• DOI:10.4230/LIPIcs.STACS.2009.1817
Corpus ID: 15619408

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

@inproceedings{Cheraghchi2009AlmostUniformSO,
  title={Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties},
  author={Mahdi Cheraghchi and A. Shokrollahi},
  booktitle={STACS},
  year={2009}
}

Mahdi Cheraghchi, A. Shokrollahi

Published in STACS 2009

Mathematics, Computer Science

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… CONTINUE READING

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