Efficient Construction of Minimum Makespan Schedules for Tasks with a Fixed Number of Distinct Execution Times

Abstract.

This paper addresses scheduling problems for tasks with release and execution times. We present a number of efficient and easy to implement algorithms for constructing schedules of minimum makespan when the number of distinct task execution times is fixed. For a set of independent tasks, our algorithm in the single processor case runs in time linear in the number of tasks; with precedence constraints, our algorithm runs in time linear in the sum of the number of tasks and the size of the precedence constraints. In the multi-processor case, our algorithm constructs minimum makespan schedules for independent tasks with uniform execution times. The algorithm runs in O(n log  m) time where n is the number of tasks and m is the number of processors.