Set k-cover algorithms for energy efficient monitoring in wireless sensor networks
Proceedings of the 3rd international symposium on Information processing in sensor networks
OPT Versus LOAD in Dynamic Storage Allocation
SIAM Journal on Computing
Decomposition of multiple coverings into many parts
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Decomposition of multiple coverings into many parts
Computational Geometry: Theory and Applications
Decomposition of multiple coverings into more parts
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Coloring geometric range spaces
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Weighted geometric set cover via quasi-uniform sampling
Proceedings of the forty-second ACM symposium on Theory of computing
Cover-decomposition and polychromatic numbers
ESA'11 Proceedings of the 19th European conference on Algorithms
Polychromatic coloring for half-planes
Journal of Combinatorial Theory Series A
Single and multiple device DSA problems, complexities and online algorithms
Theoretical Computer Science
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
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
A better approximation ratio and an IP formulation for a sensor cover problem
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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
Octants are cover-decomposable into many coverings
Computational Geometry: Theory and Applications
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Suppose we are given a set of objects that cover a region and a duration associated with each object. Viewing the objects as jobs, can we schedule their beginning times to maximize the length of time that the original region remains covered? We call this problem the SENSOR COVER PROBLEM. It arises in the context of covering a region with sensors. For example, suppose you wish to monitor activity along a fence (interval) by sensors placed at various fixed locations. Each sensor has a range (also an interval) and limited battery life. The problem is then to schedule when to turn on the sensors so that the fence is fully monitored for as long as possible. This one-dimensional problem involves intervals on the real line. Associating a duration to each yields a set of rectangles in space and time, each specified by a pair of fixed horizontal endpoints and a height. The objective is to assign a bottom position to each rectangle (by moving them up or down) so as to maximize the height at which the spanning interval is fully covered. We call this one-dimensional problem RESTRICTED STRIP COVERING. If we replace the covering constraint by a packing constraint (rectangles may not overlap, and the goal is to minimize the highest point covered), then the problem becomes identical to DYNAMIC STORAGE ALLOCATION, a well-studied scheduling problem, which is in turn a restricted case of the well known problem STRIP PACKING. We present a collection of algorithms for RESTRICTED STRIP COVERING. We show that the problem is NP-hard and present an O(log log log n)-approximation algorithm. We also present better approximation or exact algorithms for some special cases, including when all intervals have equal width. For the general SENSOR COVER PROBLEM, we distinguish between cases in which elements have uniform or variable durations. The results depend on the structure of the region to be covered: We give a polynomial-time, exact algorithm for the uniform-duration case of RESTRICTED STRIP COVERING but prove that the uniform-duration case for higher-dimensional regions is NP-hard. We give some more specific results for two-dimensional regions. Finally, we consider regions that are arbitrary sets, and we present an O(log n)-approximation algorithm for the most general case.