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Work-time optimal parallel prefix matching

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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

Consider the prefix matching problem: Given a pattern P of length m and a text T of length n, find for all positions i in T the longest prefix of P starting at i. We present a parallel algorithm for the prefix matching problem over general alphabets whose text search takes optimal O(α(m)) time and preprocessing takes optimal O(log log m) time, where α(m) is the inverse Ackermann function. An Ω(log log m) lower bound for the prefix matching problem is implied by the same lower bound for string matching. However, the lower bound is applied only to preprocessing of the pattern and the searching phase can be faster. We prove an Ω(α(m)) lower bound for any linear-work searching phase. Therefore our algorithm is work-time optimal in both preprocessing and text search. The idea of leftmost witnesses is introduced to obtain the algorithm.

Supported by the EC Cooperative Action IC 1000 Algorithms for Future Technologies “ALTEC”.

Supported by S.N.U. Posco Research Fund 94-15-1112.

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Author information

Authors and Affiliations

  1. Instytut Informatyki, Uniwersytet Warszawski, Banacha 2, 02-097, Warszawa, Poland

    Leszek Gasieniec

  2. Department of Computer Engineering, Seoul National University, 151-742, Seoul, Korea

    Kunsoo Park

Authors
  1. Leszek Gasieniec
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  2. Kunsoo Park
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Jan van Leeuwen

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© 1994 Springer-Verlag Berlin Heidelberg

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Gasieniec, L., Park, K. (1994). Work-time optimal parallel prefix matching. 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/BFb0049432

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  • DOI: https://doi.org/10.1007/BFb0049432

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58434-6

  • Online ISBN: 978-3-540-48794-4

  • eBook Packages: Springer Book Archive

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