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Deterministic and randomized polynomial-time approximation of radii

Part of: Polytopes and polyhedra

Published online by Cambridge University Press:  26 February 2010

Andreas Brieden ,
Peter Gritzmann ,
Ravindran Kannan ,
Victor Klee ,
László Lovász  and
Miklós Simonovits
Andreas Brieden
Affiliation:
Zentrum Mathematik, Technische Universitôt München, D-80290 Munich, Gernmany E-mail: brieden@mathematik.tu-muenchen.de
Peter Gritzmann
Affiliation:
Zentrum Mathematik, Technische Universitôt München, D-80290 Munich, Gernmany E-mail: brieden@mathematik.tu-muenchen.de
Ravindran Kannan
Affiliation:
Department of Computer Science, Yale University, New Haven. CT 06520, U.S.A. E-mail: kannan@cs.yale.edu
Victor Klee
Affiliation:
Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, U.S.A. E-mail: klee@math.washington.edu
László Lovász
Affiliation:
Microsoft Research, One Microsoft Way, Redmond, WA 98053, U.S.A. E-mail: lovasz@microsoft.com
Miklós Simonovits
Affiliation:
Alfréd Renyi Institute of Mathematics, Reáltanoda u. 13-15, H-1053, Budapest, Hungary E-mail: miki@math-inst.hu

Abstract

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This paper is concerned with convex bodies in n-dimensional lp, spaces, where each body is accessible only by a weak separation or optimization oracle. It studies the asymptotic relative accuracy, as n→∞, of polynomial-time approximation algorithms for the diameter, width, circumradius, and inradius of a body K, and also for the maximum of the norm over K.

MSC classification

Secondary: 52B55: Computational aspects related to convexity
Type
Research Article
Information
Mathematika , Volume 48 , Issue 1-2 , December 2001 , pp. 63 - 105
Copyright
Copyright © University College London 2001

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