A Random Polynomial-Time Algorithm for Approximating the Volume of Convex Bodies

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. © 1991, ACM. All rights reserved.