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arXiv · 2607.24621

Heaps and Their Working Sets

Bernhard Haeupler·Richard Hladík·Václav Rozhoň·Robert E. Tarjan
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Abstract

We construct a heap with strong beyond-worst-case performance guarantees and explore the analysis of such heaps. First, we unify existing notions of the working-set bound for heaps by proving that essentially all of them are equivalent - with the notable exception of the so-called stack-like bound, which is strictly stronger. This equivalence simplifies the theoretical landscape and extends the range of applications of heaps with working-set bounds. Second, we present the first heap implementation that has the amortized stack-like bound and supports $\mathcal O(1)$-time decrease-key and $o(\log^*n)$-time insert.

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Bernhard Haeupler, Richard Hladík, Václav Rozhoň, Robert E. Tarjan. 2026-07-27. Heaps and Their Working Sets. https://arxiv.org/abs/2607.24621

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