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Existence of an Optimal Perpetual Gossiping Scheme for Arbitrary Networks

  • Ivan AvramovicEmail author
  • Dana S. Richards
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 69)

Abstract

Gossiping is a problem in which a peer-to-peer network must disperse the information held by each machine to all other machines in the minimum number of communication steps. In perpetual gossiping, new information may be introduced to any machine at any time, and the objective is to find a perpetual communication scheme which guarantees that new information will be completely dispersed in optimal time. The basic gossiping problem has a well-known solution, but the perpetual gossiping extension has defied a general solution. Additionally, prior to this paper, it has not been shown that there is even a means to arrive at an optimal solution on a case-by-case basis. Attempts at optimization have thus far taken place in a series of progressive refinements, broadening the scope of network topologies for which optimal or near-optimal solutions are known. This paper proceeds from the opposite direction, by demonstrating an algorithm which is guaranteed to find an optimal perpetual gossiping scheme for an arbitrary graph. The network model is then generalized so as to apply to a broader class of communication schemes.

Keywords

Perpetual gossip Peer-to-peer networks Optimization Network topology 

References

  1. 1.
    Baker, B., Shostak, R.: Gossips and telephones. Discret. Math. 2(3), 191–193 (1972).  https://doi.org/10.1016/0012-365X(72)90001-5MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bumby, R.T.: A problem with telephones. SIAM J. Algebraic Discret. Methods 2(1), 13–18 (1981)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Chang, G.J., Tsay, Y.J.: The partial gossiping problem. Discret. Math. 148(1), 9–14 (1996).  https://doi.org/10.1016/0012-365X(94)00257-JMathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    van Ditmarsch, H., van Eijck, J., Pardo, P., Ramezanian, R., Schwarzentruber, F.: Epistemic protocols for dynamic gossip. J. Appl. Logic 20, 1–31 (2017).  https://doi.org/10.1016/j.jal.2016.12.001MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Fertin, G.: A study of minimum gossip graphs. Discret. Math. 215(1–3), 33–57 (2000)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Fertin, G., Labahn, R., et al.: Compounding of gossip graphs. Networks 36(2), 126–137 (2000)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Hajnal, A., Milner, E.C., Szemerédi, E.: A cure for the telephone disease. Canad. Math. Bull 15(3), 447–450 (1972)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hedetniemi, S.M., Hedetniemi, S.T., Liestman, A.L.: A survey of gossiping and broadcasting in communication networks. Networks 18(4), 319–349 (1988)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Khuller, S., Kim, Y.A., Wan, Y.C.J.: On generalized gossiping and broadcasting. J. Algorithms 59(2), 81–106 (2006).  https://doi.org/10.1016/j.jalgor.2005.01.002MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Knoedel, W.: New gossips and telephones. Discret. Math. 13(1), 95 (1975).  https://doi.org/10.1016/0012-365X(75)90090-4MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Krumme, D.W.: Reordered gossip schemes. Discret. Math. 156(1), 113–140 (1996).  https://doi.org/10.1016/0012-365X(94)00302-YMathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Labahn, R., Hedetniemi, S.T., Laskar, R.: Periodic gossiping on trees. Discret. Appl. Math. 53(1), 235–245 (1994).  https://doi.org/10.1016/0166-218X(94)90187-2MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Liestman, A.L., Richards, D.: Perpetual gossiping. Parallel Process. Lett. 3(04), 347–355 (1993)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Scott, A.D.: Better bounds for perpetual gossiping. Discret. Appl. Math. 75(2), 189–197 (1997)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Tijdeman, R.: On a telephone problem. Nieuw Archief voor Wiskunde 3(19), 188–192 (1971)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Tsay, Y.J., Chang, G.J.: The exact gossiping problem. Discret. Math. 163(1), 165–172 (1997).  https://doi.org/10.1016/S0012-365X(96)00317-2MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.George Mason UniversityFairfaxUSA

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