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

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... s. We present a parallel algorithm that runs in Oðlg 2 NÞ time for the RNB networks of complexities ranging from OðN lg NÞ to OðN 1:5 lg NÞ crosspoints and parallel algorithms that run in Oðminfd à lg N; ffiffiffiffi ffi N p gÞ time for the SNB networks of OðN 1:5 lg NÞ crosspoints, using a completely connected multiprocessor system of N processing elements. Our algorithms can be translated into algorithms with an Oðlg N lg lg NÞ slowdown factor for the class of N-processor hypercubic networks, whose structures are no more complex than a single plane in the RNB and SNB networks considered.