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Behrooz Parhami, Mikhail A. Rakov, "Performance, Algorithmic, and Robustness Attributes of Perfect Difference Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 16, no. 8, pp. 725736, August, 2005.  
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@article{ 10.1109/TPDS.2005.98, author = {Behrooz Parhami and Mikhail A. Rakov}, title = {Performance, Algorithmic, and Robustness Attributes of Perfect Difference Networks}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {16}, number = {8}, issn = {10459219}, year = {2005}, pages = {725736}, doi = {http://doi.ieeecomputersociety.org/10.1109/TPDS.2005.98}, 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  Performance, Algorithmic, and Robustness Attributes of Perfect Difference Networks IS  8 SN  10459219 SP725 EP736 EPD  725736 A1  Behrooz Parhami, A1  Mikhail A. Rakov, PY  2005 KW  Bipartite graph KW  chordal ring KW  diameter KW  emulation KW  fault tolerance KW  hyperstar KW  interconnection network KW  permutation routing KW  robust network KW  routing algorithm KW  scalability. VL  16 JA  IEEE Transactions on Parallel and Distributed Systems ER   
Abstract—Perfect difference networks (PDNs) that are based on the mathematical notion of perfect difference sets have been shown to comprise an asymptotically optimal method for connecting a number of nodes into a network with diameter 2. Justifications for, and mathematical underpinning of, PDNs appear in a companion paper. In this paper, we compare PDNs and some of their derivatives to interconnection networks with similar cost/performance, including certain generalized hypercubes and their hierarchical variants. Additionally, we discuss pointtopoint and collective communication algorithms and derive a general emulation result that relates the performance of PDNs to that of complete networks as ideal benchmarks. We show that PDNs are quite robust, both with regard to node and link failures that can be tolerated and in terms of blandness (not having weak spots). In particular, we prove that the fault diameter of PDNs is no greater than 4. Finally, we study the complexity and scalability aspects of these networks, concluding that PDNs and their derivatives allow the construction of very low diameter networks close to any arbitrary desired size and that, in many respects, PDNs offer optimal performance and fault tolerance relative to their complexity or implementation cost.
[1] S.B. Akers and B. Krishnamurthy, “A GroupTheoretic Model for Symmetric Interconnection Networks,” IEEE Trans. Computers, vol. 38, no. 4, pp. 555566, Apr. 1989.
[2] A.E. AlAyyoub and K. Day, “The Cross Product of Interconnection Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 2, pp. 109118, Feb. 1997.
[3] A.E. AlAyyoub and K. Day, “Comparative Study of Product Networks,” J. Parallel and Distributed Computing, vol. 62, pp. 118, 2002.
[4] B.W. Arden and H. Lee, “Analysis of Chordal Ring Networks,” IEEE Trans. Computers, vol. 30, no. 4, pp. 291295, Apr. 1981.
[5] J.C. Bermond, F. Comellas, and D.F. Du, “Distributed Loop Computer Networks: A Survey,” J. Parallel and Distributed Computing, vol. 24, no. 1, pp. 210, Jan. 1995.
[6] L.N. Bhuyan and D.P. Agrawal, “Generalized Hypercube and Hyperbus Structures for a Computer Network,” IEEE Trans. Computers, vol. 33, no. 4, pp. 323333, Apr. 1984.
[7] G. Bilardi and F.P. Preparata, “Horizons of Parallel Computation,” J. Parallel and Distributed Computing, vol. 27, pp. 172182, June 1995.
[8] D.A. Carlson, “Modified MeshConnected Parallel Computers,” IEEE Trans. Computers, vol. 37, no. 10, pp. 13151321, Oct. 1988.
[9] K. Day and A.E. AlAyyoub, “Minimal Fault Diameter for Highly Resilient Product Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 11, no. 9, pp. 926930, Sept. 2000.
[10] A.M. Hobbs, “Network Survivability,” Applications of Discrete Math., J. G. Michaels and K. H. Rosen, eds., McGrawHill, pp. 332353, 1991.
[11] M.S. Krishnamoorthy and B. Krishnamurthy, “Fault Diameter of Interconnection Networks,” Computers & Math. with Applications, vol. 13, nos. 5/6, pp. 577582, 1987.
[12] S. Lakshmivarahan, J.S. Jwo, and S.K. Dahl, “Symmetry in Interconnection Networks Based on Cayley Graphs of Permutation Group: A Survey,” Parallel Computing, vol. 19, pp. 361401, 1993.
[13] F.T. Leighton, Introduction to Parallel Algorithms and Architectures: Arrays, Trees, and Hypercubes. Morgan Kaufmann, 1992.
[14] K.J. Liszka, J.K. Antonio, and H.J. Siegel, “Problems with Comparing Interconnection Networks: Is an Alligator Better than an Armadillo?” IEEE Concurrency, vol. 5, no. 4, pp. 1828, Oct.Dec. 1997.
[15] B. Parhami, Introduction to Parallel Processing: Algorithms and Architectures. Plenum Press, 1999.
[16] B. Parhami, “Swapped Interconnection Networks: Topological, Performance, and Robustness Attributes,” J. Parallel and Distributed Computing, to appear.
[17] B. Parhami and D.M. Kwai, “Challenges in Interconnection Network Design in the Era of Multiprocessor and Massively Parallel Microchips,” Proc. Int'l Conf. Comm. in Computing, pp. 241246, June 2000.
[18] B. Parhami and D.M. Kwai, “Incomplete kary ncube and Its Derivatives,” J. Parallel and Distributed Computing, vol. 64, no. 2, pp. 183190, Feb. 2004.
[19] B. Parhami and M. Rakov, “Perfect Difference Networks and Related Interconnection Structures for Parallel and Distributed Systems,” IEEE Trans. Parallel and Distributed Systems, vol. 16, no. 8, pp. 714724, Aug. 2005.
[20] M. Rakov, “Method of Interconnecting Nodes and a Hyperstar Interconnection Structure,” US Patent No. 5 734 580, Mar. 1998.
[21] M. Rakov, “Multidimensional Hyperstar and Hyperhub Interconnection Methods and Structures,” US Patent Application No. 09/410 175, Sept. 1999.
[22] M. Rakov, “Hyperstar and Hyperhub Optical Networks Interconnection Methods and Structures,” US Patent Application No. 09/634 129, Aug. 2000.
[23] M. Rakov and J. Mackall, “Method of Interconnecting Functional Nodes and a Hyperstar Interconnection Structure,” US Patent No. 6 330 706, Dec. 2001.
[24] M.J. Serrano and B. Parhami, “Optimal Architectures and Algorithms for MeshConnected Computers with Separable Row/Column Buses,” IEEE Trans. Parallel and Distributed Systems, vol. 4, no. 10, pp. 10731080, Oct. 1993.
[25] J. Singer, “A Theorem in Finite Projective Geometry and Some Applications to Number Theory,” Trans. Am. Math. Soc., vol. 43, pp. 377385, 1938.
[26] L.D. Wittie, “Communication Structures for Large Networks of Microcomputers,” IEEE Trans. Computers, vol. 30, no. 4, pp. 264273, Apr. 1981.
[27] W. Xiao and B. Parhami, “Some Mathematical Properties of Cayley Digraphs with Applications to Interconnection Network Design,” Int'l J. Computer Math., to appear.
[28] C.H. Yeh and B. Parhami, “Swapped Networks: Unifying the Architectures and Algorithms of a Wide Class of Hierarchical Parallel Processors,” Proc. Int'l Conf. Parallel and Distributed Systems, pp. 230237, June 1996.
[29] C.H. Yeh and B. Parhami, “Hierarchical Swapped Networks: Efficient LowDegree Alternatives to Hypercube and Generalized Hypercube,” Proc. Int'l Symp. Parallel Architectures, Algorithms, and Networks, pp. 9096, June 1996.
[30] S.G. Ziavras, Q. Wang, and P. Papathanasiou, “Viable Architectures for HighPerformance Computing,” The Computer J., vol. 46, no. 1, pp. 3654, 2003.