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Separating Two Points with Obstacles in the Plane: Improved Upper and Lower Bounds

Authors Jack Spalding-Jamieson , Anurag Murty Naredla

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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • obstacle separation
  • point separation
  • geometric intersection graph
  • Z₂-homology
  • fine-grained lower bounds

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Abstract

Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for a minimum-weight subset of the obstacles separating the two points. A few computational models for this problem have been previously studied. We give a unified approach to this problem in all models via a reduction to a particular shortest-path problem, and obtain improved running times in essentially all cases. In addition, we also give fine-grained lower bounds for many cases.

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Jack Spalding-Jamieson and Anurag Murty Naredla. Separating Two Points with Obstacles in the Plane: Improved Upper and Lower Bounds. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 90:1-90:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.90

Author Details

Jack Spalding-Jamieson
  • Independent, Vancouver, Canada
Anurag Murty Naredla
  • University of Bonn, Germany

Acknowledgements

This work originated from a problem discussion group in the Fall of 2021, whose members collectively contributed to the discussion and development of some of this work’s preliminary results in the "arrangement model", as well as a better understanding of the problem as a whole. In addition to the authors, this group included (in alphabetical order) Sam Barr, Therese Biedl, Reza Bigdeli, Anna Lubiw, Jayson Lynch, Karthik Murali, and Graeme Stroud. In addition, we want to thank Jeff Erickson, Elizabeth Xiao, and Da Wei Zheng for helpful discussions about homology.

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