论文标题
一般稳定构成图形中影响传播的一般稳定
A General Stabilization Bound for Influence Propagation in Graphs
论文作者
论文摘要
我们研究了图表上宽类过程的稳定时间，在该过程中，每个节点只能通过至少$ \ frac {1+λ} {2} $的邻居分数进行$ 0 <λ<1 $而进行切换。此类过程的两个示例是图形中充分研究的动态变化：在大多数过程中，节点切换到附近最频繁的颜色，而在少数族裔过程中，节点切换到附近最不常见的颜色。我们描述了一个非元素函数$ f（λ）$，我们表明，在顺序模型中，这些过程的最坏情况稳定时间可以完全以$ f（λ）$为特征。更确切地说，我们证明，对于任何$ε> 0 $，$ o（n^{1+f（λ）+ε}）$是任何比例多数/少数族裔过程的稳定时间上的上限，并且我们还表明，稳定性确实需要$ω（n^{1+f（λ） - λ） - ε{1+f（λ） - ε}）$ speess。
We study the stabilization time of a wide class of processes on graphs, in which each node can only switch its state if it is motivated to do so by at least a $\frac{1+λ}{2}$ fraction of its neighbors, for some $0 < λ< 1$. Two examples of such processes are well-studied dynamically changing colorings in graphs: in majority processes, nodes switch to the most frequent color in their neighborhood, while in minority processes, nodes switch to the least frequent color in their neighborhood. We describe a non-elementary function $f(λ)$, and we show that in the sequential model, the worst-case stabilization time of these processes can completely be characterized by $f(λ)$. More precisely, we prove that for any $ε>0$, $O(n^{1+f(λ)+ε})$ is an upper bound on the stabilization time of any proportional majority/minority process, and we also show that there are graph constructions where stabilization indeed takes $Ω(n^{1+f(λ)-ε})$ steps.
