Node connectivity plays a central role in temporal network analysis. We provide a broad study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but arc sets changing over time. Taking into account the temporal aspect leads to a rich set of optimization criteria for “shortest” walks. Extending and broadening state-of-the-art work of Wu et al. [IEEE TKDE 2016], we provide an algorithm for computing shortest walks that is capable to deal with various optimization criteria and any linear combination of these. It runs in O(|V|+|E|log|E|) time where |V| is the number of vertices and |E| is the number of time-arcs. A central distinguishing factor to Wu et al.’s work is that our model allows to, motivated by real-world applications, respect waiting-time constraints for vertices, that is, the minimum and maximum waiting time allowed in intermediate vertices of a walk. Moreover, other than Wu et al. our algorithm also allows to search for walks that pass multiple subsequent time-arcs in one time step, and it can deal with a richer set of optimization criteria. Our experimental studies indicate that our richer modeling can be achieved without significantly worsening the running time when compared to Wu et al.’s algorithms.

节点连接在时态网络分析中起着核心作用。我们对时间图中的走动的各种概念进行了广泛的研究，即具有固定顶点集但弧集随时间变化的图。考虑到时间方面，会导致针对“最短”步行的一系列优化标准。扩展和扩展了Wu等人的最新技术。[IEEE TKDE 2016]，我们提供了一种用于计算最短步行的算法，该算法能够处理各种优化标准以及这些标准的任何线性组合。它在O（| V | + | E | log | E |）时间中运行| V | 是顶点数，| |是 Ë| 是时间弧的数量。Wu等人工作的一个主要区别因素是，我们的模型允许在实际应用的激励下，尊重顶点的等待时间约束，即步行中间顶点所允许的最小和最大等待时间。此外，除了吴等。我们的算法还允许搜索在一个时间步中经过多个后续时间弧的步行，并且它可以处理一组更丰富的优化标准。我们的实验研究表明，与Wu等人的算法相比，可以实现更丰富的建模而不会显着降低运行时间。