Betke, U., and Henk, M., Approximating the Volume of Convex Bodies, Discrete Computational Geometry, Vol. 10, pp. 15--21, 1993. Home/Search Document Not in Database Summary Related Articles Check |
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The Complexity of Yamnitsky and Levin's Simplices Algorithm - Bartels (1995) (Correct)
....one immediately gets bounds with a relative error that is arbitrarily close to n n . This compares favourably with the 23 relative error n 3n=2 from a corresponding algorithm based on the ellipsoid method (see [9] The method is, however, worse than an algorithm by U. Betke and M. Henk [4] that produces bounds with a relative error that is arbitrarily close to n . A different approach based on Markov chains was used in algorithms given in [7] and [14] The bounds from these methods have a relative error that is arbitrarily small, but they can only be guaranteed with a certain ....
U. Betke and M. Henk, Approximating the volume of convex bodies, Discrete Comput. Geom. 10 (1993), 15-21.
On The Complexity Of Computing Mixed Volumes - Dyer, Gritzmann, Hufnagel (1998) (16 citations) (Correct)
....complexity theory it is not. Theorems 6 and 7 show that the problem of computing any specific mixed volume of polytopes (or zonotopes) is #P easy. Section 2 will also discuss the problem of how e#ciently mixed volumes can be approximated by means of deterministic algorithms. GLS88] AK90] and [BH93] 358 MARTIN DYER, PETER GRITZMANN, AND ALEXANDER HUFNAGEL give exponential upper bounds for the error of deterministic polynomial approximations of the volume, and [BF86] gives an almost matching lower bound in the oracular model. We discuss possible extensions to mixed volumes and derive a ....
U. BETKE AND M. HENK, Approximating the volume of convex bodies, Discrete Comput. Geom., 10 (1993), pp. 15--21.
Minimum-Volume Enclosing Ellipsoids and Core - Sets Kumar And (Correct)
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Betke, U., and Henk, M., Approximating the Volume of Convex Bodies, Discrete Computational Geometry, Vol. 10, pp. 15--21, 1993.
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