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C.M. Fiduccia, K.J. Rappoport, "Perfect shifters," IEEE Transactions on Computers, vol. 43, no. 3, pp. 340349, March, 1994.  
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@article{ 10.1109/12.272434, author = {C.M. Fiduccia and K.J. Rappoport}, title = {Perfect shifters}, journal ={IEEE Transactions on Computers}, volume = {43}, number = {3}, issn = {00189340}, year = {1994}, pages = {340349}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.272434}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  Perfect shifters IS  3 SN  00189340 SP340 EP349 EPD  340349 A1  C.M. Fiduccia, A1  K.J. Rappoport, PY  1994 KW  multiprocessor interconnection networks; parallel algorithms; parallel architectures; perfect shifters; singleinstruction multipledata networks; permutations; perfect linear arrays; difference covers; zeroone solutions; quadratic equations. VL  43 JA  IEEE Transactions on Computers ER   
Pinefficient singleinstruction multipledata networks, with p/spl ap//spl radic/(2m) pins per cell that can/spl minus/in one clock tick/spl minus/shift data by any amount k in an interval /spl lsqb//spl minus/m,m/spl rsqb/ are considered. Perfect barrel shifters, which perform the group of permutations c/spl rarr/c+k(mod n), 0/spl les/k/spl les/n/spl minus/1, using p=q+1 pins per cell, are known to exist for all n=q/sup 2/+q+1, where q is any prime power. In sharp contrast, it is shown that for any permutation /spl pi/ of order greater than 3m, onetick perfect shifters for the set of permutations /spl pi//sup /spl lsqb//spl minus/m,m/spl rsqb//=/spl lcub//spl pi//sup k//spl verbar//spl minus/m/spl les/k/spl les/m/spl rcub/ exist only for the three cases (m=1, p=2), (m=3, p=3), and (m=6, p=4). In particular, only three perfect linear arrays, c/spl rarr/c+k, exist. The proof is based on a relationship between the difference covers and zeroone solutions to certain quadratic equations.
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