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Linear Time Single-Source Shortest Path Algorithms in Euclidean Graph Classes

Authors Joachim Gudmundsson , Yuan Sha , Sampson Wong

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LIPIcs.SoCG.2026.55.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Graph algorithms
  • Single-Source Shortest Path
  • Euclidean Graphs
  • Recursive Division

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Abstract

In the celebrated paper of Henzinger, Klein, Rao and Subramanian (1997), it was shown that planar graphs admit a linear time single-source shortest path algorithm. Their algorithm unfortunately does not extend to Euclidean graph classes. We give criteria and prove that any Euclidean graph class satisfying the criteria admits a linear time single-source shortest path algorithm. As a main ingredient, we show that the contracted graphs of these Euclidean graph classes admit sublinear separators.

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Joachim Gudmundsson, Yuan Sha, and Sampson Wong. Linear Time Single-Source Shortest Path Algorithms in Euclidean Graph Classes. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 55:1-55:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.55

Author Details

Joachim Gudmundsson
  • The University of Sydney, Australia
Yuan Sha
  • The University of Sydney, Australia
Sampson Wong
  • The University of Copenhagen, Denmark

Funding

  • Gudmundsson, Joachim: Supported by the Australian Government through the Australian Research Council (project number DP240101353).
  • Sha, Yuan: Supported in part by the the Australian Research Council project number DP240101353.
  • Wong, Sampson: Supported by the European Union’s Marie Skłodowska-Curie Actions Postdoctoral Fellowship, grant number 101146276.

Acknowledgements

We would like to thank David Eppstein for his helpful discussions.

References

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