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Comments on "Low Diameter Interconnections for Routing in High-Performance Parallel Systems," with Connections and Extensions to Arc Coloring of Coset Graphs
December 2008 (vol. 57 no. 12)
pp. 1726-1728
Wenjun Xiao, South China University of Technology, Guangzhou
Wenhong Wei, South China University of Technology, Guangzhou
Weidong Chen, South China University of Technology, Guangzhou
Mingxin He, South China University of Technology, Guangzhou
Behrooz Parhami, University of California, Santa Barbara
Recently, Melhem presented a "new" class of low-diameter interconnection (LDI) networks, (IEEE Trans. Computers, Vol. 56, No. 4, pp. 502-510). We note that LDI networks are the same as the previously known generalized de Bruijn graphs, point out an error in the decomposition of LDI networks into permutations, and find that the correct decomposition scheme is an instance of arc coloring for coset graphs. Hence, we pursue a number of general results on arc coloring of coset graphs that can be applied to this particular decomposition problem as well as within many other contexts, including complete arc coloring and normality of coset graphs.

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Index Terms:
Interconnection architectures, MIMD processors, Parallel processors, Interprocessor communications
Citation:
Wenjun Xiao, Wenhong Wei, Weidong Chen, Mingxin He, Behrooz Parhami, "Comments on "Low Diameter Interconnections for Routing in High-Performance Parallel Systems," with Connections and Extensions to Arc Coloring of Coset Graphs," IEEE Transactions on Computers, vol. 57, no. 12, pp. 1726-1728, Dec. 2008, doi:10.1109/TC.2008.164
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