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Robustly Guarding Polygons

Authors Rathish Das , Omrit Filtser , Matthew J. Katz , Joseph S.B. Mitchell

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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • geometric optimization
  • approximation algorithms
  • guarding

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Abstract

We propose precise notions of what it means to guard a domain "robustly", under a variety of models. While approximation algorithms for minimizing the number of (precise) point guards in a polygon is a notoriously challenging area of investigation, we show that imposing various degrees of robustness on the notion of visibility coverage leads to a more tractable (and realistic) problem for which we can provide approximation algorithms with constant factor guarantees.

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Rathish Das, Omrit Filtser, Matthew J. Katz, and Joseph S.B. Mitchell. Robustly Guarding Polygons. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 47:1-47:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SoCG.2024.47

Author Details

Rathish Das
  • University of Houston, TX, USA
Omrit Filtser
  • The Open University of Israel, Israel
Matthew J. Katz
  • Ben-Gurion University of the Negev, Beer-Sheva, Israel
Joseph S.B. Mitchell
  • Stony Brook University, NY, USA

Funding

  • Katz, Matthew J.: Partially supported by Grant 495/23 from the Israel Science Foundation and Grant 2019715/CCF-20-08551 from the US-Israel Binational Science Foundation/US National Science Foundation.
  • Mitchell, Joseph S.B.: Partially supported by the National Science Foundation (CCF-2007275).

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