Cheraghchi, Mahdi ;
Shokrollahi, Amin
AlmostUniform Sampling of Points on HighDimensional Algebraic Varieties
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 = {{AlmostUniform Sampling of Points on HighDimensional Algebraic Varieties}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {277288},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897095},
ISSN = {18688969},
year = {2009},
volume = {3},
editor = {Susanne Albers and JeanYves Marion},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2009/1817},
URN = {urn:nbn:de:0030drops18174},
doi = {http://dx.doi.org/10.4230/LIPIcs.STACS.2009.1817},
annote = {Keywords: Uniform sampling, Algebraic varieties, Randomized algorithms, Computational complexity}
}
2009
Keywords: 

Uniform sampling, Algebraic varieties, Randomized algorithms, Computational complexity 
Seminar: 

26th International Symposium on Theoretical Aspects of Computer Science

Related Scholarly Article: 


Issue date: 

2009 
Date of publication: 

2009 