Art gallery theorems and algorithms
Art gallery theorems and algorithms
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)
A polynomial-time approximation scheme for base station positioning in UMTS networks
DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
A Geometric Theorem for Network Design
IEEE Transactions on Computers
Minimum-cost coverage of point sets by disks
Proceedings of the twenty-second annual symposium on Computational geometry
The coverage problem in a wireless sensor network
Mobile Networks and Applications
Coverage in wireless ad hoc sensor networks
IEEE Transactions on Computers
2-Covered paths by a set of antennas with minimum power transmission range
Information Processing Letters
Projected Perspective Reformulations with Applications in Design Problems
Operations Research
Radar placement along banks of river
Journal of Global Optimization
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The paper addresses the problem of locating sensors with a circular field of view so that a given line segment is under full surveillance, which is termed as the disc covering problem on a line. The cost of each sensor includes a fixed component f, and a variable component that is a convex function of the diameter of the field-of-view area. When only one type of sensor or, in general, one type of disc, is available, then a simple polynomial algorithm solves the problem. When there are different types of sensors, the problem becomes hard. A branch-and-bound algorithm as well as an efficient heuristic are developed for the special case in which the variable cost component of each sensor is proportional to the square of the measure of the field-of-view area. The heuristic very often obtains the optimal solution as shown in extensive computational testing. Scope and purpose: Problems of locating facilities to cover sets of points on networks and planes have been widely studied. This paper focuses on a new covering problem that is motivated by an application where a line segment is to be kept under surveillance using different types of radars. Using reasonable assumptions, some nonlinear covering problems are formulated. Efficient exact algorithms and heuristics are developed and analyzed for ''easy'' and ''hard'' cases, respectively.