Open AccessProceedings Article10.1145/73007.73043

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

- 01 Feb 1989

- pp 375-381

342

TL;DR: A randomised polynomial time algorithm for approximating the volume of a convex body K in n -dimensional Euclidean space and the proof of correctness of the algorithm relies on recent theory of rapidly mixing Markov chains and isoperimetric inequalities.

Abstract: 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.

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The authors present a randomised polynomial time algorithm for approximating the volume of a convex body K in n-dimensional Euclidean space.. In this paper the authors give an algorithm for approximating the volume of a convex body in Euclidean space.. Observe that the authors can make the failure probability as small as they like by repeatedly running the algorithm and taking the median value as output.

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References

•Book

An introduction to probability theory and its applications

William Feller

- 01 Jan 1950

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Elliptic Partial Differential Equations of Second Order

David Gilbarg, +1 more

- 07 Jan 2013

TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.

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20.4K

Journal Article•10.2307/2306534

An Introduction to Probability Theory and Its Applications.

A. T. Bharucha-Reid, +1 more

- 01 Apr 1952

- American Mathematical Monthly

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•Book Chapter•10.1007/978-1-4612-0865-5_26

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Wassily Hoeffding

- 01 Mar 1963

- Journal of the American Statistical Asso...

TL;DR: In this article, upper bounds for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt are derived for certain sums of dependent random variables such as U statistics.

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•Book

Geometric Algorithms and Combinatorial Optimization

Martin Grötschel, +2 more

- 01 Jan 1988

TL;DR: In this article, the Fulkerson Prize was won by the Mathematical Programming Society and the American Mathematical Society for proving polynomial time solvability of problems in convexity theory, geometry, and combinatorial optimization.

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

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AI Agents for this Paper

Most frequently asked questions

1. What are the contributions in "A random polynomial time algorithm for approximating the volume of convex bodies" ?

Citations

Selection of relevant features and examples in machine learning

Random Walks on Graphs: A Survey

Quantum random walks: an introductory overview

Reversible Markov Chains and Random Walks on Graphs

Approximating probabilistic inference in Bayesian belief networks is NP-hard

References

An introduction to probability theory and its applications

Elliptic Partial Differential Equations of Second Order

An Introduction to Probability Theory and Its Applications.

Probability Inequalities for sums of Bounded Random Variables

Geometric Algorithms and Combinatorial Optimization

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