Parallel Scheduling for Early Completion

This chapter assumes knowledge of some basic scheduling terminology provided in Part I of this book.We are concerned in this chapter with classical deterministic parallel scheduling with the objectiveof minimizing the makespan. Both preemptive and nonpreemptive schedules are considered. Therecan be precedence relationships between jobs. Excluded from consideration in this chapter are paral-lel scheduling models of other typical job characteristics, on-line and randomized algorithms, all of whichare covered in separate chapters of this book. We will address the following aspects of the schedulingproblems: Polynomial solvability and approximability Enumerative algorithms Polynomial-time approximationsAlthough we also consider scheduling jobs of different release dates, we will mainly concentrate onmodels of equal job release dates. The reason is as follows. If all jobs are not released at the same time, thenthe scheduling problems of minimizing the makespan can be viewed as special cases of the correspondingproblems of minimizing maximum lateness, which is dealt with in a separate chapter. To see this, notethat due to schedule symmetry on the time axis, there is an equivalence relationship (with respect to theobjective value) between scheduling of the former objective and that of the latter: To a schedule