Abstract

We define a deterministic metric of “well-behaved data” that enables searching along the lines of interpolation search. Specifically, define ∆ to be the ratio of distances between the farthest and nearest pair of adjacent elements. We develop a data structure that stores a dynamic set of n integers subject to insertions, deletions, and predecessor/successor queries in O(lg ∆) time per operation. This result generalizes interpolation search and interpolation search trees smoothly to nonrandom (in particular, non-independent) input data. In this sense, we capture the amount of “pseudorandomness” required for effective interpolation search. 1

Citations