License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.SOSA.2019.9
URN: urn:nbn:de:0030-drops-100358
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/10035/
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Barba, Luis ; Mulzer, Wolfgang

Asymmetric Convex Intersection Testing

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OASIcs-SOSA-2019-9.pdf (0.6 MB)

Abstract

We consider asymmetric convex intersection testing (ACIT).
Let P subset R^d be a set of n points and H a set of n halfspaces in d dimensions. We denote by {ch(P)} the polytope obtained by taking the convex hull of P, and by {fh(H)} the polytope obtained by taking the intersection of the halfspaces in H. Our goal is to decide whether the intersection of H and the convex hull of P are disjoint. Even though ACIT is a natural variant of classic LP-type problems that have been studied at length in the literature, and despite its applications in the analysis of high-dimensional data sets, it appears that the problem has not been studied before.
We discuss how known approaches can be used to attack the ACIT problem, and we provide a very simple strategy that leads to a deterministic algorithm, linear on n and m, whose running time depends reasonably on the dimension d.

BibTeX - Entry

@InProceedings{barba_et_al:OASIcs:2018:10035,
  author =	{Luis Barba and Wolfgang Mulzer},
  title =	{{Asymmetric Convex Intersection Testing}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{9:1--9:14},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{69},
  editor =	{Jeremy T. Fineman and Michael Mitzenmacher},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10035},
  URN =		{urn:nbn:de:0030-drops-100358},
  doi =		{10.4230/OASIcs.SOSA.2019.9},
  annote =	{Keywords: polytope intersection, LP-type problem, randomized algorithm}
}

Keywords: polytope intersection, LP-type problem, randomized algorithm
Collection: 2nd Symposium on Simplicity in Algorithms (SOSA 2019)
Issue Date: 2018
Date of publication: 08.01.2019

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