The Complexity of Preemptive Scheduling Given Interprocessor Communication Delays

Abstract We discuss the problem of scheduling af set of independent tasks T, each t i ϵ T of lenght l i ϵ Z + , on m identical processors. We allow preemption but assume a communication delay of time k ϵ N . Whenever a task is preempted from one processor to another, there must be a delay of at least k time units. We show that if k = 1, an optimal schedule can be found in polynomial time but if k ⩾ 2, the corresponding decision problem is NP-complete.