Temporal graphs abstractly model real-life inherently dynamic networks. Given a graph G, a temporal graph with G as the underlying graph is a sequence of subgraphs (snapshots) $G_t$ of G, where $t\ge 1$. In this paper we study stochastic temporal graphs, i.e. stochastic processes $\mathcal{G}$ whose random variables are the snapshots of a temporal graph on G. A natural feature observed in various real-life scenarios is a memory effect in the appearance probabilities of particular edges; i.e. the probability an edge $e\in E$ appears at time step t depends on its appearance (or absence) at the previous k steps. We study the hierarchy of models of memory-k, $k\ge 0$, in an edge-centric network evolution setting: every edge of G has its own independent probability distribution for its appearance over time. We thoroughly investigate the complexity of two naturally related, but fundamentally different, temporal path problems, called Minimum Arrival and Best Policy.

时间图抽象地模拟了现实生活中固有的动态网络。给定一个图G，以G作为基础图的时间图是一系列子图（快照）$G_{Ť}$的G ^，其中$Ť\ge \mathrm{1个}$。在本文中，我们研究随机时间图，即随机过程$\mathcal{G}$其随机变量是G上时间图的快照。在各种实际场景中观察到的自然特征是特定边缘的外观概率中的记忆效应。即边缘的概率$Ë\in Ë$在时间步t出现的时间取决于它在前k个步的出现（或不存在）。我们研究记忆模型k的层次，$ķ\ge 0$，在以边缘为中心的网络演化设置中：G的每个边缘随时间的推移都有自己独立的概率分布。我们彻底研究了两个自然相关但根本不同的时间路径问题（称为最小到达和最佳策略）的复杂性。