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- W4287100596 abstract "We study the stabilization time of two common types of influence propagation. In majority processes, nodes in a graph want to switch to the most frequent state in their neighborhood, while in minority processes, nodes want to switch to the least frequent state in their neighborhood. We consider the sequential model of these processes, and assume that every node starts out from a uniform random state. We first show that if nodes change their state for any small improvement in the process, then stabilization can last for up to $Theta(n^2)$ steps in both cases. Furthermore, we also study the proportional switching case, when nodes only decide to change their state if they are in conflict with a $frac{1+lambda}{2}$ fraction of their neighbors, for some parameter $lambda in (0,1)$. In this case, we show that if $lambda < frac{1}{3}$, then there is a construction where stabilization can indeed last for $Omega(n^{1+c})$ steps for some constant $c>0$. On the other hand, if $lambda > frac{1}{2}$, we prove that the stabilization time of the processes is upper-bounded by $O(n cdot log{n})$." @default.
- W4287100596 created "2022-07-25" @default.
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- W4287100596 date "2021-07-05" @default.
- W4287100596 modified "2023-09-27" @default.
- W4287100596 title "Stabilization Bounds for Influence Propagation from a Random Initial State" @default.
- W4287100596 doi "https://doi.org/10.48550/arxiv.2107.02076" @default.
- W4287100596 hasPublicationYear "2021" @default.
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