Optimal Bounds for Open Addressing Without Reordering
Data Structures and Algorithms
2025-03-03 v2 Combinatorics
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.
Cite
@article{arxiv.2501.02305,
title = {Optimal Bounds for Open Addressing Without Reordering},
author = {Martin Farach-Colton and Andrew Krapivin and William Kuszmaul},
journal= {arXiv preprint arXiv:2501.02305},
year = {2025}
}