On a circle-cover minimization problem

Given a set of n circular-arcs A₁, A₂,...,A_n, we consider the problem of finding a minimum number of circular-arcs whose union covers the circle. Specifically, if the endpoints of these n arcs are given, we show that O(n log n) is both sufficient and necessary for solving the minimum cover problem. Furthermore, with O(n log n) preprocessing time we find the minimum cover in O(n) time.