Abstract
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.
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Acknowledgements
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.
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van Ditmarsch, H., Gattinger, M., Kokkinis, I., Kuijer, L.B. (2019). Reachability of Five Gossip Protocols. In: Filiot, E., Jungers, R., Potapov, I. (eds) Reachability Problems. RP 2019. Lecture Notes in Computer Science(), vol 11674. Springer, Cham. https://doi.org/10.1007/978-3-030-30806-3_17
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DOI: https://doi.org/10.1007/978-3-030-30806-3_17
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