Article révisé par les pairs
Résumé : 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. © 2010 Springer Science+Business Media, LLC.