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A Coreset for Approximate Furthest-Neighbor Queries in a Simple Polygon

Authors Mark de Berg , Leonidas Theocharous

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Furthest-neighbor queries
  • polygons
  • geodesic distance
  • coreset

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Abstract

Let 𝒫 be a simple polygon with m vertices and let P be a set of n points inside 𝒫. We prove that there exists, for any ε > 0, a set C ⊂ P of size O(1/ε²) such that the following holds: for any query point q inside the polygon 𝒫, the geodesic distance from q to its furthest neighbor in C is at least 1-ε times the geodesic distance to its further neighbor in P. Thus the set C can be used for answering ε-approximate furthest-neighbor queries with a data structure whose storage requirement is independent of the size of P. The coreset can be constructed in O(1/(ε) (nlog(1/ε) + (n+m)log(n+m))) time.

Cite As Get BibTex

Mark de Berg and Leonidas Theocharous. A Coreset for Approximate Furthest-Neighbor Queries in a Simple Polygon. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SoCG.2024.16

Author Details

Mark de Berg
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Leonidas Theocharous
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands

Funding

  • de Berg, Mark: MdB is supported by the Dutch Research Council (NWO) through Gravitation-grant NETWORKS-024.002.003.
  • Theocharous, Leonidas: LT is supported by the Dutch Research Council (NWO) through Gravitation-grant NETWORKS-024.002.003.

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