Issue No.04 - April (1995 vol.44)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.376176
<p><it>Abstract</it>—This paper introduces a simple <it>O</it>(<it>NlogN</it>) sequential algorithm that determines the admissibility of an arbitrary permutation to an <it>N</it>×<it>N</it> Multistage Cube-Type Network (MCTN) implemented by 2 × 2 switching elements (SEs) in contrast to previous <it>O</it>(<it>Nlog</it><super>2</super><it>N</it>) 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 (<it>N</it>/<it>4</it>)<it>logN</it> different bits among the total <it>NlogN</it> bits in the binary representations of the destinations numbered from <it>0</it> through <it>N</it>−<it>1</it>.</p>
Adversary strategy, multistage interconnection network, permutation admissibility, transition matrix, window method.
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