Name
Abstract | ||
|---|---|---|
This paper is concerned with the various inner and outer radii of a convex body C in a d-dimensional normed space. The inner j-radius r(j)(C) is the radius of a largest j-ball contained in C, and the outer j-radius R(j)(C) measures how well C can be approximated, in a minimax sense, by a (d-j)-flat. In particular, r(d)(C) and R(d)(C) are the usual inradius and circumradius of C, while 2r1(C) and 2R1(C) are C's diameter and width.Motivation for the computation of polytope radii has arisen from problems in computer science and mathematical programming. The radii of polytopes are studied in [GK1] and [GK2] from the viewpoint of the theory of computational complexity. This present paper establishes the basic geometric and algebraic properties of radii that are needed in that study. |
Year | DOI | Venue |
|---|---|---|
1992 | 10.1007/BF02187841 | Discrete & Computational Geometry |
Keywords | Field | DocType |
finite-dimensional normed space,outer j-radii,convex body,normed space | Extreme point,Topology,Combinatorics,Normed vector space,Convex body,Strictly convex space,Regular polygon,Circumscribed circle,Polytope,Convex polytope,Mathematics | Journal |
Volume | Issue | ISSN |
7 | 3 | 0179-5376 |
Citations | PageRank | References |
33 | 3.32 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Peter Gritzmann | 1 | 412 | 46.93 |
| Victor Klee | 2 | 169 | 17.23 |