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On the complexity of two circle strongly connecting problems

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1 Author(s)
Nen-Fu Huang ; Dept. of Comput. Sci., Nat. Tsing Hua Univ., Hsinchu, Taiwan

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 ν1 in V stands for the point pi, and a directed edge ⟨νi, νj⟩ in E, if and only if pj located within the circle of p 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 ⟨νi, νj⟩ in E, if and only if pj is located within the circle of pi and no obstacles exist between them. It is proven that both these geometric problems are NP-hard. An O( n log n) approximation algorithm that can produce a solution no greater than twice an optimal one is also proposed

Published in:

IEEE Transactions on Computers  (Volume:41 ,  Issue: 9 )