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arXiv · 2607.17494

Linear Probing with Non-Greedy Insertions

Andrew Krapivin·William Kuszmaul·Jolyne Wang
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Abstract

Linear probing hash tables classically use a \emph{greedy} insertion strategy, placing a key $u$ in the first available position out of $h(u), h(u) + 1, h(u) + 2, \ldots$. If the hash table is filled to $1 - 1/x$ full, this results in $\Theta(x^{2})$ worst-case expected insertion time. In this note, we show that there is a simple \emph{non-greedy} insertion strategy that does better, and without requiring elements to be reordered within the table over time. Given $x$ in advance, the strategy is able to bring the worst-case expected insertion time down to $O(x \log x)$.

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Andrew Krapivin, William Kuszmaul, Jolyne Wang. 2026-07-20. Linear Probing with Non-Greedy Insertions. https://arxiv.org/abs/2607.17494

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