Near-Optimal Working-Set Heaps and Dijkstra on Pointer Machines

Ivor van der Hoog; John Iacono; Eva Rotenberg; Daniel Rutschmann

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arXiv · 2604.24134

Near-Optimal Working-Set Heaps and Dijkstra on Pointer Machines

Ivor van der Hoog·John Iacono·Eva Rotenberg·Daniel Rutschmann

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Abstract

A heap is a dynamic data structure that stores a set of labeled values under the following operations: pop returns the minimum value of the heap, Push($x_i$) pushes a new value $x_i$ onto the heap, and DecreaseKey($i$, $v$) decreases the value $x_i$ to $v$. A working-set heap is a heap that supports the $x_i \gets$ pop$()$ operation in $O(\log \Gamma(x_i) )$ time where $\Gamma(x_i)$ is the size of the \emph{working set}: the number of elements that were pushed onto the heap while $x_i$ was in the heap. The goal of working set heap design is to maintain the working set property while minimizing the overhead of the Push and DecreaseKey operations. On a word RAM, there exist working set heaps that support Push and DecreaseKey in amortized constant time. In this paper, we show via a simple construction that pointer machines, one of the most general and least-assuming computational models, support working set heaps that support Push in amortized constant time and DecreaseKey in inverse-Ackermann time. A by-product of this analysis is that Dijkstra's shortest path algorithm can be near-universally optimal on a pointer machine -- incurring only an additive $O(m \, \alpha(m))$ overhead compared to the optimal running time for distance ordering, where $m$ denotes the number of edges in the graph.

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BibTeX RIS

Ivor van der Hoog, John Iacono, Eva Rotenberg, Daniel Rutschmann. 2026-04-27. Near-Optimal Working-Set Heaps and Dijkstra on Pointer Machines. https://arxiv.org/abs/2604.24134

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