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N. Das, B.B. Bhattacharya, J. Dattagupta, "Hierarchical Classification of Permutation Classes in Multistage Interconnection Networks," IEEE Transactions on Computers, vol. 43, no. 12, pp. 14391444, December, 1994.  
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@article{ 10.1109/12.338106, author = {N. Das and B.B. Bhattacharya and J. Dattagupta}, title = {Hierarchical Classification of Permutation Classes in Multistage Interconnection Networks}, journal ={IEEE Transactions on Computers}, volume = {43}, number = {12}, issn = {00189340}, year = {1994}, pages = {14391444}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.338106}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Hierarchical Classification of Permutation Classes in Multistage Interconnection Networks IS  12 SN  00189340 SP1439 EP1444 EPD  14391444 A1  N. Das, A1  B.B. Bhattacharya, A1  J. Dattagupta, PY  1994 KW  multistage interconnection networks; hierarchical classification; permutation classes; multistage interconnection networks; linearcomplement class; bitpermute class; bitpermuteclosure; shuffleexchange networks; Benes networks. VL  43 JA  IEEE Transactions on Computers ER   
This paper explores a new hierarchy among different permutation classes, that has many applications in multistage interconnection networks. The wellknown LC (linearcomplement) class is shown to be merely a subset of the closure set of the BP (bitpermute) class, known as the BPCL (bitpermuteclosure) class; the closure is obtained by applying certain grouptransformation rules on the BPpermutations. It indicates that for every permutation P of the LC class, there exists a permutation PI in the BP class, such that the conflict graphs of P and P* are isomorphic, for nstage MIN's. This obviates the practice of treating the LC class as a special case; the existing algorithm for optimal routing of BPC class in an nstage MIN can take care of optimal routing of the LC class as well. Finally, the relationships of BPCL with other classes of permutations, e.g., LIE (linearinputequivalence), BPIE (bitpermuteinputequivalence), BPOE (bitpermuteoutputequivalence) are also exposed. Apart from lending better understanding and an integral view of the universe of permutations, these results are found to be useful in accelerating routability in nstage MIN's as well as in (2n1)stage Benes and shuffleexchange networks.
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