Optimal Bounds for Open Addressing Without Reordering

TL;DR

This paper demonstrates that open-addressed hash tables can achieve significantly better search complexities without reordering, disproving a longstanding conjecture and establishing tight bounds for their performance.

Contribution

It introduces new bounds for open addressing without reordering, showing improved expected search complexities and disproving Yao's conjecture with matching lower bounds.

Findings

Achieves better expected search complexities without reordering

Disproves Yao's conjecture on uniform hashing optimality

Provides matching lower bounds for open addressing performance

Abstract

In this paper, we revisit one of the simplest problems in data structures: the task of inserting elements into an open-addressed hash table so that elements can later be retrieved with as few probes as possible. We show that, even without reordering elements over time, it is possible to construct a hash table that achieves far better expected search complexities (both amortized and worst-case) than were previously thought possible. Along the way, we disprove the central conjecture left by Yao in his seminal paper ``Uniform Hashing is Optimal''. All of our results come with matching lower bounds.