文章基本信息

标题：Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties
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作者：Mahdi Cheraghchi ; Amin Shokrollahi
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2009
卷号：3
页码：277-288
DOI：10.4230/LIPIcs.STACS.2009.1817
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Uniform sampling; Algebraic varieties; Randomized algorithms; Computational complexity