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\(\varepsilon \)-Mnets: Hitting Geometric Set Systems with Subsets

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Abstract

The existence of Macbeath regions is a classical theorem in convex geometry  (Macbeath in Ann Math 56:269–293, 1952), with recent applications in discrete and computational geometry. In this paper, we initiate the study of Macbeath regions in a combinatorial setting and establish near-optimal bounds for several basic geometric set systems.

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Acknowledgements

The work of Nabil H. Mustafa in this paper has been supported by the Grant ANR SAGA (JCJC-14-CE25-0016-01).

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Authors and Affiliations

  1. Université Paris-Est, Laboratoire d’Informatique Gaspard-Monge, Equipe A3SI, ESIEE Paris, Noisy-le-Grand, France

    Nabil H. Mustafa

  2. Computer Science, New York University, Abu Dhabi, UAE

    Saurabh Ray

Authors
  1. Nabil H. Mustafa
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  2. Saurabh Ray
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Correspondence to Nabil H. Mustafa.

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Editor in Charge: János Pach

A preliminary version of this article appeared in [19].

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Mustafa, N.H., Ray, S. \(\varepsilon \)-Mnets: Hitting Geometric Set Systems with Subsets. Discrete Comput Geom 57, 625–640 (2017). https://doi.org/10.1007/s00454-016-9845-8

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  • DOI: https://doi.org/10.1007/s00454-016-9845-8

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