LIPIcs.STACS.2009.1817.pdf
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Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties
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26th International Symposium on Theoretical Aspects of Computer Science (STACS 2009)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NoDerivs 3.0 Unported license
- Publication Date: 2009-02-19
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Mahdi Cheraghchi and Amin Shokrollahi. Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 277-288, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/LIPIcs.STACS.2009.1817
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.
Subject Classification
Keywords
- Uniform sampling
- Algebraic varieties
- Randomized algorithms
- Computational complexity
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