An optimal scheduling algorithm based on task duplication

The task scheduling problem in distributed memory machines is to allocate the tasks of an application into processors in order to minimize the total execution time. This is known as an NP-complete problem. Under the condition where the communication time is relatively shorter than the computation time for every task, the task duplication based scheduling (TDS) algorithm proposed by Darbha and Agrawal (1998) generates an optimal schedule. We propose an extended TDS algorithm whose optimality condition is less restricted than the TDS algorithm. Given a DAG where the condition is met, our algorithm has the time complexity of O(|V|²d²) where |V| represents the number of tasks, and d represents the maximum degree of tasks