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arXiv · 2603.22948

Linear time single-source shortest path algorithms in Euclidean graph classes

Joachim Gudmundsson·Yuan Sha·Sampson Wong
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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, Sampson Wong. 2026-03-24. Linear time single-source shortest path algorithms in Euclidean graph classes. https://arxiv.org/abs/2603.22948

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