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DOI: 10.4230/LIPIcs.STACS.2009.1817
URN: urn:nbn:de:0030-drops-18174
URL: http://drops.dagstuhl.de/opus/volltexte/2009/1817/
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Cheraghchi, Mahdi ; Shokrollahi, Amin

Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties

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Abstract

We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common zero of the polynomials almost uniformly at random. The statistical distance between the output distribution of the algorithm and the uniform distribution on the set of common zeros is polynomially small in the field size, and the running time of the algorithm is polynomial in the description of the polynomials and their degrees provided that the number of the polynomials is a constant.

BibTeX - Entry

@InProceedings{cheraghchi_et_al:LIPIcs:2009:1817,
  author =	{Mahdi Cheraghchi and Amin Shokrollahi},
  title =	{{Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{277--288},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Susanne Albers and Jean-Yves Marion},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/1817},
  URN =		{urn:nbn:de:0030-drops-18174},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2009.1817},
  annote =	{Keywords: Uniform sampling, Algebraic varieties, Randomized algorithms, Computational complexity}
}

Keywords: Uniform sampling, Algebraic varieties, Randomized algorithms, Computational complexity
Seminar: 26th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2009
Date of publication: 19.02.2009


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