Abstract
This paper addresses the problem of the nD-hypercube interconnection networks rearrangeability that is the capability of such networks to route optimally arbitrary permutations under queueless communication constraints. To that purpose, the paper exploits the recursive structure of nD-hypercube as two (n-1)D-hypercubes and proposes the k-partitioning paradigm. For n = 4, the paper characterizes permutations that do not admit 1-partitioning. It then exhibits representatives of some of the subclasses of such permutations. Each representative is then proved to admit 2-partitioning and one of its corresponding routing strategies is exhibited. Such routing strategy is obtained as a concatenation of a routing strategy of one of the upstream permutations of the considered permutation and a routing strategy of each of the two downstream permutations induced by the considered upstream permutation.
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References
Draper, J.T., Ghosh, J.: Multipath e-cube algorithms (MECA) for adaptive wormhole routing and broadcasting in k-ary n-cubes. In: International Parallel Processing Symposium, pp. 407–410 (1992)
Szymanski, T.: On the permutation capability of a circuit switched hypercube. In: International Conference on Parallel Processing, pp. I-103–I-110. IEEE Computer Society Press, Silver Spring (1989)
Lubiw, A.: Counter example to a conjecture of Szymanski on hypercube routing. Informations Processing Letters 35, 57–61 (1990)
Zhang, L.: Optimal bounds for matching routing on trees. In: 8th Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, pp. 445–453 (1997)
Hwang, F., Yao, Y., Grammatikakis, M.: A d-move local permutation routing for d-cube. Discrete Applied Mathematics 72, 199–207 (1997)
Hwang, F., Yao, Y., Dasgupta, B.: Some permutation routing algorithms for low dimensional hypercubes. Theoretical Computer Science 270, 111–124 (2002)
Vöcking, B.: Almost optimal permutation routing on hypercubes. In: 33rd Annual ACM-Symposium on Theory of Computing, pp. 530–539. ACM Press (2001)
Ramras, M.: Routing permutations on a graph. Networks 23, 391–398 (1993)
Laing, A.K., Krumme, D.W.: Optimal Permutation Routing for Low-dimensional Hypercubes. Networks 55, 149–167 (2010)
Jung, J.P., Sakho, I.: Towards Understanding Optimal MIMD Queueless Routing of Arbitrary Permutations on Hypercubes. Int. J. of Supercomp., doi: 10.1007/s11227-011-0574-8
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Sakho, I., Jung, JP. (2014). One Step Ahead towards the Rearrangeability of 4D-Hypercube Interconnection Networks. In: Nguyen, N.T., Attachoo, B., Trawiński, B., Somboonviwat, K. (eds) Intelligent Information and Database Systems. ACIIDS 2014. Lecture Notes in Computer Science(), vol 8398. Springer, Cham. https://doi.org/10.1007/978-3-319-05458-2_39
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DOI: https://doi.org/10.1007/978-3-319-05458-2_39
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05457-5
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