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

We present a randomised polynomial time algorithm for approximating the volume of a convex body K in n-dimensional Euclidean space. 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.

• Type: Conference
• Year: 1989
• Where: STOC
• Authors: Martin E. Dyer, Alan M. Frieze, Ravi Kannan
• Keywords: Algorithms, Certain Random Walk, N-dimensional Euclidean Space, Polynomial Time Algorithm, STOC 1989