We prove that for every centrally symmetric convex polygon Q, there exists a constant α such that any locally finite α k-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 Toth. The question is motivated by a sensor network problem, in which a region has to be monitored by sensors with limited battery life.
['Greg Aloupis', 'Jean Cardinal', 'Sébastien Collette', 'Stefan Langerman', 'David Orden', 'Pedro P. Ramos']
Decomposition of Multiple Coverings into More Parts