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<p><it>Abstract</it>—A <it>k</it>-EMCTN is obtained by adding <it>k</it> more stages in front of a multistage cube-type network (MCTN). It is shown that a permutation is admissible to a <it>k</it>-EMCTN if and only if the conflict graph is 2<super><it>k</it></super>-colorable. For the case <it>k</it>= 1, an <it>O</it>(<it>NlgN</it>) algorithm is given for constructing the conflict graph, which leads to an <it>O</it>(<it>NlgN</it>) admissibility algorithm. Furthermore, it is shown that Ω(<it>NlgN</it>) bits must be checked in the binary representation of a permutation for determining its admissibility.</p>
Conflict graph, extra-stage cube-type network, lower bound, graph coloring, permutation admissibility.
Xiaojun Shen, "An Optimal O(NlgN) Algorithm for Permutation Admissibility to Extra-Stage Cube-Type Networks", IEEE Transactions on Computers, vol. 44, no. , pp. 1144-1149, September 1995, doi:10.1109/12.464393
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