Consider a dynamic network and a given distributed problem. At any point in time, there might exist several solutions that are equally good with respect to the problem specification, but that are different from an algorithmic perspective, because some could be easier to update than others when the network changes. In other words, one would prefer to have a solution that is more robust to topological changes in the network; and in this direction the best scenario would be that the solution remains correct despite the dynamic of the network. In~\cite{CasteigtsDPR20}, the authors introduced a very strong robustness criterion: they required that for any removal of edges that maintain the network connected, the solution remains valid. They focus on the maximal independent set problem, and their approach consists in characterizing the graphs in which there exists a robust solution (the existential problem), or even stronger, where any solution is robust (the universal problem). As the robustness criteria is very demanding, few graphs have a robust solution, and even fewer are such that all of their solutions are robust. In this paper, we ask the following question: \textit{Can we have robustness for a larger class of networks, if we bound the number $k$ of edge removals allowed}? (See the full paper for the full abstract.)

翻译：考虑一个动态网络及给定的分布式问题。在任意时刻，可能存在多个在问题规范上同样优秀的解，但从算法视角来看，这些解可能有所不同，因为当网络变化时，某些解可能比其他解更容易更新。换言之，人们更倾向于选择一个对网络拓扑变化更具鲁棒性的解；在此方向上，最佳场景是该解在动态网络中仍保持正确性。在文献~\cite{CasteigtsDPR20}中，作者提出了一种非常强的鲁棒性准则：他们要求，对于任何保持网络连通的边移除操作，解仍然有效。他们聚焦于最大独立集问题，其方法在于刻画存在鲁棒性解（存在性问题）的图，甚至更进一步，要求所有解都是鲁棒性解（普适性问题）。由于该鲁棒性准则要求极为苛刻，仅有少数图存在鲁棒性解，而能使所有解都具有鲁棒性的图则更为稀少。本文提出以下问题：\textit{如果限制允许移除的边的数量为$k$，我们能否在更大类别的网络中实现鲁棒性？}（完整摘要详见论文全文。）