Deleting edges to restrict the size of an epidemic in temporal networks
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A variety of potentially disease-spreading contact networks can be naturally modeled with graphs whose structure is subject to discrete changes over time, i.e. with temporal graphs. In such a temporal graph, vertices represent meaningful entities (such as animals or farms) and edges represent potentially infectious contacts between those entities. Furthermore the `availability' of an edge e at time t means that, at time t, the entities at the endpoints of e are in contact. In this paper, motivated by network epidemiology applications in the dynamics of disease spreading on a data-derived network, we study the problem of deleting edges and/or edge availabilities from a given temporal graph in order to reduce its (temporal) connectivity. In particular, our aim is to find a temporal subgraph, in which the potential disease of any vertex u can be transferred to only a limited number of other vertices v using a temporal path (i.e. a path from u to v, along which the times of the edge availabilities increase). We introduce two natural deletion problems for temporal graphs (for deletion of edges and of edge availabilities, respectively) and we provide positive and negative results on their computational complexity, both in the traditional and the parameterized sense, subject to various natural parameters.
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