An optimal O(NlgN) algorithm for permutation admissibility to extra-stage cube-type networks

A k-EMCTN is obtained by adding k more stages in front of a multistage cube-type network (MCTN). It is shown that a permutation is admissible to a k-EMCTN if and only if the conflict graph is 2/sup k/-colorable. For the case k=1, an O(NlgN) algorithm is given for constructing the conflict graph, which leads to an O(NlgN) admissibility algorithm. Furthermore, it is shown that /spl Omega/(NlgN) bits must be checked in the binary representation of a permutation for determining its admissibility.<
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