Expected time analysis of interpolation merge — a simple new merging algorithm

Abstract

Binary merge is the best general-purpose merging algorithm known to date. Binary merge consists of two components: a first component in which an array index is incremented by a number nearly equal to the ratio of the sizes of the two arrays being merged followed by a second component, binary search. In this paper we formulate a simple algorithm called interpolation merge, where the binary search component is replaced with linear search, and analyze its expected behavior over data drawn from a uniform distribution. Our results, both theoretical and experimental, indicate a constant factor (≈0.75) speed-up over straight two-way merge. Further, our analysis of interpolation merge, which uses a mechanism of incremental indexing similar to that in binary merge, will hopefully lead to a better understanding of the latter algorithm. Currently, no significant results are known about the expected behavior of binary merge over data drawn from any standard probability distribution.