Scheduling Unit–Time Tasks with Arbitrary Release Times and Deadlines

The basic problem considered is that of scheduling n unit-time tasks, with arbitrary release times and deadlines, so as to minimize the maximum task completion time. Previous work has shown that this problem can be solved rather easily when all release times are integers. We are concerned with the general case in which noninteger release times are allowed, a generalization that considerably increases the difficulty of the problem even for only a single processor. Our results are for the one-processor case, where we provide an $O(n\log n)$ algorithm based on the concept of “forbidden regions”.