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An Optimal O(NlgN) Algorithm for Permutation Admissibility to Extra-Stage Cube-Type Networks
September 1995 (vol. 44 no. 9)
pp. 1144-1149

Abstract—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 2k-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 Ω(NlgN) bits must be checked in the binary representation of a permutation for determining its admissibility.

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Index Terms:
Conflict graph, extra-stage cube-type network, lower bound, graph coloring, permutation admissibility.
Citation:
Xiaojun Shen, "An Optimal O(NlgN) Algorithm for Permutation Admissibility to Extra-Stage Cube-Type Networks," IEEE Transactions on Computers, vol. 44, no. 9, pp. 1144-1149, Sept. 1995, doi:10.1109/12.464393
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