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<p><b>Abstract</b>—We study the connection capacity of a class of rearrangeable nonblocking (RNB) and strictly nonblocking (SNB) networks with/without crosstalk-free constraint, model their routing problems as weak or strong edge-colorings of bipartite graphs, and propose efficient routing algorithms for these networks using parallel processing techniques. This class of networks includes networks constructed from Banyan networks by horizontal concatenation of extra stages and/or vertical stacking of multiple planes. We present a parallel algorithm that runs in <tmath>O(\lg^2 N)</tmath> time for the RNB networks of complexities ranging from <tmath>O(N\lg N)</tmath> to <tmath>O(N^{1.5}\lg N)</tmath> crosspoints and parallel algorithms that run in <tmath>O(\min \{d^*\lg N, \sqrt{N}\})</tmath> time for the SNB networks of <tmath>O(N^{1.5}\lg N)</tmath> crosspoints, using a completely connected multiprocessor system of <tmath>N</tmath> processing elements. Our algorithms can be translated into algorithms with an <tmath>O(\lg N \lg\lg N)</tmath> slowdown factor for the class of <tmath>N{\hbox{-}}{\rm{processor}}</tmath> hypercubic networks, whose structures are no more complex than a single plane in the RNB and SNB networks considered.</p>
Banyan network, crosstalk, optical switching, rearrangeable nonblocking network, strictly nonblocking network, switch control, self-routing, graph coloring, parallel algorithm.

E. Lu and S. Zheng, "Parallel Routing Algorithms for Nonblocking Electronic and Photonic Switching Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 16, no. , pp. 702-713, 2005.
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