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An O(nlog n) Algorithm for Single-Source Shortest Paths in Disk Graphs

Authors Mark de Berg , Sergio Cabello

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • shortest path
  • geometric intersection graph
  • disk graph
  • fat triangles

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Abstract

We prove that the single-source shortest-path problem on disk graphs can be solved in O(n log n) expected time, and that it can be solved on intersection graphs of fat triangles in O(n log³ n) time.

Cite As Get BibTex

Mark de Berg and Sergio Cabello. An O(nlog n) Algorithm for Single-Source Shortest Paths in Disk Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 81:1-81:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.81

Author Details

Mark de Berg
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Sergio Cabello
  • Faculty of Mathematics and Physics, University of Ljubljana, Slovenia
  • Institute of Mathematics, Physics and Mechanics, Slovenia

Funding

  • de Berg, Mark: Supported by the Dutch Research Council (NWO) through Gravitation-grant NETWORKS-024.002.003.
  • Cabello, Sergio: Funded in part by the Slovenian Research and Innovation Agency (P1-0297, N1-0218, N1-0285). Funded in part by the European Union (ERC, KARST, project number 101071836). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.

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