License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2022.69
URN: urn:nbn:de:0030-drops-160773
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16077/
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Mantas, Ioannis ; Papadopoulou, Evanthia ; Suderland, Martin ; Yap, Chee

Subdivision Methods for Sum-Of-Distances Problems: Fermat-Weber Point, n-Ellipses and the Min-Sum Cluster Voronoi Diagram (Media Exposition)

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LIPIcs-SoCG-2022-69.pdf (4 MB)

Abstract

Given a set P of n points, the sum of distances function of a point x is d_{P}(x) : = ∑_{p ∈ P} ||x - p||. Using a subdivision approach with soft predicates we implement and visualize approximate solutions for three different problems involving the sum of distances function in ℝ². Namely, (1) finding the Fermat-Weber point, (2) constructing n-ellipses of a given set of points, and (3) constructing the nearest Voronoi diagram under the sum of distances function, given a set of point clusters as sites.

BibTeX - Entry

@InProceedings{mantas_et_al:LIPIcs.SoCG.2022.69,
  author =	{Mantas, Ioannis and Papadopoulou, Evanthia and Suderland, Martin and Yap, Chee},
  title =	{{Subdivision Methods for Sum-Of-Distances Problems: Fermat-Weber Point, n-Ellipses and the Min-Sum Cluster Voronoi Diagram}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{69:1--69:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16077},
  URN =		{urn:nbn:de:0030-drops-160773},
  doi =		{10.4230/LIPIcs.SoCG.2022.69},
  annote =	{Keywords: Fermat point, geometric median, Weber point, Fermat distance, sum of distances, n-ellipse, multifocal ellipse, min-sum Voronoi diagram, cluster Voronoi diagram}
}

Keywords: Fermat point, geometric median, Weber point, Fermat distance, sum of distances, n-ellipse, multifocal ellipse, min-sum Voronoi diagram, cluster Voronoi diagram
Collection: 38th International Symposium on Computational Geometry (SoCG 2022)
Issue Date: 2022
Date of publication: 01.06.2022
Supplementary Material: Audiovisual (Video): https://youtu.be/wgG8uqLIizo

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