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Farthest-Point Voronoi Diagrams in the Presence of Rectangular Obstacles

Authors Mincheol Kim, Chanyang Seo, Taehoon Ahn, Hee-Kap Ahn

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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Geodesic distance
  • L₁ metric
  • farthest-point Voronoi diagram

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Abstract

We present an algorithm to compute the geodesic L₁ farthest-point Voronoi diagram of m point sites in the presence of n rectangular obstacles in the plane. It takes O(nm+n log n + mlog m) construction time using O(nm) space. This is the first optimal algorithm for constructing the farthest-point Voronoi diagram in the presence of obstacles. We can construct a data structure in the same construction time and space that answers a farthest-neighbor query in O(log(n+m)) time.

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Mincheol Kim, Chanyang Seo, Taehoon Ahn, and Hee-Kap Ahn. Farthest-Point Voronoi Diagrams in the Presence of Rectangular Obstacles. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 51:1-51:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.SoCG.2022.51

Author Details

Mincheol Kim
  • Department of Computer Science and Engineering, Pohang University of Science and Technology, South Korea
Chanyang Seo
  • Graduate School of Artificial Intelligence, Pohang University of Science and Technology, South Korea
Taehoon Ahn
  • Department of Computer Science and Engineering, Pohang University of Science and Technology, South Korea
Hee-Kap Ahn
  • Graduate School of Artificial Intelligence, Department of Computer Science and Engineering, Pohang University of Science and Technology, South Korea

Funding

This research was partly supported by the Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (No. 2017-0-00905, Software Star Lab (Optimal Data Structure and Algorithmic Applications in Dynamic Geometric Environment)) and (No. 2019-0-01906, Artificial Intelligence Graduate School Program(POSTECH)).

References

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