Hostname: page-component-5db58dd55d-d6ndz Total loading time: 0 Render date: 2026-05-31T07:37:36.337Z Has data issue: false hasContentIssue false
  • English
  • Français

Reliable Broadcasting in Hypercubes with Random Link and Node Failures

Published online by Cambridge University Press:  12 September 2008

Bogdan S. Chlebus ,
Krzysztof Diks  and
Andrzej Pelc
Bogdan S. Chlebus
Affiliation:
Instytut Informatyki, Uniwersytet Warszawski, ul. Banacha 2, 02-097 Warszawa, Poland
Krzysztof Diks
Affiliation:
Instytut Informatyki, Uniwersytet Warszawski, ul. Banacha 2, 02-097 Warszawa, Poland
Andrzej Pelc
Affiliation:
Département d'Informatique, Université du Québec à Hull, C.P. 1250, succ. ‘B’, Hull, Québec J8X 3X7, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the problem of broadcasting in an n–node hypercube whose links and nodes fail independently with given probabilities p < 1 and q < 1, respectively. Information held in a fault-free node, called the source, has to reach all other fault-free nodes. Messages may be directly transmitted to adjacent nodes only, and every node may communicate with at most one neighbour in a unit of time. A message can be transmitted only if both communicating neighbours and the link joining them are fault-free. For parameters p and q satisfying (1 – p)(1 – q) ≽ 0.99 (e.g. p = q = 0.5%), we give an algorithm working in time O(log n) and broadcasting source information to all fault-free nodes with probability exceeding 1 – cn-e for some positive constant ε, c depending on p and q but not depending on n.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 4 , December 1996 , pp. 337 - 350
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Angluin, D. and Valiant, L. G. (1979) Fast probabilistic algorithms for Hamiltonian circuits and matchings. J. Comput. Systems Sci. 18 155–193.Google Scholar
[2]Banerjee, P. (1990) Strategies for reconfiguring hypercubes under faults. Proc. 20th Int. Symp. on Fault-Tolerant Computing, Newcastle, UK 210–217.Google Scholar
[3]Berman, K. A. and Hawrylycz, M. (1986) Telephone problems with failures. SIAM J. Alg. Disc. Meth. 7 13–17.Google Scholar
[4]Bienstock, D. (1988) Broadcasting with random faults. Disc. Appl. Math. 20 1–7.Google Scholar
[5]Chlebus, B. S., Diks, K. and Pelc, A. (1994) Sparse networks supporting efficient reliable broadcasting. Nordic J. on Computing 1 332–345.Google Scholar
[6]Chlebus, B. S., Diks, K. and Pelc, A. (1991) Optimal broadcasting in faulty hypercubes. Proc. 21st Int. Symp. on Fault-Tolerant Computing, Montreal, Canada, 266–273.Google Scholar
[7]Diks, K. and Pelc, A. (1990) Reliable gossip schemes with random link failures. Proc. 28th Ann. Allerton Conf. on Comm. Control and Comp. 978–987.Google Scholar
[8]Diks, K. and Pelc, A. (1992) Almost safe gossiping in bounded degree networks. SIAM J. Disc. Math. 5 338–344.Google Scholar
[9]Fill, J. A. and Pemantle, R. (1993) Percolation, first-passage percolation and covering times for Richardson's model on the n–cube. Annals of Applied Probability 3 593–629.CrossRefGoogle Scholar
[10]Gargano, L. (1992) Tighter time bounds on fault tolerant broadcasting and gossiping (1988). Networks 22 469–486.CrossRefGoogle Scholar
[11]Haddad, R. W., Roy, S. and Schaffer, A. A. (1987) On gossiping with faulty telephone lines. SIAM J. Alg. Disc. Meth. 8 439–445.CrossRefGoogle Scholar
[12]Hagerup, T. and Rub, C. (1989/1990) A guided tour of Chernoff bounds. Inf. Proc. Letters 33 305–308.CrossRefGoogle Scholar
[13]Hastad, J., Leighton, T. and Newman, M. (1987) Reconfiguring a hypercube in the presence of faults. Proc. 19th Ann. Symp. on Theory of Computing, 274–284.Google Scholar
[14]Hastad, J., Leighton, T. and Newman, M. (1989) Fast computation using faulty hypercubes. Proc. 21st Ann. Symp. on Theory of Computing 251–263.Google Scholar
[15]Heath, M. T. (1988) Hypercube Multiprocessors, SIAM, Philadelphia.Google Scholar
[16]Hedetniemi, S. M., Hedetniemi, S. T. and Liestman, A. L. (1988) A survey of gossiping and broadcasting in communication networks. Networks 18 319–349.Google Scholar
[17]Krumme, D. W. (1992) Fast gossiping for the hypercube. SIAM J. Computing 21 365–380.CrossRefGoogle Scholar
[18]Krumme, D. W., Cybenko, G. and Venkataraman, K. N. 1992 Gossiping in minimal time. SIAM J. Computing 21 111–139.Google Scholar
[19]Pelc, A. (1991) Broadcasting in complete networks with faulty nodes using unreliable calls. Inf. Proc. Letters 40 169–174.Google Scholar
[20]Ramanathan, P. and Shin, K. G. (1988) Reliable broadcast in hypercube multicomputers. IEEE Trans. Computers 37 1654–1657.Google Scholar
[21]Scheinerman, E. R. and Wierman, J. C. (1989) Optimal and near-optimal broadcast in random graphs. Disc. Appl. Math. 25 289–297.Google Scholar
[22]Seitz, Ch. (1985) The Cosmic Cube. Comm. ACM 28 22–33.CrossRefGoogle Scholar