Abstract
We propose and theoretically analyze a new probabilistic permutation routing algorithm, which is based on two-phases of 1-1 permutation routing. We show that the probability of routing all N packets on the N-node, base-b generalized hypercube in asymptotically optimal C logb N time (constant C≥1) approaches exponentially one, as N increases. Further, for any generalized hypercube and especially for the binary hypercube (b=2), our derived upper bound on the above probability improves on existing ones. Comparison tables of these upper bounds are also provided.
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References
Abraham, S. and Padmanabhan, K.: Performance of the Direct Binary N-cube Network for Multiprocessors. IEEE Transactions on Computers, C-38 (7) 1989, 1000–1011.
Bhuyan L. N. and Agrawal D. P.: Generalized hypercube and hyperbus structures for a computer network. IEEE Transactions on Computers, C-33 (4), 1984, 323–334.
Chernoff H.: A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Annals of Mathematical Statistics. 23, 1952, 493–507.
Cypher, R., Plaxton, C. G.: Deterministic Sorting in Nearly Logarithmic Time on the Hypercube and Related Co mputers. In Proc. 22nd ACM Symposium of Theory of Computing. 1990 193–203.
Grammatikakis, M. D., Hsu, D. F., Hwang, F. K.: Adaptive and Oblivious Routing on the D-cube. In Proc. 4th Annual International Symposium on Algorithms and Computation, Lecture Notes in Computer Science, Springer-Verlag. 1994 to appear.
Grammatikakis M. D. and Jwo J. S.: Greedy Deterministic Permutation Routing on Cayley Graphs. In Proc. 2nd Joint International Conference on Vector and Parallel Processing, Lecture Notes in Computer Science, Springer-Verlag. 1992, Vol. 634, 839–840.
Hoeffding W.: On the distribution of the number of successes in independent trials. Annals of Mathematical Statistics. 27, 1956 713–721.
Kaklamanis C., Krizanc D., Tsantilas T.: Tight Bounds for Oblivious Routing on the Hypercube. In Proc. 2nd Annual ACM Symposium of Parallel Algorithms and Architectures. 1990 31–36.
Leighton, T.: Average case analysis of greedy routing algorithms. In Proc. 2nd Annual ACM Symposium on Parallel Algorithms and Architectures. 1990, 2–8.
Szymanski T.: On the permutation capability of a circuit-switched hypercube. In Proc. IEEE International Conference on Parallel Processing. 1989, Vol. I 103–110.
Valiant, L. G., and Brebner, G. J.: Universal Schemes for parallel communication. In Proc. 13th ACM Symposium of Theory of Computing. 1981 263–277.
Valiant, L. G.: A scheme for fast parallel communication. SIAM Journal on Computing. 11 (2) 1985 350–361.
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© 1994 Springer-Verlag Berlin Heidelberg
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Ferreira, A.G., Grammatikakis, M.D. (1994). Improved probabilistic routing on generalized hypercubes. In: Halatsis, C., Maritsas, D., Philokyprou, G., Theodoridis, S. (eds) PARLE'94 Parallel Architectures and Languages Europe. PARLE 1994. Lecture Notes in Computer Science, vol 817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58184-7_85
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DOI: https://doi.org/10.1007/3-540-58184-7_85
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