Worst-Case Analysis of Scheduling Heuristics of Parallel Systems

Abstract It is well-known that most scheduling problems arising from parallel systems are NP -hard, even under very special assumptions. Thus, various suboptimal algorithms, in particular heuristics, were proposed in the literature. Worst-case error bounds are established in this paper for heuristics of makespan minimization of parallel computations. Different parallel computation models are investigated, including interprocessor communication, task duplication, multiprocessor tasks and parallel tasks. Due to the heterogeneity of these systems, scheduling heuristics can be far away from the optimal solutions. These bounds provide insights to the design of scheduling heuristics in order to obtain good performance guarantee than arbitrary heuristics. Moreover, the performance guarantee of these special heuristics is independent of model parameters such as the maximal duplication degree, processor requirement and parallelization degree.

[1]  Mihalis Yannakakis,et al.  Towards an architecture-independent analysis of parallel algorithms , 1990, STOC '88.

[2]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[3]  Victor J. Rayward-Smith,et al.  UET scheduling with unit interprocessor communication delays , 1987, Discret. Appl. Math..

[4]  Errol L. Lloyd,et al.  Concurrent Task Systems , 1981, Oper. Res..

[5]  Jing-Jang Hwang,et al.  Deterministic scheduling in systems with interprocessor communication times , 1987 .

[6]  Joseph Y.-T. Leung,et al.  Complexity of Scheduling Parallel Task Systems , 1989, SIAM J. Discret. Math..

[7]  Zhen Liu,et al.  A Note on Graham's Bound , 1990, Inf. Process. Lett..

[8]  Jing-Jang Hwang,et al.  Multiprocessor scheduling with interprocessor communication delays , 1988 .

[9]  Jean-Claude König,et al.  A Heuristic for a Scheduling Problem with Communication Delays , 1997, Oper. Res..

[10]  Kam-Hoi Cheng,et al.  A Heuristic of Scheduling Parallel Tasks and its Analysis , 1992, SIAM J. Comput..

[11]  Claire Hanen,et al.  Using Duplication for Scheduling Unitary Tasks on m Processors with Unit Communication Delays , 1997, Theor. Comput. Sci..

[12]  Mihalis Yannakakis,et al.  Towards an Architecture-Independent Analysis of Parallel Algorithms , 1990, SIAM J. Comput..

[13]  Ronald L. Graham,et al.  Bounds for certain multiprocessing anomalies , 1966 .

[14]  Zhen Liu,et al.  Effectiveness of Heuristics and Simulated Annealing for the Scheduling of Concurrent Tasks - An Empirical Comparison , 1993, PARLE.

[15]  Kam-Hoi Cheng,et al.  List Scheduling of Parallel Tasks , 1991, Inf. Process. Lett..

[16]  Zhen Liu,et al.  Profile Scheduling by List Algorithms , 1994 .

[17]  Jacek Blazewicz,et al.  Scheduling in Computer and Manufacturing Systems , 1990 .

[18]  J. Labetoulle,et al.  A heuristic method for loading and scheduling flexible manufacturing systems , 1988 .

[19]  Jacek Blazewicz,et al.  Scheduling Independent Multiprocessor Tasks on a Uniform k-Processor System , 1994, Parallel Comput..

[20]  Zhen Liu,et al.  Preemptive Scheduling with Variable Profile, Precedence Constraints and Due Dates , 1995, Discret. Appl. Math..

[21]  Zhen Liu,et al.  Scheduling multiprocessor tasks with chain constraints , 1996 .

[22]  Z Liu,et al.  Scheduling Theory and its Applications , 1997 .

[23]  Zhen Liu.  Scheduling of random task graphs on parallel processors , 1995, MASCOTS '95. Proceedings of the Third International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems.