Scheduling periodic events

Problem 1.1 is solved explicitly by Burkard [3] for the case n = 2 and for arbitrary n, but with at most two distinct values mi. Burkard attributes the problem to Guldan [S], who, in turn, attributes it to Cerny [4]. In [4,5] the problem is stated as follows: How should regular pi-gons, i= 1,2, . . . , n, be inscribed in a circle so as to maximize the distance between the closest vertices on the circle. In [3] the max-min polygon problem is generalized to minimizing the objective function