License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2016.31
URN: urn:nbn:de:0030-drops-68667
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6866/
Kumar, Nirman ;
Raichel, Benjamin ;
Suri, Subhash ;
Verbeek, Kevin
Most Likely Voronoi Diagrams in Higher Dimensions
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: |
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Uncertainty, Lower bounds, Voronoi Diagrams, Stochastic |
Collection: |
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36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016) |
Issue Date: |
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2016 |
Date of publication: |
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10.12.2016 |