# 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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