Scheduling directed acyclic graphs with optimal duplication strategy on homogeneous multiprocessor systems

Abstract

Modern applications generally need a large volume of computation and communication to fulfill the goal. These applications are often implemented on multiprocessor systems to meet the requirements in computing capacity and communication bandwidth, whereas, how to obtain a good or even the optimal performance on such systems remains a challenge. When tasks of the application are mapped onto different processors for execution, inter-processor communications become inevitable, which delays some tasks’ execution and deteriorates the schedule performance. To mitigate the overhead incurred by inter-processor communications and improve the schedule performance, task duplication strategy has been employed in the schedule. Most available techniques for the duplication-based scheduling problem utilize heuristic strategies to produce sub-optimal solutions, however, how to find the optimal duplication-based solution with the minimal schedule makespan remains an unsolved issue. To fill in this gap, this paper proposes a novel Mixed Integer Linear Programming (MILP) formulation for this problem, together with a set of key theorems which enable and simplify the MILP formulation. The proposed MILP formulation can optimize the duplication strategy, serialize the execution of task instances on each processor and determine data precedences among different task instances, thus producing the optimal solution. The proposed method is tested on a set of synthesized applications and platforms and compared with the well-known algorithm. The experimental results demonstrate the effectiveness of the proposed method.