Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Covering a rectangle with six and seven circles
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
An energy aware coverage-preserving scheme for wireless sensor networks
PE-WASUN '05 Proceedings of the 2nd ACM international workshop on Performance evaluation of wireless ad hoc, sensor, and ubiquitous networks
IEEE Communications Magazine
Wireless Personal Communications: An International Journal
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In the context of mobile communication, an efficient algorithm for the base-station placement problem is developed in this paper. The objective is to place a given number of base-stations in a given convex region, and to assign range to each of them such that every point in the region is covered by at least one base-station, and the maximum range assigned is minimized. It is basically covering a region by a given number of equal radius circles where the objective is to minimize the radius. We develop an efficient algorithm for this problem using Voronoi diagram which works for covering a convex region of arbitrary shape. Existing results for this problem are available when the region is a square [K.J. Nurmela, P.R.J. Ostergard, Coveting a square with up to 30 equal circles, Research Report HUT-TCS-A62, Laboratory for Theoretical Computer Science, Helsinky University of Technology, 2000] and an equilateral triangle [K.J. Nurmela, Conjecturally optimal coverings of an equilateral triangle with up to 36 equal circles, Exp. Math. 9 (2) (2000)]. The minimum radius obtained by our method favorably compares with the results presented in [K.J. Nurmela, P.R.J. Ostergard, Covering a square with up to 30 equal circles, Research Report HUT-TCS-A62, Laboratory for Theoretical Computer Science, Helsinky University of Technology, 2000; K.J. Nurmela, Conjecturally optimal coverings of an equilateral triangle with up to 36 equal circles, Exp. Math. 9 (2) (2000)]. But the execution time of our algorithm is a fraction of a second, whereas the existing methods may even take about two weeks' time for a reasonable value of the number of circles (≥ 27) as reported in [K.J. Nurmela, P.R.J. Ostergard, Covering a square with up to 30 equal circles, Research Report HUT-TCS-A62, Laboratory for Theoretical Computer Science, Helsinky University of Technology, 2000; K.J. Nurmela, Conjecturally optimal coverings of an equilateral triangle with up to 36 equal circles, Exp. Math. 9 (2) (2000)].