Scheduling Dyadic Intervals

We consider the problem of computing the shortest schedule of the intervals [j2-‘, (j + 1)2-‘), for 0 < j < 2’ 1 and 1 < i < k such that separation of intersecting intervals is at least R. This problem arises in an application of wavelets to medical imaging. It is a generalization of the graph separation problem for the intersection graph of the intervals, which is to assign the numbers 1 to Zkfl 2 to the vertices, other than the root, of a complete binary tree of height k in such a way as to maximize the minimum difference between all ancestor descendent pairs. We give an efficient algorithm to construct optimal schedules.