Stabilization Time in Minority Processes

07/03/2019

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by   Pál András Papp, et al.

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We analyze the stabilization time of minority processes in graphs. A minority process is a dynamically changing coloring, where each node repeatedly changes its color to the color which is least frequent in its neighborhood. First, we present a simple Ω(n^2) stabilization time lower bound in the sequential adversarial model. Our main contribution is a graph construction which proves a Ω(n^2-ϵ) stabilization time lower bound for any ϵ>0. This lower bound holds even if the order of nodes is chosen benevolently, not only in the sequential model, but also in any reasonable concurrent model of the process.