Work Stealing Technique and Scheduling on the Critical Path

In this paper we propose new insights into the problem of concurrently scheduling threads through mainly the Work Stealing (WS) technique which is one of the technique, with Parallel Depth First (PDF) technique able to efficiently manage fine-grained mutithreaded programs. We investigate a nice result of Bender and Rabin about the scheduling of threads in an heterogeneous context, show the limits in terms of (theoretical) performance and we propose to enhance the efficiency of the processor use by keeping the fastest processor busy and working on the critical path of the application. Then we provide a bound on the completion time. We also investigate the problem of execution time penalies when scheduling according to WS faced to PDF and we show how to adapt our initial algorithm to behave ’like’ a PDF schedule. We hope that such frame work could help multi-threaded or multi-core architect to rely on well founded mathematical results to build appropriate hardware controling the scheduling of threads or for implementing software schedulers