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A. Youssef, B.W. Arden, "Equivalence Between Functionality and Topology of Log NStage Banyan Networks," IEEE Transactions on Computers, vol. 39, no. 6, pp. 829832, June, 1990.  
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@article{ 10.1109/12.53604, author = {A. Youssef and B.W. Arden}, title = {Equivalence Between Functionality and Topology of Log NStage Banyan Networks}, journal ={IEEE Transactions on Computers}, volume = {39}, number = {6}, issn = {00189340}, year = {1990}, pages = {829832}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.53604}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Equivalence Between Functionality and Topology of Log NStage Banyan Networks IS  6 SN  00189340 SP829 EP832 EPD  829832 A1  A. Youssef, A1  B.W. Arden, PY  1990 KW  functionality; topology; log Nstage banyan networks; network equivalence; permutations; multiprocessor interconnection networks. VL  39 JA  IEEE Transactions on Computers ER   
Existing procedures to decide network equivalence in log Nstage banyan networks are based on analysis of permutations, take polynomial but costly time, and do not shed light on or take advantage of the relationship between functionality and topology. This relationship is addressed and it is shown that two log Nstage banyan networks of the same switch size are functionally equivalent if and only if they have the same underlying topology. An O(N log N) algorithm is derived which decides if two Nstage banyan networks of N inputs, N outputs, and r*r crossbar switches as building blocks realize the same permutations. The algorithm works by comparing the underlying topologies of the two networks. The algorithm is optimal because the size of the networks is O(N log N).
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