Dynamic Interpolation Search in o(log log n) Time

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(log2n) to θ(log n) for searches and from θ(n) to θ(log n) for updates.

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