A temporal graph is a graph whose edge set changes over a sequence of discrete time steps. This can be viewed as a discrete sequence G₁, G₂, ... of static graphs, each with a fixed vertex set V. Research in this area is motivated by the fact that many modern systems are highly dynamic and relations (edges) between objects (vertices) vary with time. Although static graphs have been extensively studied for decades from an algorithmic point of view, we are still far from having a concrete set of structural and algorithmic principles for temporal graphs. Many notions and algorithms from the static case can be naturally transferred in a meaningful way to their temporal counterpart, while in other cases new approaches are needed to define the appropriate temporal notions. In particular, some problems become radically different, and often substantially more difficult, when the time dimension is additionally taken into account. In this talk we will discuss some natural but only recently introduced temporal problems and some algorithmic approaches to them.

This lecture has been recorded.