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<p><it>Abstract—</it>The performance of a multiprocessor system depends heavily on its ability to provide conflict free paths among its processors. In this paper, we explore the possibility of using a nonblocking network with <math><tmath>$O(N \log N)$</tmath></math> edges (crosspoints) to interconnect the processors of an <math><tmath>$N$</tmath></math> processor system. We combine Bassalygo and Pinsker's implicit design of strictly nonblocking networks with an explicit construction of expanders to obtain a strictly nonblocking network with <math><tmath>$-765.18 N + 352.8 N \log N$</tmath></math> edges and <math><tmath>$2+\log (N/5)$</tmath></math> depth. We present an efficient parallel algorithm for routing connection requests on this network and implement it on three parallel processor topologies. The implementation on a parallel processor whose processing elements are interconnected as in the Bassalygo–Pinsker network requires <math><tmath>$O(N\log N)$</tmath></math> processing elements, <math><tmath>$O(N\log N)$</tmath></math> interprocessor links and it takes <math><tmath>$O(\log N)$</tmath></math> steps to route any single connection request where each step involves a small number (<math><tmath>$\approx$</tmath></math>72) of bit-level operations. A contracted or folded version of the same implementation reduces the processing element count to <math><tmath>$O(N)$</tmath></math> without increasing the link count or the routing time. Finally, we establish that the same algorithm takes <math><tmath>$O(\log^3 N)$</tmath></math> steps on a perfect shuffle processor with <math><tmath>$O(N)$</tmath></math> processing elements. These results improve the crosspoint, depth and routing time complexities of the previously reported strictly nonblocking networks.</p><p><it>Index Terms—</it>Bassalygo–Pinsker network, Clos network, Cantor network, extensive graph, expander, parallel routing algorithm, strictly nonblocking network.</p>

F. Shao and A. Y. Oruç, "Efficient Nonblocking Switching Networks for Interprocessor Communications in Multiprocessor Systems," in IEEE Transactions on Parallel & Distributed Systems, vol. 6, no. , pp. 132-141, 1995.
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