We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how such a spreading process, emerging from a given set of sources, can be contained to a small part of the graph. To this end we consider two ways of modifying the graph, which are (1) deleting connections and (2) delaying connections. We show a close relationship between the two associated problems and give a polynomial time algorithm when the graph has tree structure. For the general version, we consider parameterization by the number of vertices to which the spread is contained. Surprisingly, we prove W[1]-hardness for the deletion variant but fixed-parameter tractability for the delaying variant.
@article{arxiv.2102.10814,
title = {Temporal Reachability Minimization: Delaying vs. Deleting},
author = {Hendrik Molter and Malte Renken and Philipp Zschoche},
journal= {arXiv preprint arXiv:2102.10814},
year = {2021}
}