Discrete & Computational Geometry

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

A geometric inequality and the complexity of computing volume

  • G. Elekes


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.


Polynomial Time Convex Hull Convex Body Polynomial Time Algorithm Discrete Comput Geom 
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    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
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    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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