Abstract
This paper presents some new results on homogeneous multi-processor scheduling. Given the lengths, precedences and speedup functions of a set of tasks, the optimal scheduling problem is to determine the number of processors assigned to each task and the task sequencing to minimize the completion time. We show that the problem is tractable through the techniques of continuous optimization in many cases, that it includes intractable combinatorial complexity in the other cases and that the continuous optimization can produce a schedule which is within 4/3 times the length of the optimal non-preemptive schedule. We propose a heuristic method for further possible improvement. Finally, we show that the completion time is very close after the optimal integer perturbation.
Chapter PDF
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
K. P. Belkhale and P. Banerjee. A Scheduling Algorithm For Parallelizable Dependent Tasks. In 1991 International Parallel Processing Symposium, 1991.
V. G. Boltyanskii. Mathematical Methods of Optimal Control. Holt, Rinehart and Winston, Inc., translation edition, 1971.
Jianzhong Du and Joseph Y-T. Leung. Complexity of Scheduling Parallel Task Systems. SIAM Journal of Discrete Mathematics, 2(4):473–487, November 1989.
Coffman E.F., editor. Computer and Job Shop Sheduling Theory. John Wiley and Sons, N.Y., first edition, 1976.
M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman, San Francisco, 1979.
John L. Gustafson, Gary R. Montry, and Robert E. Benner. Development of Parallel Methods For a 1024-Processor Hypercube. SIAM Journal on Scientific and Satastical Computing, 9(4):609–638, July 1988.
Zhonghua Li. Scheduling and Partitioning of Parallel Programs. PhD thesis, Manchester University, 1996. in preparation.
M.J.D. Powell. A Hybrid Method for Nonlinear Algebraic Equations. In P. Rabinowitz, editor, Numerical Methods for Nonlinear Algebraic Equations, 1970.
G.N. Srinivasa Prasanna, A. Agarwal, and B. R. Musicus. Hierarchical Compilation of Macro Dataflow Graphs for Multiprocessors with Local Memory. IEEE Transactions on Parallel and Distributed Systems, 5(7):720–736, July 1994.
G.N. Srinivasa Prasanna and Bruce R. Musicus. Generalized Multiprocessor Scheduling for Directed Acyclic Graphs. In Supercomputing'94, 1994.
S. Ramaswamy and P. Banerjee. Processor Allocation and Scheduling of Macro Dataflow Graphs on Distributed Memory Multicomputers by the PARADIGM Compiler. In International Conference on Parallel Processing, 1993.
P. Shi. Articulating the Power of Parallelism Using Steady State Timing Models. Technical report, Computer and Information Sciences Department, Temple University, May 1995.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, Z., Kirkham, C.C. (1996). Generalized multiprocessor scheduling. In: Bougé, L., Fraigniaud, P., Mignotte, A., Robert, Y. (eds) Euro-Par'96 Parallel Processing. Euro-Par 1996. Lecture Notes in Computer Science, vol 1124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024749
Download citation
DOI: https://doi.org/10.1007/BFb0024749
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61627-6
Online ISBN: 978-3-540-70636-6
eBook Packages: Springer Book Archive