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.
Dedicated to my teacher Kõváry Károly
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