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Optimizing Visibility-Based Search in Polygonal Domains

Authors Kien C. Huynh , Joseph S. B. Mitchell , Linh Nguyen , Valentin Polishchuk

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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Quota watchman route problem
  • budgeted watchman route problem
  • visibility-based search
  • approximation

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Abstract

Given a geometric domain P, visibility-based search problems seek routes for one or more mobile agents ("watchmen") to move within P in order to be able to see a portion (or all) of P, while optimizing objectives, such as the length(s) of the route(s), the size (e.g., area or volume) of the portion seen, the probability of detecting a target distributed within P according to a prior distribution, etc. The classic watchman route problem seeks a shortest route for an observer, with omnidirectional vision, to see all of P. In this paper we study bicriteria optimization problems for a single mobile agent within a polygonal domain P in the plane, with the criteria of route length and area seen. Specifically, we address the problem of computing a minimum length route that sees at least a specified area of P (minimum length, for a given area quota). We also study the problem of computing a length-constrained route that sees as much area as possible. We provide hardness results and approximation algorithms. In particular, for a simple polygon P we provide the first fully polynomial-time approximation scheme for the problem of computing a shortest route seeing an area quota, as well as a (slightly more efficient) polynomial dual approximation. We also consider polygonal domains P (with holes) and the special case of a planar domain consisting of a union of lines. Our results yield the first approximation algorithms for computing a time-optimal search route in P to guarantee some specified probability of detection of a static target within P, randomly distributed in P according to a given prior distribution.

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Kien C. Huynh, Joseph S. B. Mitchell, Linh Nguyen, and Valentin Polishchuk. Optimizing Visibility-Based Search in Polygonal Domains. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SWAT.2024.27

Author Details

Kien C. Huynh
  • Linköping University, Sweden
Joseph S. B. Mitchell
  • Stony Brook University, NY, USA
Linh Nguyen
  • Stony Brook University, NY, USA
Valentin Polishchuk
  • Linköping University, Sweden

Funding

This work is partially supported by the National Science Foundation (CCF-2007275) and the Swedish Research Council and the Swedish Transport Administration.

References

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