On contiguous and non-contiguous parallel task scheduling

In this paper we study differences between contiguous and non-contiguous parallel task schedules. Parallel tasks can be executed on more than one processor simultaneously. In the contiguous schedules, indices of the processors assigned to a task must be a sequence of consecutive numbers. In the non-contiguous schedules, processor indices may be arbitrary. Optimum non-preemptive schedules are considered. Given a parallel task instance, the optimum contiguous and non-contiguous schedules can be of different lengths. We analyze minimal instances where such a difference may arise, provide bounds on the difference of the two schedules lengths, and prove that deciding whether the difference in schedule length exists is NP-complete.