Abstract
Inspired by the increasing interest in self-organizing social opportunistic networks, we investigate the problem of distributed detection of unknown communities in dynamic random graphs. As a formal framework, we consider the dynamic version of the well-studied Planted Bisection Model \(\mbox{dyn-}\mathcal{G}(n,p,q)\) where the node set [n] of the network is partitioned into two unknown communities and, at every time step, each possible edge (u,v) is active with probability p if both nodes belong to the same community, while it is active with probability q (with q < < p) otherwise. We also consider a time-Markovian generalization of this model.
We propose a distributed protocol based on the popular Label Propagation Algorithm and prove that, when the ratio p/q is larger than n b (for an arbitrarily small constant b > 0), the protocol finds the right “planted” partition in O(logn) time even when the snapshots of the dynamic graph are sparse and disconnected (i.e. in the case p = Θ(1/n)).
Partially supported by Italian MIUR under the PRIN 2010-11 Project ARS TechnoMedia.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-319-03578-9_29
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Clementi, A., Di Ianni, M., Gambosi, G., Natale, E., Silvestri, R. (2013). Distributed Community Detection in Dynamic Graphs. In: Moscibroda, T., Rescigno, A.A. (eds) Structural Information and Communication Complexity. SIROCCO 2013. Lecture Notes in Computer Science, vol 8179. Springer, Cham. https://doi.org/10.1007/978-3-319-03578-9_1
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