Date: 28 May 2005

Dynamic interpolation search in o(log log n) time

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Abstract

A new efficient data structure, based on the augmentation technique used in the interpolation search tree by Mehlhorn and Tsakalidis, is presented. We achieve:

  • a trade-off between input distribution and search cost for dynamic interpolation search.

  • θ(log log n) expected time for search and update operations for a larger class of densities than Mehlhorn and Tsakalidis.

  • o(log log n) expected time for search and update operations for a large class of densities. As an example, we give an unbounded density for which we achieve θ(log* n) expected time. We also show θ(1) expected time for all bounded densities, in particular, the uniform distribution.

  • improved worst-case cost from θ(log2 n) to θ(log n) for searches and from θ(n) to θ(log n) for updates.

  • We also include a discussion of terminology: which methods should be termed “interpolation search”?