Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties
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.
Uniform sampling
Algebraic varieties
Randomized algorithms
Computational complexity
277-288
Regular Paper
Mahdi
Cheraghchi
Mahdi Cheraghchi
Amin
Shokrollahi
Amin Shokrollahi
10.4230/LIPIcs.STACS.2009.1817
Creative Commons Attribution-NoDerivs 3.0 Unported license
https://creativecommons.org/licenses/by-nd/3.0/legalcode