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A. Edelman, S. Heller, S.L. Johnsson, "Index Transformation Algorithms in a Linear Algebra Framework," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 12, pp. 13021309, December, 1994.  
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@article{ 10.1109/71.334903, author = {A. Edelman and S. Heller and S.L. Johnsson}, title = {Index Transformation Algorithms in a Linear Algebra Framework}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {5}, number = {12}, issn = {10459219}, year = {1994}, pages = {13021309}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.334903}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Index Transformation Algorithms in a Linear Algebra Framework IS  12 SN  10459219 SP1302 EP1309 EPD  13021309 A1  A. Edelman, A1  S. Heller, A1  S.L. Johnsson, PY  1994 KW  Index Termslinear algebra; encoding; decoding; Gray codes; hypercube networks; indextransformation algorithms; linear algebra framework; Gray code encoding; decoding;matrix transpose; bit reversal; vector reversal; shuffles; hypercube multiprocessors;hypercube communications algorithms; GaussJordan elimination VL  5 JA  IEEE Transactions on Parallel and Distributed Systems ER   
We present a linear algebraic formulation for a class of index transformations such asGray code encoding and decoding, matrix transpose, bit reversal, vector reversal,shuffles, and other index or dimension permutations. This formulation unifies, simplifies,and can be used to derive algorithms for hypercube multiprocessors. We show how all the widely known properties of Gray codes, and some not so wellknown properties as well, can be derived using this framework. Using this framework, we relate hypercube communications algorithms to GaussJordan elimination on a matrix of 0's and 1's.
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