This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Rotator Graphs: An Efficient Topology for Point-to-Point Multiprocessor Networks
September 1992 (vol. 3 no. 5)
pp. 622-626
Rotator graphs, a set of directed permutation graphs, are proposed as an alternative to star and pancake graphs. Rotator graphs are defined in a way similar to the recently proposed Faber-Moore graphs. They have smaller diameter, n-1 in a graph with n factorial vertices, than either the star or pancake graphs or the k-ary n-cubes. A simple optimal routing algorithm is presented for rotator graphs. The n-rotator graphs are defined as a subset of all rotator graphs. The distribution of distances of vertices in the n-rotator graphs is presented, and the average distance between vertices is found. The n-rotator graphs are shown to be optimally fault tolerant and maximally one-step fault diagnosable. The n-rotator graphs are shown to be Hamiltonian, and an algorithm for finding a Hamiltonian circuit in the graphs is given.

[1] S. B. Akers, D. Harel, and B. Krishnamurthy, "The star graph: An attractive alternative to then-cube," inProc. Int. Conf. Parallel Processing, St. Charles, IL, Aug. 1987, pp. 393-400.
[2] S. B. Akers and B. Krishnamurthy, "Group graphs as interconnection networks," inProc. 14th Int. Conf. Fault Tolerant Comput., 1984, pp. 422-427.
[3] S. B. Akers and B. Krishnamurthy, "A group-theoretic model for symmetric interconnection networks,"IEEE Trans. Comput., vol. 38, no. 4, pp. 555-566, Apr. 1989.
[4] P. F. Corbett, "Network structures and algorithms for large multiprocessors," Ph.D. dissertation, Princeton Univ., Princeton, NJ, 1990.
[5] F. P. Preparata, G. Metze, and R. T. Chien, "On the connection assignment problem of diagnosable systems,"IEEE Trans. Electron. Comput., vol. EC-16, no. 6, pp. 848-853, Dec. 1967.
[6] V. Faber and J. W. Moore, "High-degree, low-diameter interconnection networks with vertex symmetry: The directed case," Available upon request LA-UR-88-1051, Los Alamos National Lab., Los Alamos, NM, 1988.
[7] W. H. Gates and C. H. Papadimitriou, "Bounds for sorting by prefix reversal,"Discrete Mathemat., vol. 27, no. 1, pp. 47-57, 1979.
[8] J. D. Russel and C. R. Kime, "System fault diagnosis: Closure and diagnosability with repairs,"IEEE Trans. Comput., vol. C-24, no. 11, pp. 1078-1089, Nov. 1975.
[9] J. D. Russel and C. R. Kime, "System fault diagnosis: Masking, exposure and diagnosability without repair,"IEEE Trans. Comput., vol. C-24, no. 12, pp. 1155-1161, Dec. 1975.

Index Terms:
Index Termstopology; point-to-point multiprocessor networks; directed permutation graphs; Faber-Moore graphs; optimal routing algorithm; rotator graphs; fault tolerant; one-step fault diagnosable; Hamiltonian circuit; directed graphs; multiprocessor interconnection networks
Citation:
P.F. Corbett, "Rotator Graphs: An Efficient Topology for Point-to-Point Multiprocessor Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 3, no. 5, pp. 622-626, Sept. 1992, doi:10.1109/71.159045
Usage of this product signifies your acceptance of the Terms of Use.