The Art Gallery theorem for polygons with holes
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
The coverage problem in a wireless sensor network
WSNA '03 Proceedings of the 2nd ACM international conference on Wireless sensor networks and applications
Integrated coverage and connectivity configuration in wireless sensor networks
Proceedings of the 1st international conference on Embedded networked sensor systems
Connected sensor cover: self-organization of sensor networks for efficient query execution
IEEE/ACM Transactions on Networking (TON)
Minimum-cost coverage of point sets by disks
Proceedings of the twenty-second annual symposium on Computational geometry
Optimal Relay Location for Resource-limited Energy-efficient Wireless Communication
Journal of Global Optimization
Approximation algorithms for NP-complete problems on planar graphs
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Covering a line segment with variable radius discs
Computers and Operations Research
Polynomial time approximation schemes for base station coverage with minimum total radii
Computer Networks: The International Journal of Computer and Telecommunications Networking
The complexity of base station positioning in cellular networks
Discrete Applied Mathematics
Maximum lifetime coverage preserving scheduling algorithms in sensor networks
Journal of Global Optimization
Geometric clustering to minimize the sum of cluster sizes
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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In this paper, we consider the Radar Placement and Power Assignment problem (RPPA) along a river. In this problem, a set of crucial points in the river are required to be monitored by a set of radars which are placed along the two banks. The goal is to choose the locations for the radars and assign powers to them such that all the crucial points are monitored and the total power is minimized. If each crucial point is required to be monitored by at least k radars, the problem is a k-Coverage RPPA problem (k-CRPPA). Under the assumption that the river is sufficiently smooth, one may focus on the RPPA problem along a strip (RPPAS). In this paper, we present an O(n 9) dynamic programming algorithm for the RPPAS, where n is the number of crucial points to be monitored. In the special case where radars are placed only along the upper bank, we present an O(kn 5) dynamic programming algorithm for the k-CRPPAS. For the special case that the power is linearly dependent on the radius, we present an O(n log n)-time $${2\sqrt 2}$$ -approximation algorithm for the RPPAS.