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.
@InProceedings{molter_et_al:LIPIcs.MFCS.2021.76, author = {Molter, Hendrik and Renken, Malte and Zschoche, Philipp}, title = {{Temporal Reachability Minimization: Delaying vs. Deleting}}, booktitle = {46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)}, pages = {76:1--76:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-201-3}, ISSN = {1868-8969}, year = {2021}, volume = {202}, editor = {Bonchi, Filippo and Puglisi, Simon J.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.76}, URN = {urn:nbn:de:0030-drops-145161}, doi = {10.4230/LIPIcs.MFCS.2021.76}, annote = {Keywords: Temporal Graphs, Temporal Paths, Disease Spreading, Network Flows, Parameterized Algorithms, NP-hard Problems} }
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