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Optimal fault-tolerant broadcasting in trees

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  • Session 4A
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Algorithms and Computation (ISAAC 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1350))

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Abstract

We consider broadcasting a message from one node of a tree to all other nodes. In the presence of up to k link failures the tree becomes disconnected, and only nodes in the connected component C containing the source can be informed. The maximum ratio between the time used by a broadcasting scheme B to inform C and the optimal time to inform C, taken over all components C yielded by configurations of at most k faults, is the k-vulnerability of B. This is the maximum slowdown incurred by B due to the lack of a priori knowledge of fault location, for at most k faults. This measure of fault-tolerance is similar to the competitive factor of on-line algorithms: in both cases, the performance of an algorithm lacking some crucial information is compared to the performance of an “off-line” algorithm, one that is given this information as input. It is also the first known tool to measure and compare fault-tolerance of broadcasting schemes in trees.

We seek broadcasting schemes with low vulnerability, working for tree networks. It turns out that schemes that give the best broadcasting time in a fault-free environment may have very high vulnerability, i.e., poor fault-tolerance, for some trees. The main result of this paper is an algorithm that, given an arbitrary tree T and an integer k, computes a broadcasting scheme B with lowest possible k-vulnerability among all schemes working for T. Our algorithm has running time O(kn 2 +n 21og n), where n is the size of the tree.

Research supported in part by NSERC grant OGP 0008136.

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References

  1. K.A. Berman and M. Hawrylycz, Telephone problems with failures, SIAM J. Alg. Disc. Meth. 7 (1986), 13–17.

    Google Scholar 

  2. D. Bienstock, Broadcasting with random faults, Disc. Appl. Math. 20 (1988), 1–7.

    Google Scholar 

  3. B.S. Chlebus, K. Diks and A. PeIc, Sparse networks supporting efficient reliable broadcasting, Proc. ICALP'93, LNCS 700, 388-397.

    Google Scholar 

  4. K. Diks and A. Pelc, Almost safe gossiping in bounded degree networks, SIAM J. Disc. Math. 5 (1992), 338–344.

    Google Scholar 

  5. K. Diks and A. Pelc, Efficient gossiping by packets in networks with random faults, SIAM J. Disc. Math. 9 (1996), 7–18.

    Google Scholar 

  6. P. Fraigniaud and E. Lazard, Methods and problems of communication in usual networks, Disc. Appl. Math. 53 (1994), 79–133.

    Google Scholar 

  7. L. Gargano, Tighter bounds on fault-tolerant broadcasting and gossiping, Networks 22 (1992), 469–486.

    Google Scholar 

  8. L. Gargano and U. Vaccaro, Minimum time networks tolerating a logarithmic number of faults, SIAM J. Disc. Math. 5 (1992), 178–198.

    Google Scholar 

  9. R.W. Haddad, S. Roy and A.A. Schiffer, On gossiping with faulty telephone lines, SIAM J. Alg. Disc. Meth. 8 (1987), 439–445.

    Google Scholar 

  10. S.M. Hedetniemi, S.T. Hedetniemi and A.L. Liestman, A survey of gossiping and broadcasting in communication networks, Networks 18 (1988), 319–349.

    Google Scholar 

  11. J. Hromkovič, R. Klasing, B. Monien and R. Peine, Dissemination of information in interconnection networks (broadcasting and gossiping), in: F. Hsu and D.-Z. Du (Eds.), Combinatorial Network Theory, Kluwer Academic Publishers 1996, 125–212.

    Google Scholar 

  12. A.L. Liestman, Fault-tolerant broadcast graphs, Networks 15 (1985), 159–171.

    Google Scholar 

  13. A. Pelc, Fault-tolerant broadcasting and gossiping in communication networks, Networks 28 (1996), 143–156.

    Google Scholar 

  14. D. Peleg and A.A. Schiffer, Time bounds on fault-tolerant broadcasting, Networks 19 (1989), 803–822.

    Google Scholar 

  15. E.R. Scheinerman and J.C. Wierman, Optimal and near-optimal broadcast in random graphs, Disc. Appl. Math. 25 (1989), 289–297.

    Google Scholar 

  16. P.J. Slater, E.J. Cockayne and S.T. Hedetniemi, Information dissemination in trees, SIAM J. Comput. 10 (1981), 692–701.

    Google Scholar 

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Authors and Affiliations

  1. Département d'Informatique, Université du Québec à Hull, J8X 3X7, Hull, Québec, Canada

    Petri§or Panaite & Andrzej Pelc

Authors
  1. Petri§or Panaite
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  2. Andrzej Pelc
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Hon Wai Leong Hiroshi Imai Sanjay Jain

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© 1997 Springer-Verlag Berlin Heidelberg

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Panaite, P., Pelc, A. (1997). Optimal fault-tolerant broadcasting in trees. In: Leong, H.W., Imai, H., Jain, S. (eds) Algorithms and Computation. ISAAC 1997. Lecture Notes in Computer Science, vol 1350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63890-3_17

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  • DOI: https://doi.org/10.1007/3-540-63890-3_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63890-2

  • Online ISBN: 978-3-540-69662-9

  • eBook Packages: Springer Book Archive

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