Abstract
The volume of the convex hull of anym points of ann-dimensional ball with volumeV is at mostV·m/2n. 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.
Article PDF
Similar content being viewed by others
References
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.
Author information
Authors and Affiliations
Additional information
Dedicated to my teacher Kõváry Károly
Rights and permissions
About this article
Cite this article
Elekes, G. A geometric inequality and the complexity of computing volume. Discrete Comput Geom 1, 289–292 (1986). https://doi.org/10.1007/BF02187701
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02187701