Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Cheng, Siu-Wing; Wong, Man Ting https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-154418
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Self-Improving Voronoi Construction for a Hidden Mixture of Product Distributions

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Abstract

We propose a self-improving algorithm for computing Voronoi diagrams under a given convex distance function with constant description complexity. The n input points are drawn from a hidden mixture of product distributions; we are only given an upper bound m = o(√n) on the number of distributions in the mixture, and the property that for each distribution, an input instance is drawn from it with a probability of Ω(1/n). For any ε ∈ (0,1), after spending O(mn log^O(1)(mn) + m^ε n^(1+ε) log(mn)) time in a training phase, our algorithm achieves an O(1/ε n log m + 1/ε n 2^O(log^* n) + 1/ε H) expected running time with probability at least 1 - O(1/n), where H is the entropy of the distribution of the Voronoi diagram output. The expectation is taken over the input distribution and the randomized decisions of the algorithm. For the Euclidean metric, the expected running time improves to O(1/ε n log m + 1/ε H).

BibTeX - Entry

@InProceedings{cheng_et_al:LIPIcs.ISAAC.2021.8,
  author =	{Cheng, Siu-Wing and Wong, Man Ting},
  title =	{{Self-Improving Voronoi Construction for a Hidden Mixture of Product Distributions}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{8:1--8:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15441},
  URN =		{urn:nbn:de:0030-drops-154418},
  doi =		{10.4230/LIPIcs.ISAAC.2021.8},
  annote =	{Keywords: entropy, Voronoi diagram, convex distance function, hidden mixture of product distributions}
}

Keywords: entropy, Voronoi diagram, convex distance function, hidden mixture of product distributions
Seminar: 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
Issue date: 2021
Date of publication: 30.11.2021


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