Adaptive Search over Sorted Sets

TL;DR

Adaptive Search is a refined algorithm for searching sorted sets that combines features of Interpolation and Binary search, achieving fast average-case performance with guaranteed worst-case bounds, and outperforming existing methods on large datasets.

Contribution

It introduces Adaptive Search, a new algorithm that blends Interpolation and Binary search, offering improved practical performance while maintaining theoretical guarantees.

Findings

Achieves O(log log n) average-case complexity similar to Interpolation search.

Maintains O(log n) worst-case complexity like Binary search.

Outperforms existing search algorithms on large synthetic and real datasets.

Abstract

We revisit the classical algorithms for searching over sorted sets to introduce an algorithm refinement, called Adaptive Search, that combines the good features of Interpolation search and those of Binary search. W.r.t. Interpolation search, only a constant number of extra comparisons is introduced. Yet, under diverse input data distributions our algorithm shows costs comparable to that of Interpolation search, i.e., O(log log n) while the worst-case cost is always in O(log n), as with Binary search. On benchmarks drawn from large datasets, both synthetic and real-life, Adaptive search scores better times and lesser memory accesses even than Santoro and Sidney's Interpolation-Binary search.