The Power of Choice in Scheduling Parallel Tasks

A malleable parallel task is one that can be executed on any number of processors, with its execution time being a function of the number of processors allotted to it. A nonmalleable parallel task is one that requires a speciic number of processors. Given n independent parallel tasks and m identical processors, we consider the problem of scheduling these tasks to minimize average completion time. Even though this is a classical scheduling problem, the rst results in this direction were obtained only recently They presented an algorithm for scheduling nonmalleable parallel tasks with an approximation factor of 32. We give an algorithm for scheduling malleable tasks that has an approximation factor of 2, under the assumption that for each task, work is a nondecreasing function of the number of processors allotted to the task. Our algorithm and analysis incorporate an improved lower bound on average completion time for the nonmalleable problem. We also show that Turek et al.'s algorithm for the nonmalleable problem can be extended to the malleable problem, while preserving the approximation factor. The resulting algorithm does not require any assumptions on the task execution times. The running time of our malleable schedulers is dominated by the cost of determining a minimumweight perfect matching in a bipartite graph.