A random polynomial-time algorithm for approximating the volume of convex bodies-Reference-Cited by-同舟云学术

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

Published:1991-01-03 Issue:1 Volume:38 Page:1-17
ISSN:0004-5411
Container-title:Journal of the ACM
language:en
Short-container-title:J. ACM

Author:

Dyer Martin¹,Frieze Alan²,Kannan Ravi²

Affiliation:

1. Univ. of Leeds, UK

2. Carnegie-Mellon Univ., Pittsburgh, PA

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 .

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Link

https://dl.acm.org/doi/pdf/10.1145/102782.102783

Reference16 articles.

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3. How hard is it to marry at random? (On the approximation of the permanent)

4. ~DYER M E. AND FRIEZE h.M. On the complexity of computing the volume of a polyhedron. ~S1AMJ Com?ut 17 5 (Oct. 1988) 967-975. 10.1137/0217060 ~DYER M E. AND FRIEZE h.M. On the complexity of computing the volume of a polyhedron. ~S1AMJ Com?ut 17 5 (Oct. 1988) 967-975. 10.1137/0217060

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