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P.J. Bernhard, "Bounds on the Performance of Message Routing Heuristics," IEEE Transactions on Computers, vol. 42, no. 10, pp. 12531256, October, 1993.  
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@article{ 10.1109/12.257719, author = {P.J. Bernhard}, title = {Bounds on the Performance of Message Routing Heuristics}, journal ={IEEE Transactions on Computers}, volume = {42}, number = {10}, issn = {00189340}, year = {1993}, pages = {12531256}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.257719}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Bounds on the Performance of Message Routing Heuristics IS  10 SN  00189340 SP1253 EP1256 EPD  12531256 A1  P.J. Bernhard, PY  1993 KW  performance; message routing heuristics; omega network; communication conflicts; conflictfree; minimum round partitioning problem; heuristics; message patterns; lower bounds; upper bounds; computational complexity; message passing; multiprocessor interconnection networks; network routing; performance evaluation. VL  42 JA  IEEE Transactions on Computers ER   
Let S be a set of messages to be routed on an N*N omega network. In addition, suppose that S contains communication conflicts. One strategy to deal with such conflicts is to partition S into some number of subsets, called rounds, such that each subset is conflictfree. The messages are then routed through the network by successively routing the messages in each subset. The minimum round partitioning problem is the problem of partitioning a given message set into a minimum number of rounds. The author establishes upper and lower bounds on the performance ratio for two heuristics for partitioning message patterns into rounds. For both of these heuristics they give upper and lower bounds of O (log N) and Omega (logN), respectively.
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