General bounds for the assignment of irregular dependency graphs

  • Sathiamoorthy Manoharan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 980)


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.


Allocation Dependency graphs Instruction-level parallelism Scheduling Processor assignment 


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  1. 1.
    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.CrossRefGoogle Scholar
  2. 2.
    Coffman, E. G., Ed. Computer and Job Shop Scheduling Theory. John Wiley and Sons, 1976.Google Scholar
  3. 3.
    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.CrossRefGoogle Scholar
  4. 4.
    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.Google Scholar
  5. 5.
    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.Google Scholar
  6. 6.
    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.Google Scholar
  7. 7.
    Graham, R. L. Bounds on multiprocessing timing anomalies. SIAM Journal of Applied Mathematics 17, 2 (March 1969), 416–429.CrossRefGoogle Scholar
  8. 8.
    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.MathSciNetGoogle Scholar
  9. 9.
    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.CrossRefGoogle Scholar
  10. 10.
    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.Google Scholar
  11. 11.
    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.CrossRefGoogle Scholar
  12. 12.
    Manoharan, S., and Thanisch, P. Assigning dependency graphs onto processor networks. Parallel Computing 17, 1 (April 1991), 63–73.Google Scholar
  13. 13.
    Manoharan, S., and Topham, N. P. An assessment of assignment schemes for dependency graphs. Parallel Computing 21, 1 (January 1995), 85–1107.MathSciNetGoogle Scholar
  14. 14.
    McNaughton, R. Scheduling with deadlines and loss functions. Management Science 6 (October 1959).Google Scholar
  15. 15.
    Rayward-Smith, V. J. UET scheduling with unit interprocessor communication delays. Discrete Applied Mathematics 18 (1987), 55–71.CrossRefGoogle Scholar
  16. 16.
    Sarkar, V.Partitioning and Scheduling Parallel Programs for Multiprocessors. MIT Press, Cambridge MA, 1989.Google Scholar
  17. 17.
    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.Google Scholar
  18. 18.
    Veltman, B., Lageweg, B. J., and Lenstra, J. K. Multiprocessor scheduling with communication delays. Parallel Computing 16 (1990), 173–182.CrossRefGoogle Scholar
  19. 19.
    Wu, M.-Y., and Gajski, D. D. A programming aid for hypercube architectures. The Journal of Supercomputing 2, 3 (November 1988), 349–372.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Sathiamoorthy Manoharan
    • 1
  1. 1.Department of Computer ScienceUniversity of AucklandNew Zealand

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