Summary: The problem of finding a minimum cut of n arcs on a unit circle is considered. It is shown that this problem can be solved in \(\Theta\) (n log n) time, which is optimal to within a constant factor. If the endpoints of the arcs are sorted, the problem can be solved in linear time. The solution to the minimum cut problem can be used to solve a minimum new facility problem in competitive location and a minimum partition set problem for the intersection model of a circle graph. As a by-product it is also shown that the maximum independent set of n arcs can be obtained in linear time, assuming the endpoints are sorted, which is much simpler than the most recent result of \textit{S. Masuda} and \textit{K. Nakajima} [SIAM J. Comput. 17, No.1, 41-52 (1988; Zbl 0646.68084)].