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Behrooz Parhami, DingMing Kwai, "Periodically Regular Chordal Rings," IEEE Transactions on Parallel and Distributed Systems, vol. 10, no. 6, pp. 658672, June, 1999.  
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@article{ 10.1109/71.774913, author = {Behrooz Parhami and DingMing Kwai}, title = {Periodically Regular Chordal Rings}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {10}, number = {6}, issn = {10459219}, year = {1999}, pages = {658672}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.774913}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Periodically Regular Chordal Rings IS  6 SN  10459219 SP658 EP672 EPD  658672 A1  Behrooz Parhami, A1  DingMing Kwai, PY  1999 KW  Chordal rings KW  fault tolerance KW  greedy routing KW  hierarchical parallel architectures KW  interconnection networks KW  routing algorithms KW  skip links. VL  10 JA  IEEE Transactions on Parallel and Distributed Systems ER   
Abstract—Chordal rings have been proposed in the past as networks that combine the simple routing framework of rings with the lower diameter, wider bisection, and higher resilience of other architectures. Virtually all proposed chordal ring networks are nodesymmetric, i.e., all nodes have the same in/out degree and interconnection pattern. Unfortunately, such regular chordal rings are not scalable. In this paper, periodically regular chordal (PRC) ring networks are proposed as a compromise for combining low node degree with small diameter. By varying the PRC ring parameters, one can obtain architectures with significantly different characteristics (e.g., from linear to logarithmic diameter), while maintaining an elegant framework for computation and communication. In particular, a very simple and efficient routing algorithm works for the entire spectrum of PRC rings thus obtained. This flexibility has important implications for key system attributes such as architectural scalability, software portability, and fault tolerance. Our discussion is centered on unidirectional PRC rings with in/outdegree of 2. We explore the basic structure, topological properties, optimization of parameters, VLSI layout, and scalability of such networks, develop packet and wormhole routing algorithms for them, and briefly compare them to competing fixeddegree architectures such as symmetric chordal rings, meshes, tori, and cubeconnected cycles.
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