Abstract
This paper proposes a simple yet efficient algorithm to distribute loads evenly on multiprocessor computers with hypercube interconnection networks. This algorithm was developed based upon the well-known dimension exchange method. However, the error accumulation suffered by other algorithms based on the dimension exchange method is avoided by exploiting the notion of regular distributions, which are commonly deployed for data distributions in parallel programming. This algorithm achieves a perfect load balance over P processors with an error of 1 and the worst-case time complexity of O(M log2 P), where M is the maximum number of tasks initially assigned to each processor. Furthermore, perfect load balance is achieved over subcubes as well—once a hypercube is balanced, if the cube is decomposed into two subcubes by the lowest bit of node addresses, then the difference between the numbers of the total tasks of these subcubes is at most 1.
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References
F. Meyer auf der Heide, B. Osterdiekhoff, and R. Wanka. Strongly adaptive token distribution. In Proceedings of the 20th International Colloquium on Automata, Languages, and Programming, pp. 398–409, 1993.
B. S. Chlebus, J. D. P. Rolim, and G. Slutzki. Distrubuting tokens on a hypercube without error accumulation. In Proceedings of the 1996 International Parallel Processing Symposium, pp. 573–578, 1996.
G. Cybenko. Dynamic load balancing for distributed memory multiprocessors. Journal of Parallel and Distributed Computing, 7:279–301, 1989.
G. Fox, S. Hiranandani, K. Kennedy, C. Koelbel, U. Kremer, C. Tseng, and M. Wu. Fortran D language specification. Technical report COMP TR90–141. Department of Computer Science, Rice University, December 1990.
High Performance Fortran Forum. High Performance Fortran language specification. Scientific Programming, 2(1–2):1–170, 1993.
J. JáJá and K. W. Ryu. Load balancing and routing on the hypercube and related networks. Journal of Parallel and Distributed Computing, 14:431–435, 1992.
Gene Eu Jan and Ming-Bo Lin. Effective load balancing on highly parallel multicomputers based on superconcentrators. In Proceedings of the International Conference on Parallel and Distributed Systems, pp. 216–221, 1994.
C. G. Plaxton. Load balancing, selection and sorting on the hypercube. In Proceedings of the ACM Symposium on Parallel Algorithms and Architectures, pp. 64–73, 1989.
S. Raghavendra, C. S. Chalasani, and R. V. Boppmana. Improved algorithms for load balancing in circuit switching hypercubes. In Proceedings of the 5th International Parallel Processing Symposium, pp. 537–542, 1991.
Sanjay Ranka and Sartaj Sahni. Hypercube Algorithms with Applications to Image Processing and Pattern Recognition. Springer Verlag, 1990.
Sanjay Ranka, Youngju Won, and Sartaj Sahni. Programming a hypercube multicomputer. In IEEE Software, pp. 69–77, 1988.
Hwakyung Rim, Ju-Wook Jang, and Sungchun Kim. An efficient dynamic load balancing using the dimension exchange method for balancing of quantized loads on hypercube multiprocessor. In Proceedings of 1999 IPPS/SPDP, pp. 708–712, 1999.
J. Woo and S. Sahni. Load balancing on a hypercube. In Proceedings of the 5th International Parallel Processing Symposium, pp. 525–530, 1991.
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Jan, G.E., Hwang, YS. An Efficient Algorithm for Perfect Load Balancing on Hypercube Multiprocessors. The Journal of Supercomputing 25, 5–15 (2003). https://doi.org/10.1023/A:1022878105480
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DOI: https://doi.org/10.1023/A:1022878105480