Reachability of Five Gossip Protocols

  • Hans van Ditmarsch
  • Malvin Gattinger
  • Ioannis KokkinisEmail author
  • Louwe B. Kuijer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11674)


Gossip protocols use point-to-point communication to spread information within a network until every agent knows everything. Each agent starts with her own piece of information (‘secret’) and in each call two agents will exchange all secrets they currently know. Depending on the protocol, this leads to different distributions of secrets among the agents during its execution. We investigate which distributions of secrets are reachable when using several distributed epistemic gossip protocols from the literature. Surprisingly, a protocol may reach the distribution where all agents know all secrets, but not all other distributions. The five protocols we consider are called \(\mathsf {ANY}\), \(\mathsf {LNS}\), \(\mathsf {CO}\), \(\mathsf {TOK}\), and \(\mathsf {SPI}\). We find that \(\mathsf {TOK}\) and \(\mathsf {ANY}\) reach the same distributions but all other protocols reach different sets of distributions, with some inclusions. Additionally, we show that all distributions are subreachable with all five protocols: any distribution can be reached, if there are enough additional agents.


Gossip Networks Reachability 



We would like to thank the anonymous reviewers for their helpful corrections and suggestions. Hans van Ditmarsch is also affiliated to IMSc, Chennai, as associate researcher.


  1. 1.
    Apt, K., Grossi, D., van der Hoek, W.: Epistemic protocols for distributed gossiping. In: Proceedings of 15th TARK (2015). Scholar
  2. 2.
    Attamah, M., van Ditmarsch, H., Grossi, D., van der Hoek, W.: Knowledge and gossip. In: Proceedings of 21st ECAI, pp. 21–26. IOS Press (2014).
  3. 3.
    Attamah, M., van Ditmarsch, H., Grossi, D., van der Hoek, W.: The pleasure of gossip. In: Başkent, C., Moss, L.S., Ramanujam, R. (eds.) Rohit Parikh on Logic, Language and Society. OCL, vol. 11, pp. 145–163. Springer, Cham (2017). 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). Scholar
  5. 5.
    van Ditmarsch, H., van Eijck, J., Pardo, P., Ramezanian, R., Schwarzentruber, F.: Dynamic gossip. Bull. Iran. Math. Soc. 45(3), 701–728 (2019). Scholar
  6. 6.
    van Ditmarsch, H., Kokkinis, I., Stockmarr, A.: Reachability and expectation in gossiping. In: An, B., Bazzan, A., Leite, J., Villata, S., van der Torre, L. (eds.) PRIMA 2017. LNCS (LNAI), vol. 10621, pp. 93–109. Springer, Cham (2017). Scholar
  7. 7.
    van Ditmarsch, H., Kokkinis, I.: The expected duration of sequential gossiping. In: Belardinelli, F., Argente, E. (eds.) EUMAS/AT 2017. LNCS (LNAI), vol. 10767, pp. 131–146. Springer, Cham (2018). Scholar
  8. 8.
    Gattinger, M.: New directions in model checking dynamic epistemic logic. Ph.D. thesis, University of Amsterdam (2018). (ILLC Dissertation Series DS-2018-11)
  9. 9.
    Göbel, F., Cerdeira, J.O., Veldman, H.J.: Label-connected graphs and the gossip problem. Discrete Math. 87(1), 29–40 (1991). Scholar
  10. 10.
    Hedetniemi, S., Hedetniemi, S., Liestman, A.: A survey of gossiping and broadcasting in communication networks. Networks 18, 319–349 (1988). Scholar
  11. 11.
    Kermarrec, A.M., van Steen, M.: Gossiping in distributed systems. SIGOPS Oper. Syst. Rev. 41(5), 2–7 (2007). Scholar
  12. 12.
    Knödel, W.: New gossips and telephones. Discrete Math. 13, 95 (1975). Scholar
  13. 13.
    Kokkinis, I.: Implementation for reachability and expectation in gossiping.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.CNRS, LORIA, University of LorraineNancyFrance
  2. 2.University of GroningenGroningenThe Netherlands
  3. 3.TU DortmundDortmundGermany
  4. 4.University of LiverpoolLiverpoolUK

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