2026-07-21T20:01:25Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25861 2026-06-23T12:59:49Z ddc:004 open_access

Linear Time Single-Source Shortest Path Algorithms in Euclidean Graph Classes Gudmundsson, Joachim Sha, Yuan Wong, Sampson Graph algorithms Single-Source Shortest Path Euclidean Graphs Recursive Division 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Joachim Gudmundsson and Yuan Sha and Sampson Wong 2026 Is Part Of LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2026.55 urn:nbn:de:0030-drops-258618 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.55 eng https://creativecommons.org/licenses/by/4.0/legalcode