Covering the plane with convex polygons
Discrete & Computational Geometry
Decomposition of multiple coverings into many parts
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Restricted strip covering and the sensor cover problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Multiple Coverings of the Plane with Triangles
Discrete & Computational Geometry
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
Coloring geometric range spaces
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Approximation Algorithms for Domatic Partitions of Unit Disk Graphs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Weighted geometric set cover via quasi-uniform sampling
Proceedings of the forty-second ACM symposium on Theory of computing
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Polychromatic coloring for half-planes
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
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We prove that for every centrally symmetric convex polygon Q, there exists a constant α such that any 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 (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.