Dynamic interpolation search in o(Log log n) time

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(loglog 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"?.