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Discrete & Computational Geometry

, Volume 1, Issue 4, pp 289–292 | Cite as

A geometric inequality and the complexity of computing volume

  • G. Elekes
Article

Abstract

The volume of the convex hull of anym points of ann-dimensional ball with volumeV is at mostV·m/2 n . This implies that no polynomial time algorithm can compute the volume of a convex set (given by an oracle) with less than exponential relative error. A lower bound on the complexity of computing width can also be deduced.

Keywords

Polynomial Time Convex Hull Convex Body Polynomial Time Algorithm Discrete Comput Geom 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [GLS]
    M. Grötschel, L. Lovász, and A. Schrijver, Geometric methods in combinatorial optimization, inProgress in Combinatorial Optimization, Vol. 1 (W. R. Pulleyblank, ed.), 167–183, Academic Press, New York, 1984.Google Scholar
  2. [L]
    L. Lovász,An Algorithmic Theory of Numbers, Graphs, and Convexity, AMS-SIAM Regional Conference Series, to appear.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • G. Elekes
    • 1
  1. 1.Mathematical InstituteEötvös Loránd UniversityBudapestHungary

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