On Convergence Rate of Scalar Hegselmann-Krause Dynamics
  In this work, we derive a new upper bound on the termination time of the Hegselmann-Krause model for opinion dynamics. Using a novel method, we show that the termination rate of this dynamics happens no longer than $O(n^3)$ which improves the best known upper bound of $O(n^4)$ by a factor of $n$ . 
Soheil Mohajer and Behrouz Touri
math.DS