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.
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References
Baker, B., Shostak, R.: Gossips and telephones. Discret. Math. 2(3), 191–193 (1972). https://doi.org/10.1016/0012-365X(72)90001-5
Bumby, R.T.: A problem with telephones. SIAM J. Algebraic Discret. Methods 2(1), 13–18 (1981)
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-J
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.2016.12.001
Fertin, G.: A study of minimum gossip graphs. Discret. Math. 215(1–3), 33–57 (2000)
Fertin, G., Labahn, R., et al.: Compounding of gossip graphs. Networks 36(2), 126–137 (2000)
Hajnal, A., Milner, E.C., Szemerédi, E.: A cure for the telephone disease. Canad. Math. Bull 15(3), 447–450 (1972)
Hedetniemi, S.M., Hedetniemi, S.T., Liestman, A.L.: A survey of gossiping and broadcasting in communication networks. Networks 18(4), 319–349 (1988)
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.2005.01.002
Knoedel, W.: New gossips and telephones. Discret. Math. 13(1), 95 (1975). https://doi.org/10.1016/0012-365X(75)90090-4
Krumme, D.W.: Reordered gossip schemes. Discret. Math. 156(1), 113–140 (1996). https://doi.org/10.1016/0012-365X(94)00302-Y
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)90187-2
Liestman, A.L., Richards, D.: Perpetual gossiping. Parallel Process. Lett. 3(04), 347–355 (1993)
Scott, A.D.: Better bounds for perpetual gossiping. Discret. Appl. Math. 75(2), 189–197 (1997)
Tijdeman, R.: On a telephone problem. Nieuw Archief voor Wiskunde 3(19), 188–192 (1971)
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)00317-2
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Avramovic, I., Richards, D.S. (2020). Existence of an Optimal Perpetual Gossiping Scheme for Arbitrary Networks. In: Arai, K., Bhatia, R. (eds) Advances in Information and Communication. FICC 2019. Lecture Notes in Networks and Systems, vol 69. Springer, Cham. https://doi.org/10.1007/978-3-030-12388-8_11
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