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On parallel hashing and integer sorting

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Automata, Languages and Programming (ICALP 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 443))

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Abstract

The problem of sorting n integers from a restricted range [1..m], where m is superpolynomial in n, is considered. An o(n log n) time randomized algorithm is given. Our algorithm takes O(n log log m) expected time and O(n) space. (Thus, for m=n polylog(n) we have an O(n log log n) time algorithm.) The algorithm is parallelizable. The resulting parallel algorithm achieves optimal speed up. Some features of the algorithm make us believe that it is relevant for practical applications.

A result of independent interest is a parallel hashing technique. The expected construction time is logarithmic using an optimal number of processors, and searching for a value takes O(1) time in the worst case. This technique enables drastic reduction of space requirements for the price of using randomness. Applicability of the technique is demonstrated for the parallel sorting algorithm, and for some parallel string matching algorithms.

The parallel sorting algorithm is designed for a strong and non standard model of parallel computation. Efficient simulations of the strong model on a CRCW PRAM are introduced. One of the simulations even achieves optimal speed up. This is probably a first optimal speed up simulation of a certain kind.

Extended summary

Partially supported by NSF grant CCR-890649 and ONR grant N00014-85-0046.

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Authors and Affiliations

  1. Tel-Aviv University, Israel

    Yossi Matias & Uzi Vishkin

  2. University of Maryland, USA

    Uzi Vishkin

Authors
  1. Yossi Matias
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  2. Uzi Vishkin
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Michael S. Paterson

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© 1990 Springer-Verlag Berlin Heidelberg

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Matias, Y., Vishkin, U. (1990). On parallel hashing and integer sorting. In: Paterson, M.S. (eds) Automata, Languages and Programming. ICALP 1990. Lecture Notes in Computer Science, vol 443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032070

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  • DOI: https://doi.org/10.1007/BFb0032070

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  • Print ISBN: 978-3-540-52826-5

  • Online ISBN: 978-3-540-47159-2

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