Variants of Spreading Messages

  • T. V. Thirumala Reddy
  • D. Sai Krishna
  • C. Pandu Rangan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5942)

Abstract

In a distributed computing environment a faulty node could lead other nodes in the system to behave in a faulty manor. An initial set of faults could make all the nodes in the system become faulty. Such a set is called an irreversible dynamo. This is modelled as spreading a message among individuals V in a community \(G=\left( V,E\right) \) where E represents the acquaintance relation. A particular individual will believe a message if some of the individual’s acquaintances believe the same and forward the believed messages to its neighbours. We are interested in finding the minimum set of initial individuals to be considered as convinced, called the min-seed, such that every individual in the community is finally convinced. We solve for min-seed on some special classes of graphs and then give an upper bound on the cardinality of the min-seed for arbitrary undirected graphs. We consider some interesting variants of the problem and analyse their complexities and give some approximate algorithms.

Keywords

Vertex Cover Bipartite Graphs Approximate Algorithms Fault Tolerance NP-complete 

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References

  1. 1.
    Chang, C.-L., Lyuu, Y.-D.: On irreversible dynamic monopolies in general graphs. CoRR abs/0904.2306 (2009)Google Scholar
  2. 2.
    Peleg, D.: Size bounds for dynamic monopolies. Discrete Applied Mathematics 86(2-3), 263–273 (1998)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Watts, D.: A simple model of global cascades on random networks. P. Natl. Acad. Sci. USA 99(9), 5766–5771 (2002)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Flocchini, P., Lodi, E., Luccio, F., Santoro, N.: Irreversible dynamos in tori. In: Pritchard, D., Reeve, J.S. (eds.) Euro-Par 1998. LNCS, vol. 1470, pp. 554–562. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  5. 5.
    Luccio, F., Pagli, L., Sanossian, H.: Irreversible dynamos in butterflies. In: Gavoille, C., Bermond, J.C., Raspaud, A. (eds.) SIROCCO, pp. 204–218. Carleton Scientific (1999)Google Scholar
  6. 6.
    Flocchini, P., Geurts, F., Santoro, N.: Optimal irreversible dynamos in chordal rings. Discrete Applied Mathematics 113(1), 23–42 (2001)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Chang, C.L., Lyuu, Y.D.: Spreading messages. Theor. Comput. Sci. 410(27-29), 2714–2724 (2009)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Chang, C.L., Lyuu, Y.D.: Spreading of messages in random graphs. In: Downey, R., Manyem, P. (eds.) Fifteenth Computing: The Australasian Theory Symposium (CATS 2009), Wellington, New Zealand, ACS. CRPIT, vol. 94, pp. 3–7 (2009)Google Scholar
  9. 9.
    Reddy, T., Krishna, S., Rangan, P.: Variants of spreading messages (2010), http://www.cse.iitm.ac.in/~tiru/tiru/Publications_files/var_12page.pdf
  10. 10.
    Feige, U.: A threshold of ln for approximating set cover. J. ACM 45(4), 634–652 (1998)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • T. V. Thirumala Reddy
    • 1
  • D. Sai Krishna
    • 1
  • C. Pandu Rangan
    • 1
  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology MadrasChennaiIndia

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