UET scheduling with unit interprocessor communication delays

Abstract We consider the problem of scheduling a partially ordered set of unit execution time (UET) tasks on m > 1 processors where there is a communication delay of unit time between any pair of distinct processors. We show that the problem of finding an optimal schedule is NP-hard. A greedy schedule is one where no processor remains idle if there is some task available which it could process. We establish that the length of an arbitrary greedy schedule, ω c g satisfies w c g 3− 2 m w c opt − 1− 1 m where ω c opt is the length of the optimal schedule. We define a generalized list schedule (a type of greedy schedule) and discuss anomalous behavour of such schedules with respect to speed-up. The relevance of these results to the implementation of parallel languages is discussed.