Towards Optimal Static Task Scheduling for Realistic Machine Models: Theory and Practice

Task scheduling is a key element in achieving high performance from multicomputer systems. Efficient scheduling algorithms reduce the interprocessor communication and improve processor utilization. To do so effectively, such algorithms must be based on a communication cost model appropriate for computing systems in use. The optimal scheduling of tasks is NP-hard, and a large number of heuristic algorithms have been proposed for a range of differing scheduling conditions (graph types, granularities and cost or architectural models). Unfortunately, due both to the variety of systems available and the rate at which these systems evolve, an appropriate representative cost model has yet to be established. In this paper we study the problem of task scheduling under a LogP-type model and we present both theoretical and experimental results for a cluster-based, task duplication methodology. The model is not only representative of parallel systems but also incorporates the traditional model used by the scheduling community. Results show that, for this model, an algorithm based on this LogP scheduling methodology can generate good makespans.