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An Optimal Algorithm for Permutation Admissibility to Multistage Interconnection Networks
April 1995 (vol. 44 no. 4)
pp. 604-608

Abstract—This paper introduces a simple O(NlogN) sequential algorithm that determines the admissibility of an arbitrary permutation to an N×N Multistage Cube-Type Network (MCTN) implemented by 2 × 2 switching elements (SEs) in contrast to previous O(Nlog2N) algorithms. It is proven that the new algorithm is optimal in the sense that any algorithm, based on bit-operations, has to examine at least (N/4)logN different bits among the total NlogN bits in the binary representations of the destinations numbered from 0 through N1.

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Index Terms:
Adversary strategy, multistage interconnection network, permutation admissibility, transition matrix, window method.
Citation:
Mao Xu, Xiaojun Shen, Xiangzu Wang, "An Optimal Algorithm for Permutation Admissibility to Multistage Interconnection Networks," IEEE Transactions on Computers, vol. 44, no. 4, pp. 604-608, April 1995, doi:10.1109/12.376176
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