Abstract
Given an irregular dependency graph consisting of interdependent tasks, the problem of finding an optimal assignment on a number of parallel execution units is NP-complete. Assignment schemes thus settle for some heuristics that produce sub-optimal solutions. Most popular of these are the work-greedy assignment schemes. This paper presents new bounds on the performance of work-greedy schemes, taking into account the degree of parallelism visible between the tasks and the inter-task communication delays.
Preview
Unable to display preview. Download preview PDF.
References
Al-Mouhamed, M. A. Lower bound on the number of processors and time for scheduling precedence graphs with communication costs. IEEE Transactions on Software Engineering 16, 12 (December 1990), 1390–1401.
Coffman, E. G., Ed. Computer and Job Shop Scheduling Theory. John Wiley and Sons, 1976.
El-Rewini, H., and Lewis, T. G. Scheduling parallel program tasks onto arbitrary target machines. Journal of Parallel and Distributed Computing 9 (1990), 138–153.
Fernandez, E. B., and Bussell, B. Bounds on the number of processors and time for multiprocessor optimal schedules. IEEE Transactions on Computers C-22, 8 (August 1973), 745–751.
Gerasoulis, A., Venugopal, S., and Yang, T. Clustering task graphs for message passing architectures. In Proceedings of the International Conference on Supercomputing. ACM Press, Amsterdam, The Netherlands, June 11–15, 1990, pp. 447–456.
Graham, R. L. Bounds on the performance of scheduling algorithms. In Computer and Job Shop Scheduling Theory, E. G. Coffman, Ed. John Wiley and Sons, 1976, pp. 165–227.
Graham, R. L. Bounds on multiprocessing timing anomalies. SIAM Journal of Applied Mathematics 17, 2 (March 1969), 416–429.
Graham, R. L., Lawler, E. L., Lenstra, J. K., and Kan, A. H. G. R. Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics 3 (1979), 287–326.
Hwang, J.-J., Chow, Y.-C., Anger, F. D., and Lee, C.-Y. Scheduling precedence graphs in systems with interprocessor communication times. SIAM Journal of Computing 18, 2 (April 1989), 244–257.
Kruatrachue, B., and Lewis, T. Duplication scheduling heuristics, a new precedence task scheduler for parallel systems. Tech. Rep. 87-60-3, Computer Science Department, Oregon State University, Corvallis OR, 1987.
Lee, C.-Y., Hwang, J.-J., Chow, Y.-C., and Anger, F. D. Multiprocessor scheduling with interprocessor communication delays. Operations Research Letters 7, 3 (June 1988), 141–145.
Manoharan, S., and Thanisch, P. Assigning dependency graphs onto processor networks. Parallel Computing 17, 1 (April 1991), 63–73.
Manoharan, S., and Topham, N. P. An assessment of assignment schemes for dependency graphs. Parallel Computing 21, 1 (January 1995), 85–1107.
McNaughton, R. Scheduling with deadlines and loss functions. Management Science 6 (October 1959).
Rayward-Smith, V. J. UET scheduling with unit interprocessor communication delays. Discrete Applied Mathematics 18 (1987), 55–71.
Sarkar, V.Partitioning and Scheduling Parallel Programs for Multiprocessors. MIT Press, Cambridge MA, 1989.
Ullman, J. D. Complexity of sequencing problems. In Computer and Job Shop Scheduling Theory, E. G. Coffman, Ed. John Wiley and Sons, 1976, pp. 139–164.
Veltman, B., Lageweg, B. J., and Lenstra, J. K. Multiprocessor scheduling with communication delays. Parallel Computing 16 (1990), 173–182.
Wu, M.-Y., and Gajski, D. D. A programming aid for hypercube architectures. The Journal of Supercomputing 2, 3 (November 1988), 349–372.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Manoharan, S. (1995). General bounds for the assignment of irregular dependency graphs. In: Ferreira, A., Rolim, J. (eds) Parallel Algorithms for Irregularly Structured Problems. IRREGULAR 1995. Lecture Notes in Computer Science, vol 980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60321-2_7
Download citation
DOI: https://doi.org/10.1007/3-540-60321-2_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60321-4
Online ISBN: 978-3-540-44915-7
eBook Packages: Springer Book Archive