Name
Abstract | ||
|---|---|---|
We show that the maximum combinatorial complexity of the space of hyperplane transversals to a family of n separated and strictly convex sets in Rd is &THgr;(n⌊d/2⌋), which generalizes results of Edelsbrunner and Sharir in the plane. As a key step in the argument, we show that the space of hyperplanes tangent to &kgr; ≤ d separated and strictly convex sets in Rd is a topological (d - &kgr;)-sphere. |
Year | DOI | Venue |
|---|---|---|
1990 | 10.1145/98524.98542 | Symposium on Computational Geometry 2013 |
Keywords | Field | DocType |
hyperplanes tangent,hyperplane transversals,key step,convex set,maximum combinatorial complexity | Discrete mathematics,Combinatorics,Combinatorial complexity,Half-space,Transversal (geometry),Convex function,Tangent,Hyperplane,Mathematics | Conference |
ISBN | Citations | PageRank |
0-89791-362-0 | 1 | 0.83 |
References | Authors | |
10 | 6 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sylvain E. Cappell | 1 | 1 | 1.17 |
| Jacob E. Goodman | 2 | 277 | 136.42 |
| János Pach | 3 | 2366 | 292.28 |
| R. Pollack | 4 | 32 | 4.11 |
| Micha Sharir | 5 | 8405 | 1183.84 |
| Rephael Wenger | 6 | 441 | 43.54 |