The epistemic gossip problem

Cooper, Martin, Herzig, Andreas, Maffre, Faustine, Maris, Frédéric and Régnier, Pierre (2019) The epistemic gossip problem. Discrete Mathematics, vol. 342 (n° 3). pp. 654-663.

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Abstract

In the gossip problem information (‘secrets’) must be shared among a certain number of agents using the minimum number of calls. We extend the gossip problem to arbitrary epistemic depths. For example, we may require not only that all agents know all secrets but also that all agents know that all agents know all secrets. We give optimal protocols for various versions of this epistemic gossip problem, depending on the graph of communication links, in the case of two-way communication, one-way communication and parallel communication. We show, among other things, that increasing epistemic depth from 1 (all agents know all secrets) to 2 (so that all agents know that all agents know all secrets) does not double the required number of calls but increases this number by 3/2 (for a complete graph). We also show that the following counterintuitive result generalises to the epistemic gossip problem: asymptotically the same number of calls are required whether calls are two-way or one-way.

Item Type: Article
Language: English
Date: March 2019
Refereed: Yes
Uncontrolled Keywords: communication protocol, epistemic logic, graph theory
Subjects: H- INFORMATIQUE
Divisions: Institut de Recherche en Informatique de Toulouse
Site: UT1
Date Deposited: 07 Dec 2018 14:37
Last Modified: 07 Dec 2018 14:51
OAI ID: BibTeX_Co2018.10
URI: http://publications.ut-capitole.fr/id/eprint/27707

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