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On the Complexity of Closest Pair via Polar-Pair of Point-Sets

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Abstract

Every graph G can be represented by a collection of equi-radii spheres in a d-dimensional metric Delta such that there is an edge uv in G if and only if the spheres corresponding to u and v intersect. The smallest integer d such that G can be represented by a collection of spheres (all of the same radius) in Delta is called the sphericity of G, and if the collection of spheres are non-overlapping, then the value d is called the contact-dimension of G. In this paper, we study the sphericity and contact dimension of the complete bipartite graph K_{n,n} in various L^p-metrics and consequently connect the complexity of the monochromatic closest pair and bichromatic closest pair problems.

BibTeX - Entry

@InProceedings{david_et_al:LIPIcs:2018:8741,
  author =	{Roee David and Karthik C. S. and Bundit Laekhanukit},
  title =	{{On the Complexity of Closest Pair via Polar-Pair of Point-Sets}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8741},
  URN =		{urn:nbn:de:0030-drops-87412},
  doi =		{10.4230/LIPIcs.SoCG.2018.28},
  annote =	{Keywords: Contact dimension, Sphericity, Closest Pair, Fine-Grained Complexity}
}

Keywords: Contact dimension, Sphericity, Closest Pair, Fine-Grained Complexity
Seminar: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue date: 2018
Date of publication: 2018


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