In their seminal PODC 1991 paper, Ostrovsky and Yung introduced the study of distributed computation in the presence of mobile adversaries which can dynamically appear throughout the network. Over the years, this setting has been studied mostly under the assumption that the communication graph is fully-connected. Resilient CONGEST algorithms for general graphs, on the other hand, are currently known only for the classical static setting, i.e., where the set of corrupted edges (or nodes) is fixed throughout the entire computation. We fill this gap by providing round-efficient simulations that translate given CONGEST algorithms into equivalent algorithms that are resilient against $f$-mobile edge adversaries. Our main results are: -Perfect-Security with Mobile Eavesdroppers: A translation of any $r$-round $f$-static-secure algorithm into an equivalent $\Theta(f)$-mobile-secure algorithm with $\Theta(r)$ rounds. We also show that the $f$-static-secure algorithms of [Hitron, Parter and Yogev, DISC 2022 & ITCS 2023] can be modified into $f$-mobile-secure algorithms with the same number of rounds. -Resilience with Mobile Byzantine Adversaries: An $f$-mobile-byzantine simulation which is based on a decomposition of the graph into low-diameter edge-disjoint spanning trees. This provides us with near-optimal CONGEST compilers for expander graphs. It also leads to near-optimal compilers in the congested-clique model against $\Theta(n)$-mobile adversaries. For general $(2f+1)$ edge-connected graphs with $f$-mobile adversary, we almost match the bounds known for the $f$-static setting, when provided a trusted pre-processing phase. Our results are based on a collection of tools from interactive coding [Gelles, Found. Trends Theor. Comput. Sci. 2017], linear sketches and low-congestion graph decomposition. The introduced toolkit might have further applications for resilient computation.

翻译：在其开创性的PODC 1991论文中，Ostrovsky和Yung引入了存在可在网络中动态出现的移动对手时的分布式计算研究。多年来，这一设定大多在通信图为全连接图的假设下进行研究。另一方面，针对一般图结构的弹性CONGEST算法目前仅适用于经典静态设定，即被破坏的边（或节点）集在整个计算过程中固定不变。我们通过提供轮高效的模拟来填补这一空白，将给定的CONGEST算法转化为对$f$-移动边对手具有弹性的等价算法。我们的主要结果包括：- 针对移动窃听者的完美安全性：将任意$r$轮$f$-静态安全算法转化为等价的$\Theta(f)$-移动安全算法，且轮数为$\Theta(r)$。我们还证明，[Hitron, Parter and Yogev, DISC 2022 & ITCS 2023]中的$f$-静态安全算法可修改为具有相同轮数的$f$-移动安全算法。- 针对移动拜占庭对手的弹性：一种基于图分解为低直径边不相交生成树的$f$-移动拜占庭模拟。这为扩展图提供了近乎最优的CONGEST编译器，同时在拥塞团模型中也导致了对$\Theta(n)$-移动对手近乎最优的编译器。对于具有$f$-移动对手的一般$(2f+1)$边连通图，在提供可信预处理阶段的情况下，我们几乎匹配了$f$-静态设定下的已知界限。我们的结果基于交互式编码[Gelles, Found. Trends Theor. Comput. Sci. 2017]、线性草图及低拥塞图分解等工具。所引入的工具集可能对弹性计算具有进一步应用价值。