This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Flip-Trees: Fault-Tolerant Graphs with Wide Containers
April 1988 (vol. 37 no. 4)
pp. 472-478
A family of graphs is introduced with (d(d-1)/sup l/-2)/(d-2) nodes, where d is the degree of every node and l is any positive integer. The graphs have diameter 2l-1. In the presence of at most d-1 faults, the diameter increases to at most 2l+1. Furthermore, there exists a container (set of node-disjoint paths) of width d and length at most 2l+1 between every pair of nodes. The graphs are compa

[1] S. B. Akers and B. Krishnamurthy, "Group graphs as interconnection networks," inProc. 14th Int. Symp. Fault-Tolerant Comput., Orlando, FL, June 1984, pp. 422-427.
[2] S. B. Akers and B. Krishnamurthy, "Fault-tolerance in star graphs," inProc. 1987 Int. Conf. Supercomput., San Francisco, CA, May 1987.
[3] J. L. Bentley and H. T. Kung, "A tree machine for searching problems," inProc. 1979 Int. Conf. Parallel Processing, Detroit, MI, Aug. 1979, pp. 257-266.
[4] L. N. Bhuyan and D. P. Agrawal, "Generalized hypercube and hyperbus structures for computer networks,"IEEE Trans. Comput., vol. C-33, pp. 323-333, Apr. 1984.
[5] F. T. Boesch, F. Harary, and J. H. Kabell, "Graphs as models of communication network vulnerability: Connectivity and persistence,"Networks, vol. 11, pp. 57-63, 1981.
[6] J. Bondy and U. Murthy,Graph Theory with Applications. New York: American Elsevier, 1976.
[7] Davies, D. W. 1972. The control of congestion in packet-switching networks.IEEE Trans. on Communications COM-20, pp. 546-550.
[8] C. Delorme and G. Farhi, "Large graphs with given degree and diameter-Part I,"IEEE Trans. Comput., vol. C-33, pp. 857-860, Sept. 1984.
[9] D. Dolev, "The Byzantine generals strike again,"Algorithms, vol. 3, pp. 14-30, 1982.
[10] A.-H. Esfahanian and S. L. Hakimi, "Fault-tolerant routing in de Bruijn communications networks,"IEEE Trans. Comput., vol. C-34, pp. 777-788, Sept. 1985.
[11] L. R. Ford, Jr. and D. R. Fulkerson,Flows in Networks. Princeton, NJ: Princeton Univ. Press, 1962.
[12] S. L. Hakimi, "An algorithm for construction of the least vulnerable communication network or the graph with the maximum connectivity,"IEEE Trans. Circuit Theory., vol. CT-16, pp. 229-230, May 1969.
[13] J. P. Hayes, "A graph model for fault-tolerant computing systems,"IEEE Trans. Comput., vol. C-25, pp. 875-884, Sept. 1976.
[14] M. S. Krishnamoorthy and B. Krishnamurthy, "Fault diameter of interconnection networks,"Comput. Math. Appl., vol. 13, no. 5/6, pp. 577-582, 1987.
[15] V. P. Kumar and S. M. Reddy, "A class of graphs for fault-tolerant processor interconnections," inProc. 4th Int. Conf. Distributed Comput. Syst., San Francisco, CA, May 1984, pp. 448-460.
[16] T. Lang and H. S. Stone, "A shuffle-exchange network with simplified control,"IEEE Trans. Comput., vol. C-25, pp. 55-66, Jan. 1976.
[17] W. E. Leland, "Dense interconnection graphs with small degree," Ph.D. dissertation, Dep. Comput. Sci., Univ. Wisconsin, Madison, WI, Aug. 1981.
[18] W. E. Leland and M. H. Solomon, "Dense trivalent graphs for processor interconnection,"IEEE Trans. Comput., vol. C-31, pp. 219-222, Mar. 1982.
[19] F. J. Meyer and D. K. Pradhan, "Consensus with dual failure modes," Tech. Rep., Dep. Elec. Comput. Eng., Univ. Massachusetts, Amherst, MA, Apr. 1987.
[20] F. J. Meyer and D. K. Pradhan, "Flip-trees: Graphs with wide containers," Tech. Rep., Dep. Elec. Comput. Eng., Univ. Massachusetts, Amherst, MA, Nov. 1987.
[21] E. F. Moore, "The shortest path through a maze," inProc. Int. Symp. Switching Theory, 1957, Part II. Cambridge, MA: Harvard Univ. Press, 1959, pp. 285-292.
[22] D. K. Pradhan, "Fault-tolerant multiprocessor link and bus network architectures,"IEEE Trans. Comput., vol. C-34, pp. 33-45, Jan. 1985.
[23] D. K. Pradhan and S. M. Reddy, "A fault-tolerant communication architecture for distributed systems,"IEEE Trans. Comput., vol. C- 31, pp. 863-870, Sept. 1982.
[24] F. P. Preparata and J. Vuillemin, "The cube-connected cycle: A versatile network for parallel computation,"Commun. ACM, vol. 24, pp. 300-309, May 1981.
[25] A. Rucinski and J. L. Pokoski, "Polystructural, reconfigurable, and fault-tolerant computers," inProc. 6th Int. Conf. Distributed Comput. Syst., Cambridge, MA, May 1986, pp. 175-182.
[26] A. Sengupta, A. Sen, and S. Bandyopadhyay, "On an optimally fault tolerant multiprocessor network architecture,"IEEE Trans. Comput., vol. C-36, pp. 619-623, May 1987.
[27] S. Toida, F. J. Meyer, and D. K. Pradhan, "A theorem on the faulttolerance of a modified de Bruijn network topology,"IEEE Trans. Comput., submitted for publication.
[28] D. K. Pradhan,Fault Tolerant Computing: Theory and Techniques. Englewood Cliffs, NJ: Prentice-Hall, 1986.

Index Terms:
computer networks; flip trees; graphs; positive integer; container; node-disjoint paths; fault-tolerant diameter; ease of routing; fault-tolerant routing; computer networks; fault tolerant computing; graph theory; trees (mathematics).
Citation:
F.J. Meyer, "Flip-Trees: Fault-Tolerant Graphs with Wide Containers," IEEE Transactions on Computers, vol. 37, no. 4, pp. 472-478, April 1988, doi:10.1109/12.2194
Usage of this product signifies your acceptance of the Terms of Use.