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On the exact complexity of the string prefix-matching problem

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Algorithms — ESA '94 (ESA 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 855))

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Abstract

In this paper we study the exact comparison complexity of the string prefix-matching problem in the deterministic sequential comparison model with equality tests. We derive almost tight lower and upper bounds on the number of comparisons required in the worst case by on-line prefix-matching algorithms for any fixed pattern and variable text. Unlike previous results on the comparison complexity of string-matching and prefix-matching algorithms, our bounds are almost tight for any particular pattern.

We also consider the special case where the pattern and the text are the same string. This problem, which we call the string self-prefix problem, is similar to the pattern preprocessing step of the Knuth-Morris-Pratt string-matching algorithm that is used in several comparison efficient string-matching and prefix-matching algorithms, including in our new algorithm. We develop an algorithm for the self-prefix problem that requires at most 2m−⌈2√m⌉ comparisons, matching the lower bound that we gave in a previous work.

Our algorithms can be implemented in linear-time and space in the standard random-access-machine model.

Partially supported by ESPRIT Basic Research Action Program of the EC under contract #7141 (ALCOM II). Part of the research reported in the paper was carried out while this author was visiting at the Istituto di Elaborazione dell'Informazione, Consiglio Nazionale delle Ricerche, Pisa, Italy, with the support of the European Research Consortium for Informatics and Mathematics postdoctoral fellowship.

Partially supported by “Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo” of the Italian National Research Councile under grant number 89.00026.69.

Partially supported by “Borsa di studi per attività di perfeziomento all'estero” from the University of Padua.

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Authors and Affiliations

  1. BRICS - Basic Research in Computer Science - a centre of the Danish National Research Foundation, Department of Computer Science, University of Aarhus, DK-8000, Aarhus C, Denmark

    Dany Breslauer

  2. Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni 7, I-35131, Padova, Italy

    Livio Colussi

  3. Université de Marne-la-Vallée, 2 rue de la Butte Verte, F-93166, Noisy-le-Grand Cedex, France

    Laura Toniolo

Authors
  1. Dany Breslauer
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  2. Livio Colussi
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  3. Laura Toniolo
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Jan van Leeuwen

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© 1994 Springer-Verlag Berlin Heidelberg

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Breslauer, D., Colussi, L., Toniolo, L. (1994). On the exact complexity of the string prefix-matching problem. In: van Leeuwen, J. (eds) Algorithms — ESA '94. ESA 1994. Lecture Notes in Computer Science, vol 855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049433

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  • DOI: https://doi.org/10.1007/BFb0049433

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58434-6

  • Online ISBN: 978-3-540-48794-4

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