Abstract
We propose a family of regular Cayley network graphs of degree three based on permutation groups for design of massively parallel systems. These graphs are shown to be based on the shuffle exchange operations, to have logarithmic diameter in the number of vertices, and to be maximally fault tolerant. We investigate different algebraic properties of these networks (including fault tolerance) and propose a simple routing algorithm. These graphs are shown to be able to efficiently simulate or embed other permutation group based graphs; thus they seem to be very attractive for VLSI implementation and for applications requiring bounded number of I/O ports as well as to run existing applications for other permutation group based network architectures.
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S. B. Akers and B. Krishnamurthy. Group graphs as interconnection net works. In Proceedings of FTCS-14, pages 422–427, 1984.
S. B. Akers and B. Krishnamurthy. The star graph: an attractive alternative to n-cube. In Proceedings of International Conference on Parallel Processing (ICPP-87), pages 393–400, St. Charles, Illinois, August 1987.
S. B. Akers and B. Krishnamurthy. A group-theoretic model for symmetric interconnection networks. IEEE Transactions on Computers, 38(4):555–566, April 1989.
S. G. Akl. Parallel Computation: Models and Methods. Prentice-Hall, 1997.
M. A. Armstrong. Groups and Symmetry. Springer-Verlag, 1988.
L. Bhuyan and D. P. Agrawal. Generalized hypercube and hyperbus structure for a computer netwrk. IEEE Transactions on Computers, 33(3):323–333, March 1984.
C. Chen, D. P. Agrawal, and J. R. Burke. dBCube: a new class of hierarchical multiprocessor interconnection networks with area efficient layout. IEEE Transactions on Parallel and Distributed Systems, 4(12):1332–1344, December 1993.
K. Day and A. Tripathi. Arrangement graphs: a class of generalized star graphs. Information Processing Letters, 42:235–241, July 1992.
F. Harary. Graph Theory. Addison-Wesley, Reading, MA, 1972.
S. Latifi, M. M. Azevedo, and N. Bagherzadeh. The star connected cycles: a fixed degree network for parallel processing. In Proceedings of the International Conference on Parallel Processing, volume 1, pages 91–95, 1993.
W. E. Leland and M. H. Solomon. Dense trivalent graphs for processor interconnection. IEEE Transactions on Computers, 31(3):219–222, March 1982.
D. K. Pradhan and S. M. Reddy. A fault tolerant communication architecture for distributed systems. IEEE Transactions on Computers, C-31(9):863–870, September 1982.
F. Preparata and J. Vuillemin. The cube-connected cycles: a versatile network for parallel computation. Communications of ACM, 24(5):30–39, May 1981.
K. Qiu, S. G. Akl, and H. Meijer. On some properties and algorithms for the star and pancake interconnection networks. Journal of Parallel and Distributed Computing, 22(1), July 1994.
M. R. Samatham and D. K. Pradhan. The De Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI. IEEE Transactions on Computers, 38(4):567–581, April 1989.
I. Stojmenovic. Honeycomb networks: topological properties and communication algorithms. IEEE Transactions on Parallel and Distributed Systems, 8(10):1036–1042, October 1997.
P. Vadapalli and P. K. Srimani. Trivalent Cayley graphs for interconnection networks. Information Processing Letters, 54(6):329–335, June 1995.
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Latifi, S., Srimani, P.K. Sep: A Fixed Degree Regular Network for Massively Parallel Systems. The Journal of Supercomputing 12, 277–291 (1998). https://doi.org/10.1023/A:1008018024210
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DOI: https://doi.org/10.1023/A:1008018024210