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

  title={Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties},
  author={Mahdi Cheraghchi and A. Shokrollahi},
  • 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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