The scheduling of a set of tasks, with precedence constraints and known execution times, into a set of identical processors is considered. Optimal scheduling of these tasks implies utilizing a minimum number of processors to satisfy a deadline, or finishing in minimal time using a fixed number of processors. This process can be seen as a transformation of the original graph into another graph, whose precedences do not violate the optimality constraints and has a unique basic schedule. Analysis of this transformation provides insight into the scheduling process and also into the determination of lower bounds on the number of processors and on time for optimal schedules.
Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.