Discrete & Computational Geometry

, Volume 44, Issue 3, pp 706–723 | Cite as

Decomposition of Multiple Coverings into More Parts

  • Greg Aloupis
  • Jean Cardinal
  • Sébastien Collette
  • Stefan Langerman
  • David Orden
  • Pedro Ramos
Article

Abstract

We prove that for every centrally symmetric convex polygon Q, there exists a constant α such that any locally finite αk-fold covering of the plane by translates of Q can be decomposed into k coverings. This improves on a quadratic upper bound proved by Pach and Tóth. The question is motivated by a sensor network problem, in which a region has to be monitored by sensors with limited battery life.

Keywords

Cover decomposition Geometric hypergraphs Centrally symmetric polygons 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Greg Aloupis
    • 1
  • Jean Cardinal
    • 1
  • Sébastien Collette
    • 1
  • Stefan Langerman
    • 1
  • David Orden
    • 2
  • Pedro Ramos
    • 2
  1. 1.Université Libre de Bruxelles (ULB)BruxellesBelgium
  2. 2.Universidad de AlcaláAlcaláSpain

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