A random polynomial-time algorithm for approximating the volume of convex bodies

@article{Dyer1989ARP,
  title={A random polynomial-time algorithm for approximating the volume of convex bodies},
  author={Martin E. Dyer and Alan M. Frieze and Ravi Kannan},
  journal={J. ACM},
  year={1989},
  volume={38},
  pages={1-17}
}
A randomized polynomial-time algorithm for approximating the volume of a convex body <italic>K</italic> in <italic>n</italic>-dimensional Euclidean space is presented. The proof of correctness of the algorithm relies on recent theory of rapidly mixing Markov chains and isoperimetric inequalities to show that a certain random walk can be used to sample nearly uniformly from within <italic>K</italic>. 

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