Abstract
The existence of Macbeath regions is a classical theorem in convex geometry ("A Theorem on nonhomogeneous lattices", Annals of Math, 1952). We refer the reader to the survey of I. Barany for several applications [3]. Recently there have been some striking applications of Macbeath regions in discrete and computational geometry. In this paper, we study Macbeath's problem in a more general setting, and not only for the Lebesgue measure as is the case in the classical theorem. We prove near-optimal generalizations for several basic geometric set systems. The problems and techniques used are closely linked to the study of ε-nets for geometric set systems.
| Original language | English |
|---|---|
| Title of host publication | 31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014 |
| Editors | Ernst W. Mayr, Natacha Portier |
| Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
| Pages | 578-589 |
| Number of pages | 12 |
| Volume | 25 |
| ISBN (Electronic) | 9783939897651 |
| DOIs | |
| State | Published - 1 Mar 2014 |
| Externally published | Yes |
| Event | 31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014 - Lyon, France Duration: 5 Mar 2014 → 8 Mar 2014 |
Conference
| Conference | 31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014 |
|---|---|
| Country/Territory | France |
| City | Lyon |
| Period | 5/03/14 → 8/03/14 |
Keywords
- Convex Geometry
- Cuttings
- Epsilon Nets
- Geometric Set systems
- Union Complexity
ASJC Scopus subject areas
- Software
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