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| C.M. Fiduccia, K.J. Rappoport, "Perfect shifters," IEEE Transactions on Computers, vol. 43, no. 3, pp. 340-349, March, 1994. | |||
| BibTex | x | ||
| @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 = {0018-9340}, year = {1994}, pages = {340-349}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.272434}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - Perfect shifters IS - 3 SN - 0018-9340 SP340 EP349 EPD - 340-349 A1 - C.M. Fiduccia, A1 - K.J. Rappoport, PY - 1994 KW - multiprocessor interconnection networks; parallel algorithms; parallel architectures; perfect shifters; single-instruction multiple-data networks; permutations; perfect linear arrays; difference covers; zero-one solutions; quadratic equations. VL - 43 JA - IEEE Transactions on Computers ER - | |||
Pin-efficient single-instruction multiple-data 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, one-tick 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 zero-one solutions to certain quadratic equations.
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