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Predecessor queries in dynamic integer sets

  • Algorithms I
  • Conference paper
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STACS 97 (STACS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1200))

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Abstract

We consider the problem of maintaining a set of n integers in the range 0.2w−1 under the operations of insertion, deletion, predecessor queries, minimum queries and maximum queries on a unit cost RAM with word size w bits. Let f (n) be an arbitrary nondecreasing smooth function satisfying \(n \leqslant f(n) \leqslant \sqrt {log n} \). A data structure is presented supporting insertions and deletions in worst case O(f(n)) time, predecessor queries in worst case O((logn)/f(n)) time and minimum and maximum queries in worst case constant time. The required space is O(n2∈w) for an arbitrary constant ∈ > 0. The RAM operations used are addition, arbitrary left and right bit shifts and bit-wise boolean operations. The data structure is the first supporting predecessor queries in worst case O(log n/log log n) time while having worst case O(log log n) update time.

Supported by the Danish Natural Science Research Council (Grant No. 9400044). Partially supported by the ESPRIT Long Term Research Program of the EU under contract #20244 (ALCOM-IT).

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Authors and Affiliations

  1. Basic Research in Computer Science, a Centre of the Danish National Research Foundation, Department of Computer Science, University of Aarhus, Ny Munkegade, DK-8000, Århus C, Denmark

    Gerth Stølting Brodal

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  1. Gerth Stølting Brodal
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Rüdiger Reischuk Michel Morvan

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© 1997 Springer-Verlag Berlin Heidelberg

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Brodal, G.S. (1997). Predecessor queries in dynamic integer sets. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023445

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  • DOI: https://doi.org/10.1007/BFb0023445

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62616-9

  • Online ISBN: 978-3-540-68342-1

  • eBook Packages: Springer Book Archive

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