Linear recursive networks and their applications in topological design and data routing
Pages 249 - 257
Abstract
We present a new class of interconnection topologies called the Linear Recursive Networks. It is shown that each member of this fairly large class of network topologies possesses a recursively-decomposable structure. The path and connectivity properties of the entire class of networks are analyzed and found to have useful features. It is also demonstrated that Point-To-Point or Broadcasting/Gathering operations can be performed efficiently on all Linear Recursive Networks. The preliminary results suggest that the Linear Recursive Networks potentially have many applications.
References
[1]
B. W. Arden and H. Lee, "Analysis of Chordal Ring Network," IEEE Trans. on Computers, C-30, 1981, 291-295.]]
[2]
R. C. Backhouse and B. A. Carre, "Regular Algebra Applied to Path-Finding Problems," J. Inst. Math. Applic., 15, 1975, i61-186.]]
[3]
V. E. Benes, Mathematical Theory of Connecting Networks and Telephone Trajfic, Academic Press, Orlando, FL., 1965.]]
[4]
D. Bertsekas and R. Gallagher, Data Networks, Prentice-Hall, Old Tappan, N. j. 1987.]]
[5]
R. R. Boorstyn and H. Frank, "Large Scale Network Topological Optimization," IEEE Trans. Communications, COM-26, Jan. i977, 29-47.]]
[6]
J. Carroll and D. Long, Theory of Finite Automata with an Introduction to Formal Languages, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1989.]]
[7]
W. Chou (ed.), Computer Communications: V. II,Systems and Applications, Prentice-Hall, Inc., N. J. USA, 1985.]]
[8]
N. Deo, Graph, Graph Theory wzth Application to Engineering and Computer Science, Prentice-Hall, Old Tappan, N. J., 1974.]]
[9]
R. A. Finkel and M. H. Solomon, "The Lens Interconnection Strategy," IEEE Trans. Computers, C-30, 1981.]]
[10]
M. D. Gaudreau, "Recursive Formula for the Calculation of Point-to-Point Congestion," IEEE Trans. Communications, COMM-28, March 1980, 313-316.]]
[11]
M. Gerla and L. Kleinrock, "On the Topological Design of Distributed Computer Networks," IEEE Trans. Communications, COM-25, Jan. 1977.]]
[12]
A. Ghafoor, "A Class of Fault-Tolerant Multiprocessor Networks," IEEE Trans. Reliability, R,-38, April 1989, 5-15.]]
[13]
J. N. Hagstrom, "Using the Decomposition Tree of a Network in Reliability Evaluation," IEEE Trans. Reliability, R-32, April 1983, 71-78.]]
[14]
F. Harary, Graph Theory, Addison-Wesley Pub. Co., Reading, Mass., 1969.]]
[15]
J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, Mass., 1979.]]
[16]
W.-J. Hsu, "Fibonacci (~ubcs: A New CAass of Interconnection Topologies; for Parallel Processing", IEEE Tran. on Parallel and Distributed Systems, Jan. 1993, pp. 3-12.]]
[17]
W.-J. Hsu and M. J. Chung, "Generalized Fibonacci C, ubes", accepted, to appear in Proc. Int'l Conference on Parallel Processing, 1993.]]
[18]
S. P. Jain and K. Gopal, "On Network Augmentation,'' IEEE Trans. Reliability, R-35, Dec. 1986, 541-543.]]
[19]
J. Kim, et al., "Reliability Evaluation of the Hypercube," IEEE Trans. Reliability, R-38, April 1989, 121-129.]]
[20]
J. Liu, Data Commun~catzon and Graph Embcddzng on a Large Famzly of Network Topologies, Ph.D. dissertation, Michigan S1;ate Univ., USA, 1992.]]
[21]
G. Memmi and Y. Raillard, "Some Results About the (d, k) Graph Problem", iEEE Trans. Computers, C-3 l, 1982, 784-791.]]
[22]
H. Nakazawa, "Baysian Decomposition Method for Computing the reliability of an Oriented Network," IEEE Trans. Reliability, R-25, April 1976, 77-80.]]
[23]
S. Rai and D. P. Agrawal, Dzstributed Computing: Nelwork Rehabzlily, IEEE Computer Society Press, 2nd edition, 1990.]]
[24]
S. Ranks and S. Sahni, Hypcrcube Algorithms (With Applications to Image Processzng and Pattern Rccognztion), Springer-Verlag, N. Y. 1990.]]
[25]
A. M. Rushdi, "On Reliability Evaluation by Network Decomposition," IEEE Trans. Reliability, R- 33, Dec. 1984, 379-384.]]
[26]
A. Satyanarayana and M. K. Chang, "Network Reliability and the Factoring Theorem," Networks, 13, 1983, 107-120.]]
[27]
R. L. Sharma, Network Topology Optimization: The Art and Science of Network Design, Van Nostrand Reinhold, N. Y., 1990.]]
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- Linear recursive networks and their applications in topological design and data routing
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Publication History
Published: 01 October 1993
Published in SIGCOMM-CCR Volume 23, Issue 4
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