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arXiv · 2501.02305

Optimal Bounds for Open Addressing Without Reordering

Martin Farach-Colton·Andrew Krapivin·William Kuszmaul
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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.

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Martin Farach-Colton, Andrew Krapivin, William Kuszmaul. 2025-01-04. Optimal Bounds for Open Addressing Without Reordering. https://arxiv.org/abs/2501.02305

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