10.4230/LIPICS.STACS.2009.1817
Cheraghchi, Mahdi
Mahdi
Cheraghchi
Shokrollahi, Amin
Amin
Shokrollahi
Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
2009
Article
Uniform sampling
Algebraic varieties
Randomized algorithms
Computational complexity
Albers, Susanne
Susanne
Albers
Marion, Jean-Yves
Jean-Yves
Marion
2009
2009-02-19
2009-02-19
2009-02-19
en
urn:nbn:de:0030-drops-18174
10.4230/LIPIcs.STACS.2009
978-3-939897-09-5
1868-8969
10.4230/LIPIcs.STACS.2009
LIPIcs, Volume 3, STACS 2009
26th International Symposium on Theoretical Aspects of Computer Science
2013
3
22
277
288
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Albers, Susanne
Susanne
Albers
Marion, Jean-Yves
Jean-Yves
Marion
1868-8969
Leibniz International Proceedings in Informatics (LIPIcs)
2009
3
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
12 pages
191051 bytes
application/pdf
Creative Commons Attribution-NoDerivs 3.0 Unported license
info:eu-repo/semantics/openAccess
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.
LIPIcs, Vol. 3, 26th International Symposium on Theoretical Aspects of Computer Science, pages 277-288