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
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 Axis-Parallel Rectangles
Computational Geometry and Graph Theory
Decomposition of multiple coverings into more parts
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
Coloring geometric range spaces
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Notes: Coloring axis-parallel rectangles
Journal of Combinatorial Theory Series A
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Conflict-Free coloring made stronger
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
More is more: The benefits of denser sensor deployment
ACM Transactions on Sensor Networks (TOSN)
Coloring planar homothets and three-dimensional hypergraphs
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Coloring planar homothets and three-dimensional hypergraphs
Computational Geometry: Theory and Applications
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Suppose that the whole plane (or a large region) is monitored by aset S of stationary sensors such that each element s ∈ S canobserve an axis-parallel unit square R(s) centered at s, whichis called the range of s. Each sensor s is equipped witha battery of unit lifetime. Is it true that if every point of theplane belongs to the range of many sensors, then we can monitorthe plane for a long time without running out of power? If S canbe partitioned into k parts S1, S2,..., Sk such that, foreach i, the sensors in Si together can observe the wholeplane, then the plane can be monitored with no interruption fork units of time. Indeed, we can first switch on all sensorsbelonging to S1. After these sensors run out of battery, we canswitch on all elements of S2, etc.We arrive at the following problem. Let m(k) denote the smallestpositive integer m such that any m-fold covering of the planewith axis-parallel unit squares splits into at least kcoverings. We show that m(k)=O(k2), and generalize this resultto translates of any centrally symmetric convex polygon in theplace of squares. From the other direction, we know only that m(k) ≥ ⌊4k/3⌋ -1.