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Shortest Path Separators in Unit Disk Graphs

Authors Elfarouk Harb , Zhengcheng Huang , Da Wei Zheng

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Elfarouk Harb
  • Department of Computer Science, University of Illinois at Urbana-Champaign, IL, USA
Zhengcheng Huang
  • Department of Computer Science, University of Illinois at Urbana-Champaign, IL, USA
Da Wei Zheng
  • Department of Computer Science, University of Illinois at Urbana-Champaign, IL, USA

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Elfarouk Harb, Zhengcheng Huang, and Da Wei Zheng. Shortest Path Separators in Unit Disk Graphs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 66:1-66:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.66

Abstract

We introduce a new balanced separator theorem for unit-disk graphs involving two shortest paths combined with the 1-hop neighbours of those paths and two other vertices. This answers an open problem of Yan, Xiang and Dragan [CGTA '12] and improves their result that requires removing the 3-hop neighbourhood of two shortest paths. Our proof uses very different ideas, including Delaunay triangulations and a generalization of the celebrated balanced separator theorem of Lipton and Tarjan [J. Appl. Math. '79] to systems of non-intersecting paths.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Computational geometry
Keywords
  • Balanced shortest path separators
  • unit disk graphs
  • crossings

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