Distributed community detection in dynamic graphs

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 dyn- 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 approach 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 ( log ? n ) time even when the snapshots of the dynamic graph are sparse and disconnected (i.e., when p = ? ( 1 / n ) ).

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