Scheduling Dyadic Intervals

Abstract We consider the problem of computing the shortest schedule of the intervals [ j 2 − i ,( j + 1)2 − i ), for 0 ⩽ j ⩽ 2 i − 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 2 k + 1 − 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.