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Biased Predecessor Search

Abstract

We consider the problem of performing predecessor searches in a bounded universe while achieving query times that depend on the distribution of queries. We obtain several data structures with various properties: in particular, we give data structures that achieve expected query times logarithmic in the entropy of the distribution of queries but with space bounded in terms of universe size, as well as data structures that use only linear space but with query times that are higher (but still sublinear) functions of the entropy. For these structures, the distribution is assumed to be known. We also consider individual query times on universe elements with general weights, as well as the case when the distribution is not known in advance.

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Notes

  1. 1.

    In this paper, we define \(\log x = \log _2 (x + 2)\).

  2. 2.

    As will be apparent from our results, in bounded universes this lower bound does not hold, and one can achieve query times below it.

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Author information

Correspondence to John Howat.

Additional information

Research partially supported by the Danish Council for Independent Research, Natural Sciences.

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Bose, P., Fagerberg, R., Howat, J. et al. Biased Predecessor Search. Algorithmica 76, 1097–1105 (2016). https://doi.org/10.1007/s00453-016-0146-7

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Keywords

  • Data structures
  • Predecessor search
  • Biased search trees
  • Entropy