Reachability and other path-based measures on temporal graphs can be used to understand spread of infection, information, and people in modelled systems. Due to delays and errors in reporting, temporal graphs derived from data are unlikely to perfectly reflect reality, especially with respect to the precise times at which edges appear. To reflect this uncertainty, we consider a model in which some number $\zeta$ of edge appearances may have their timestamps perturbed by $\pm\delta$ for some $\delta$. Within this model, we investigate temporal reachability and consider the problem of determining the maximum number of vertices any vertex can reach under these perturbations. We show that this problem is intractable in general but is efficiently solvable when $\zeta$ is sufficiently large. We also give algorithms which solve this problem in several restricted settings. We complement this with some contrasting results concerning the complexity of related temporal eccentricity problems under perturbation.

翻译：时态图中的可达性及其他基于路径的度量可用于理解被建模系统中的感染传播、信息扩散及人员流动。由于报告延迟和误差，从数据中导出的时态图难以完美反映现实，尤其在边出现的确切时间方面。为刻画这种不确定性，我们考虑一个模型，其中若干条边出现的时间戳可能发生±δ的扰动，扰动边数为ζ。在此模型下，我们研究时态可达性，并探讨在该扰动条件下任意顶点所能到达的最大顶点数问题。我们证明该问题在一般情况下是难解的，但当ζ足够大时可高效求解。同时，我们给出了在若干限制条件下解决该问题的算法。作为补充，我们提出了关于扰动下相关时态离心率问题复杂性的对比性结论。