  We prove that for every centrally symmetric convex polygon Q, there exists a
constant alpha such that any alpha*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 (SoCG'07). The question is motivated by a sensor
network problem, in which a region has to be monitored by sensors with limited
battery lifetime.
