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Behrooz Parhami, DingMing Kwai, "A Unified Formulation of Honeycomb and Diamond Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 12, no. 1, pp. 7480, January, 2001.  
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@article{ 10.1109/71.899940, author = {Behrooz Parhami and DingMing Kwai}, title = {A Unified Formulation of Honeycomb and Diamond Networks}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {12}, number = {1}, issn = {10459219}, year = {2001}, pages = {7480}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.899940}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  A Unified Formulation of Honeycomb and Diamond Networks IS  1 SN  10459219 SP74 EP80 EPD  7480 A1  Behrooz Parhami, A1  DingMing Kwai, PY  2001 KW  Cayley graph KW  kary ncube KW  network topology KW  processor array KW  pruned torus network KW  VLSI layout. VL  12 JA  IEEE Transactions on Parallel and Distributed Systems ER   
Abstract—Honeycomb and diamond networks have been proposed as alternatives to mesh and torus architectures for parallel processing. When wraparound links are included in honeycomb and diamond networks, the resulting structures can be viewed as having been derived via a systematic pruning scheme applied to the links of 2D and 3D tori, respectively. The removal of links, which is performed along a diagonal pruning direction, preserves the network's nodesymmetry and diameter, while reducing its implementation complexity and VLSI layout area. In this paper, we prove that honeycomb and diamond networks are special subgraphs of complete 2D and 3D tori, respectively, and show this viewpoint to hold important implications for their physical layouts and routing schemes. Because pruning reduces the node degree without increasing the network diameter, the pruned networks have an advantage when the degreediameter product is used as a figure of merit. Additionally, if the reduced node degree is used as an opportunity to increase the link bandwidths to equalize the costs of pruned and unpruned networks, a gain in communication performance may result.
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