eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2009-02-19
277
288
10.4230/LIPIcs.STACS.2009.1817
article
Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties
Cheraghchi, Mahdi
Shokrollahi, Amin
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol003-stacs2009/LIPIcs.STACS.2009.1817/LIPIcs.STACS.2009.1817.pdf
Uniform sampling
Algebraic varieties
Randomized algorithms
Computational complexity