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arXiv · 2503.13628

Optimal Non-Oblivious Open Addressing

Michael A. Bender·William Kuszmaul·Renfei Zhou
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Abstract

A hash table is said to be open-addressed (or non-obliviously open-addressed) if it stores elements (and free slots) in an array with no additional metadata. Intuitively, open-addressed hash tables must incur a space-time tradeoff: The higher the load factor at which the hash table operates, the longer insertions/deletions/queries should take. In this paper, we show that no such tradeoff exists: It is possible to construct an open-addressed hash table that supports constant-time operations even when the hash table is entirely full. In fact, it is even possible to construct a version of this data structure that: (1) is dynamically resized so that the number of slots in memory that it uses, at any given moment, is the same as the number of elements it contains; (2) supports $O(1)$-time operations, not just in expectation, but with high probability; and (3) requires external access to just $O(1)$ hash functions that are each just $O(1)$-wise independent. Our results complement a recent lower bound by Bender, Kuszmaul, and Zhou showing that oblivious open-addressed hash tables must incur $Ω(\log \log \varepsilon^{-1})$-time operations. The hash tables in this paper are non-oblivious, which is why they are able to bypass the previous lower bound.

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Michael A. Bender, William Kuszmaul, Renfei Zhou. 2025-03-17. Optimal Non-Oblivious Open Addressing. https://arxiv.org/abs/2503.13628

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