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R.I. Greenberg, "The FatPyramid and Universal Parallel Computation Independent of Wire Delay," IEEE Transactions on Computers, vol. 43, no. 12, pp. 13581364, December, 1994.  
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@article{ 10.1109/12.338095, author = {R.I. Greenberg}, title = {The FatPyramid and Universal Parallel Computation Independent of Wire Delay}, journal ={IEEE Transactions on Computers}, volume = {43}, number = {12}, issn = {00189340}, year = {1994}, pages = {13581364}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.338095}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  The FatPyramid and Universal Parallel Computation Independent of Wire Delay IS  12 SN  00189340 SP1358 EP1364 EPD  13581364 A1  R.I. Greenberg, PY  1994 KW  multiprocessor interconnection networks; parallel architectures; fat pyramid; universal parallel computation; wire delay; processor size; wire length; simulation; unit wire delay; fattree; parallel computation; routing networks; universality. VL  43 JA  IEEE Transactions on Computers ER   
This paper shows that a fatpyramid of area /spl Theta/(A) requires only O(log A) slowdown to simulate any competing network of area A under very general conditions. The result holds regardless of the processor size (amount of attached memory) and number of processors in the competing networks as long as the limitation on total area is met. Furthermore, the result is valid regardless of the relationship between wire length and wire delay. We especially focus on elimination of the common simplifying assumption that unit time suffices to traverse a wire regardless of its length, since the assumption becomes more and more untenable as the size of parallel systems increases. This paper concentrates on simulation using transmission lines (wires along which bits can be pipelined) with the message routing schedule set up off line, but it also discusses the extension to online simulation. This paper also examines the capabilities of a fatpyramid when matched against a substantially larger network and points out the surprising difficulty of doing such a comparison without the unit wire delay assumption.
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