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Communication Dans Un Congrès Année : 2014

Near-Optimal Generalisations of a Theorem of Macbeath

Résumé

The existence of Macbeath regions is a classical theorem in convex geometry ("A Theorem on non-homogeneous lattices'', Annals of Math, 1952). We refer the reader to the survey of I. Barany for several applications~\cite{B07}. 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 epsilon-nets for geometric set systems.
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Dates et versions

hal-01026333 , version 1 (21-07-2014)

Identifiants

  • HAL Id : hal-01026333 , version 1

Citer

Nabil Mustafa, Saurabh Ray. Near-Optimal Generalisations of a Theorem of Macbeath. Proc. of the 31st International Symposium on Theoretical Aspects of Computer Science (STACS '14), 2014., Mar 2014, France. pp.578-589. ⟨hal-01026333⟩
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