Covering the plane with convex polygons
Discrete & Computational Geometry
A coverage-preserving node scheduling scheme for large wireless sensor networks
WSNA '02 Proceedings of the 1st ACM international workshop on Wireless sensor networks and applications
Approximating the Domatic Number
SIAM Journal on Computing
PEAS: A Robust Energy Conserving Protocol for Long-lived Sensor Networks
ICDCS '03 Proceedings of the 23rd International Conference on Distributed Computing Systems
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
Polychromatic coloring for half-planes
Journal of Combinatorial Theory Series A
Polychromatic coloring for half-planes
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Maximizing network lifetime on the line with adjustable sensing ranges
ALGOSENSORS'11 Proceedings of the 7th international conference on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities
Changing of the guards: strip cover with duty cycling
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Brief announcement: set it and forget it - approximating the set once strip cover problem
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
Coloring hypergraphs induced by dynamic point sets and bottomless rectangles
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
ACM Transactions on Sensor Networks (TOSN)
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Let m(k) denote the smallest positive integer m such that any m-fold covering of the plane with axis-parallel unit squares splits into at least k coverings. J. Pach [J. Pach, Covering the plane with convex polygons, Discrete and Computational Geometry 1 (1986) 73-81] showed that m(k) exists and gave an exponential upper bound. We show that m(k)=O(k^2), and generalize this result to translates of any centrally symmetric convex polygon in the place of squares. From the other direction, we know only that m(k)=@?4k/3@?-1.