We study the convergence of influence networks, where each node changes its state according to the majority of its neighbors. Our main result is a new Ω(n 2 / log 2 n) bound on the convergence time in the synchronous model, solving the classic "Democrats and Republicans" problem. Furthermore, we give a bound of Θ(n 2 ) for the sequential model in which the sequence of steps is given by an adversary and a bound of Θ(n) for the sequential model in which the sequence of steps is given by a benevolent process.
Recently, REF has shown that stabilization time in majority processes can be superlinear both in the synchronous model, and in the sequential model if the order is chosen by an adversary.
Convergence in (Social) Influence Networks
DISC
Computer Science