Scheduling Interval Ordered Tasks with Non-Uniform Deadlines

Garey and Johnson defined an algorithm that finds minimum-lateness schedules for arbitrary graphs with unit-length tasks on two processors. Their algorithm can be easily generalised to an algorithm that constructs minimumlateness schedules for interval orders on m processors. In this paper, we study the problem of scheduling interval orders with deadlines without neglecting the communication costs. An algorithm is presented that finds minimum-lateness schedules. Like the algorithm by Garey and Johnson, it first computes modified deadlines; these are used to assign a starting time to every task. Unlike the algorithm by Garey and Johnson, calculating a modified deadline for every individual task is not sufficient: in order to fully use the knowledge of the precedence constraints and the communication delays, the algorithm has to compute deadlines for pairs of tasks. The algorithm constructs minimum-lateness schedules in O(n2) time.