Building, West Lafayette, IN, 47907, USA

    Alberto Apostolico

  3. Dipartimento di Ingegneria dell’ Informazione, Università di Padova, Via Gradenigo 6/A, 35131, Padova, Italy

    Cinzia Pizzi & Giorgio Satta

Authors
  1. Alberto Apostolico
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  2. Cinzia Pizzi
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  3. Giorgio Satta
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Editor information

Editors and Affiliations

  1. Department of Informatics, Graduate School of Information Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishi, 819-0395, Fukuoka, Japan

    Einoshin Suzuki

  2. Kyushu University, 6–10–1 Hakozaki Higashi-ku, 812–8581, Fukuoka, Japan

    Setsuo Arikawa

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© 2004 Springer-Verlag Berlin Heidelberg

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Apostolico, A., Pizzi, C., Satta, G. (2004). Optimal Discovery of Subword Associations in Strings. In: Suzuki, E., Arikawa, S. (eds) Discovery Science. DS 2004. Lecture Notes in Computer Science(), vol 3245. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30214-8_21

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  • DOI: https://doi.org/10.1007/978-3-540-30214-8_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23357-2

  • Online ISBN: 978-3-540-30214-8

  • eBook Packages: Springer Book Archive

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