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Summary: Decomposition of Multiple Coverings into More Parts
Greg Aloupis
Jean Cardinal
S´ebastien Collette
Stefan Langerman
David Orden§
Pedro Ramos§
Abstract
We prove that for every centrally symmetric convex
polygon Q, there exists a constant such that any
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 T´oth
(SoCG'07). The question is motivated by a sensor
network problem, in which a region has to be monitored
by sensors with limited battery life.
1 Introduction
A collection of subsets of the plane forms a f-fold
covering if any point in the plane is covered by at least
f subsets. We consider the following problem (see
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