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

Authors:
Martin Dyer;Alan Frieze;Ravi Kannan
Affiliations:
Univ. of Leeds, UK;Carnegie-Mellon Univ., Pittsburgh, PA;Carnegie-Mellon Univ., Pittsburgh, PA
Venue:
Journal of the ACM (JACM)
Year:
1991

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Abstract

A randomized polynomial-time algorithm for approximating the volume of a convex body K in n-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 K.