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-(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)).