Finding strongly connected components of circle cover graph in one-dimensional

Given a set C={c₁, c₂, . . ., c_n} of n circles in the plane, the circle cover graph is the digraph G(C)=(V, E) where a vertex υ_i in V stands for the center of circle c_i, and a directed edge <υ_i, υ_j> in E if and only if circle c_i covers the center of circle c_j. The authors propose an O (n log n) algorithm with O(n) space to find all the strongly connected components of G(C) for the one-dimensional case. Based on this result, the time complexity of the algorithm proposed by N.F. Huang, C.H. Huang (Inf. Process. Lett., vol.40, p.13-20, October, 1991) to solve the repeaters allocation problem for one-dimensional case can be improved from O(n log n+e) to O(n log n); where e is the number of edges in G(C)