Scheduling two irregular polygons (Q1104847)

The paper deals with the problem of scheduling two irregularly occuring events in such a way that the maximum (minimum) distance between two different events is minimized (maximized). Such a problem is important in constructing schedules for cyclic arrivals of trains, buses etc. It can be modelled by constructing two irregular polygons on some line and moving them in order to minimize (maximize) a distance between adjacent vertices. In the paper, two O(m\(\cdot n\cdot \log m)\) algorithms for the two above variants, are given (m, n being numbers of vertices of the two polygons).