A geometric inequality and the complexity of computing volume
- G. Elekes
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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.
- 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.
- L. Lovász,An Algorithmic Theory of Numbers, Graphs, and Convexity, AMS-SIAM Regional Conference Series, to appear.
- A geometric inequality and the complexity of computing volume
Discrete & Computational Geometry
Volume 1, Issue 1 , pp 289-292
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- G. Elekes (1)
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- 1. Mathematical Institute, Eötvös Loránd University, Muzeum krt. 6-8, H-1088, Budapest, Hungary