Optimal scheduling for real-time parallel tasks

We propose an optimal algorithm for the real-time scheduling of parallel tasks on multiprocessors, where the tasks have the properties of flexible preemption, linear speedup, bounded parallelism, and arbitrary deadline. The proposed algorithm is optimal in the sense that it always finds out a feasible schedule if one exists. Furthermore, the algorithm delivers the best schedule consuming the fewest processors among feasible schedules. In this letter, we prove the optimality of the proposed algorithm. Also, we show that the time complexity of the algorithm is O(M-2 - N-2.) in the worst case, where M and N are the number of tasks and the number of processors, respectively.