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

Authors Ivor van der Hoog , John Iacono , Eva Rotenberg , Daniel Rutschmann

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ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • Data structures
  • graph algorithms
  • amortized analysis

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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 ← pop() operation in O(log Γ(x_i)) time where Γ(x_i) is the size of the 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 α(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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Ivor van der Hoog, John Iacono, Eva Rotenberg, and Daniel Rutschmann. Near-Optimal Working-Set Heaps and Dijkstra on Pointer Machines. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 45:1-45:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.45

Author Details

Ivor van der Hoog
  • IT University of Copenhagen, Denmark
John Iacono
  • Université libre de Bruxelles, Belgium
Eva Rotenberg
  • IT University of Copenhagen, Denmark
Daniel Rutschmann
  • Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria

Funding

Ivor van der Hoog, Eva Rotenberg, and Daniel Rutschmann thank the VILLUM Foundation grant (VIL37507) "Efficient Recomputations for Changeful Problems" for supporting this work. Daniel Rutschmann is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (No. 101019564). John Iacono is supported by the Fonds de la Recherche Scientifique - FNRS.

Acknowledgements

This work started at Dagstuhl 25191: Adaptive and Scalable Data Structures.

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