An Optimal O(NlgN) Algorithm for Permutation Admissibility to Extra-Stage Cube-Type Networks

  • Authors:
  • Xiaojun Shen

  • Affiliations:
  • -

  • Venue:
  • IEEE Transactions on Computers
  • Year:
  • 1995

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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 驴(NlgN) bits must be checked in the binary representation of a permutation for determining its admissibility.