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Complexity of Sequential Pattern Matching Algorithms

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Randomization and Approximation Techniques in Computer Science (RANDOM 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1518))

Abstract

We formally define a class of sequential pattern matching algorithms that includes all variations of Morris-Pratt algorithm. For the last twenty years it was known that the complexity of such algorithms is bounded by a linear function of the text length. Recently, substantial progress has been made in identifying lower bounds. We now prove there exists asymptotically a linearity constant for the worst and the average cases. We use Subadditive Ergodic Theorem and prove an almost sure convergence. Our results hold for any given pattern and text and for stationary ergodic pattern and text. In the course of the proof, we establish some structural property, namely, the existence of “unavoidable positions” where the algorithm must stop to compare. This property seems to be uniquely reserved for Morris-Pratt type algorithms (e.g., Boyer and Moore algorithm does not possess this property).

The project was supported by NATO Collaborative Grant CRG.950060, the ESPRIT III Program No. 7141 ALCOM II, and NSF Grants NCR-9415491, NCR-9804760.

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Author information

Authors and Affiliations

  1. INRIA, Rocquencourt, 78153, Le Chesnay, France

    Mireille Régnier

  2. Dept. Computer Science, Purdue University, W. Lafayette, IN, 47907, USA

    Wojciech Szpankowski

Authors
  1. Mireille Régnier
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  2. Wojciech Szpankowski
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Editor information

Editors and Affiliations

  1. International Computer Science Institute, 1947 Center Street, Suite 600, Berkeley, CA, 94704-1198, USA

    Michael Luby

  2. Computer Science Department, University of Geneva, 24, rue Général Dufour, CH-1211, Geneva 4, Switzerland

    José D. P. Rolim

  3. University of Barcelona (UPC), Jordi Girona Salgado 1-3, E-08034, Barcelona, Spain

    Maria Serna

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© 1998 Springer-Verlag Berlin Heidelberg

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Régnier, M., Szpankowski, W. (1998). Complexity of Sequential Pattern Matching Algorithms. In: Luby, M., Rolim, J.D.P., Serna, M. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 1998. Lecture Notes in Computer Science, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49543-6_16

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  • DOI: https://doi.org/10.1007/3-540-49543-6_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65142-0

  • Online ISBN: 978-3-540-49543-7

  • eBook Packages: Springer Book Archive

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