License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.FSTTCS.2016.31
URN: urn:nbn:de:0030-drops-68667
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6866/
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Kumar, Nirman ; Raichel, Benjamin ; Suri, Subhash ; Verbeek, Kevin

Most Likely Voronoi Diagrams in Higher Dimensions

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Abstract

The Most Likely Voronoi Diagram is a generalization of the well known Voronoi Diagrams to a stochastic setting, where a stochastic point is a point associated with a given probability of existence, and the cell for such a point is the set of points which would classify the given point as its most likely nearest neighbor. We investigate the complexity of this subdivision of space in d dimensions. We show that in the general case, the complexity of such a subdivision is Omega(n^{2d}) where n is the number of points. This settles an open question raised in a recent (ISAAC 2014) paper of Suri and Verbeek, which first defined the Most Likely Voronoi Diagram. We also show that when the probabilities are assigned using a random permutation of a fixed set of values, in expectation the complexity is only ~O(n^{ceil{d/2}}) where the ~O(*) means that logarithmic factors are suppressed. In the worst case, this bound is tight up to polylog factors.

BibTeX - Entry

@InProceedings{kumar_et_al:LIPIcs:2016:6866,
  author =	{Nirman Kumar and Benjamin Raichel and Subhash Suri and Kevin Verbeek},
  title =	{{Most Likely Voronoi Diagrams in Higher Dimensions}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Akash Lal and S. Akshay and Saket Saurabh and Sandeep Sen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6866},
  URN =		{urn:nbn:de:0030-drops-68667},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.31},
  annote =	{Keywords: Uncertainty, Lower bounds, Voronoi Diagrams, Stochastic}
}

Keywords: Uncertainty, Lower bounds, Voronoi Diagrams, Stochastic
Collection: 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)
Issue Date: 2016
Date of publication: 10.12.2016

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