Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties

Details Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties

2009-02-07

arxiv.org/abs/0902.1254v1

26th International Symposium on Theoretical Aspects of Computer Science STACS 2009 (2009) 277-288

Computer Science

Data Structures and Algorithms

Scientific paper

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.

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