Abstract
A parallel computational model is defined which addresses I/O contention, latency, and pipe-lined message passing between tasks allocated to different processors and can be used for modeling parallel task-allocation on a network of workstations or on a multi-stage interconnected parallel machine. To study the performance bounds more closely, basic properties are developed for when the precedence constraints form a directed tree. Approximation algorithms are presented for scheduling directed one-level task trees on an unlimited number of processors and also on a fixed number of k, k > 1, processors, where the approximation ratios are 3 and 3 + k−2/k, respectively. The case of equal task execution times is also considered.
Research supported in part by NSC Grant 85-2213-E-001-003.
Research supported in part by Academia Sinica, Taipei, the University of Minnesota, Morris and the University of Minnesota China Center, Minneapolis.
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References
F. D. Anger, J. J. Hwang, and Y. C. Chow. Scheduling with sufficient loosely coupled processors. Journal of Parallel and Distributed Comput., 9:87–92, 1990.
T. C. E. Cheng and C. C. S. Sin. A state-of-the-art review of parallel-machine scheduling research. European J. Operational Research, 47:271–292, 1990.
P. Chrétienne. A polynomial algorithm to optimally schedule tasks on a virtual distributed system under tree-like precedence constraints. European J. Operational Research, 43:225–230, 1989.
P. Chrétienne. Task scheduling with interprocessor communication delays. European J. Operational Research, 57:348–354, 1992.
P. Chrétienne. Tree scheduling with communication delays. Discrete Applied Math., 49:129–141, 1994.
P. Chrétienne, Jr. E. G. Coffman, J. K. Lenstra, and Z. Liu, editors. Scheduling Theory and its Applications. John Wiley & Sons Ltd, 1995.
J. Y. Colin and P. Chrétienne. C.P.M. scheduling with small communication delays and task duplication. Oper. Res., 39(3):680–684, 1991.
D. Culler, R. Karp, D. Patterson, A. Sahay, K. E. Schauser, E. Santos, R. Subramonian, and T. von Eicken. LogP: Towards a realistic model of parallel computation. In Proc. 4th ACM SIGPLAN Symp. on Principles and Practices of Parallel Programming, pages 1–12, 1993.
O. El-Dissouki and W. Huen. Distributed enumeration on network computers. IEEE Trans. on Computers, C-29(9):818–825, 1980.
A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. Manchek, and V. Sunderam. PVM 3 User's Guide and Reference Manual. Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA, May 1993.
P. B. Gibbons, Y. Matias, and V. Ramachandran. The QRQW PRAM: Accounting for contention in parallel algorithms. In Proc. 5th ACM-SIAM Symp. on Discrete Algorithms, pages 638–648, 1994. SIAM J. Comput., to appear.
J. J. Hwang, Y. C. Chow, F. D. Anger, and C. Y. Lee. Scheduling precedence graphs in systems with interprocessor communication times. SIAM Journal on Computing, 18(2):244–257, 1989.
V. M. Lo. Task Assignment in Distributed Systems. PhD thesis, Univ. of Illinois at Urbana-Champaign, USA, October 1983.
V. M. Lo. Heuristic algorithms for task assignment in distributed systems. IEEE Trans. on Computers, 37(11):1284–1397, 1988.
D. R. Lopez. Models and Algorithms for Task Allocation in a Parallel Environment. PhD thesis, Texas A&M University, Texas, USA, December 1992.
P. R. Ma, E. Y. Lee, and M. Tsuchiya. A task allocation model for distributed computing systems. IEEE Trans. on Computers, C-31(1):41–47, 1982.
M. G. Norman and P. Thanisch. Models of machines and computation for mapping in multicomputers. ACM Computing Surveys, 25(3):263–302, 1993.
C. Papadimitriou and M. Yannakakis. Towards on an architecture-independent analysis of parallel algorithms. SIAM Journal on Computing, 19:322–328, 1990.
H. S. Stone. Multiprocessor scheduling with the aid of network flow algorithms. IEEE Trans. on Software Eng., SE-3(1):85–93, 1977.
L. G. Valiant. A bridging model for parallel computation. Communications of the ACM, pages 103–111, 1990.
L. G. Valiant. General purpose parallel architectures. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 944–971. North Holland, 1990.
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© 1996 Springer-Verlag Berlin Heidelberg
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Hsu, Ts., Lopez, D.R. (1996). Bounds and algorithms for a practical task allocation model (extended abstract). In: Asano, T., Igarashi, Y., Nagamochi, H., Miyano, S., Suri, S. (eds) Algorithms and Computation. ISAAC 1996. Lecture Notes in Computer Science, vol 1178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009516
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DOI: https://doi.org/10.1007/BFb0009516
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