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NenFu Huang, "On the Complexity of Two Circle Strongly Connecting Problems," IEEE Transactions on Computers, vol. 41, no. 9, pp. 11851188, September, 1992.  
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@article{ 10.1109/12.165400, author = {NenFu Huang}, title = {On the Complexity of Two Circle Strongly Connecting Problems}, journal ={IEEE Transactions on Computers}, volume = {41}, number = {9}, issn = {00189340}, year = {1992}, pages = {11851188}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.165400}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  On the Complexity of Two Circle Strongly Connecting Problems IS  9 SN  00189340 SP1185 EP1188 EPD  11851188 A1  NenFu Huang, PY  1992 KW  complexity; circle strongly connecting problems; demand points; plane; radius; digraph; directed edge; NPhard; approximation algorithm; computational complexity; computational geometry; directed graphs. VL  41 JA  IEEE Transactions on Computers ER   
Given n demand points in the plane, the circle strongly connecting problem (CSCP) is to locate n circles in the plane, each with its center in a different demand point, and determine the radius of each circle such that the corresponding digraph G=(V, E), in which a vertex nu /sub 1/ in V stands for the point p/sub i/, and a directed edge ( nu /sub i/, nu /sub j/) in E, if and only if p/sub j/ located within the circle of p/sub i/, is strongly connected, and the sum of the radii of these n circles is minimal. The constrained circle strongly connecting problem is similar to the CSCP except that the points are given in the plane with a set of obstacles and a directed edge ( nu /sub i/, nu /sub j/) in E, if and only if p/sub j/ is located within the circle of p/sub i/ and no obstacles exist between them. It is proven that both these geometric problems are NPhard. An O(n log n) approximation algorithm that can produce a solution no greater than twice an optimal one is also proposed.
[1] R. C. Chang and R. C. T. Lee, "AnO(nlogn) minimal spanning tree algorithm for n points in the plane,"BIT, vol. 26, pp. 716, 1986.
[2] L. P. Chew, "Constrained Delaunay triangulations,"Algorithmica, vol. 4, pp. 97108, 1989.
[3] M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to Theory of NPCompleteness. San Francisco, CA: Freeman, 1979.
[4] D. T. Lee and B. J. Schachter, "Two algorithms for constructing Delaunay triangulations,"Int. J. Comput. Inform. Sci., vol. 9, no. 3, pp. 219242, 1980.
[5] A. Lingas, "Voronoi diagrams with barriers and the shortest diagonal problem,"Inform. Processing Lett., vol. 32, pp. 191198, 1989.
[6] N. Megiddo and K. J. Supowit, "On the complexity of some common geometric location problems,"SIAM J. Comput., vol. 13, no. 1, pp. 182196, 1984.
[7] M. I. Shamos,Computational Geometry, New York: SpringerVerlag, 1977.
[8] C. Wang and L. Schubert, "An optimal algorithm for constructing the Delaunay triangulation of a set of line segments," inProc. 3rd ACM Symp. Computat. Geometry, Waterloo, 1987, pp. 223232.
[9] D. W. Wang and Y. S. Kuo, "A study on two geometric location problems,"Inform. Processing Lett., vol. 28, pp. 281286, 1988.