Scheduling interval-ordered tasks with non-uniform deadlines subject to non-zero communication delays

We study the problem of scheduling unit-length interval-ordered tasks subject to unit-length communication delays with the objective of minimising the maximum tardiness. Without communication delays, this problem can be solved by a generalisation of an algorithm presented by Garey and Johnson. In this paper, an algorithm is presented that considers unit-length communication delays and constructs minimum-tardiness schedules in O(n 2) time. Like the algorithm of Garey and Johnson, it computes smaller deadlines and uses these to assign a starting time to every task. Unlike the algorithm of Garey and Johnson, calculating a deadline for individual tasks is not suucient: to fully use the knowledge of the communication delays, the algorithm computes deadlines for pairs of tasks.