A quadratic lower bound for the convergence rate in the one-dimensional Hegselmann-Krause bounded confidence dynamics
Abstract
Let fk(n) be the maximum number of time steps taken to reach equilibrium by a system of n agents obeying the k-dimensional Hegselmann-Krause bounded confidence dynamics. Previously, it was known that Ω(n) = f1(n) = O(n3). Here we show that f1(n) = Ω(n2), which matches the best-known lower bound in all dimensions k >= 2.
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