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Temporal Reachability Minimization: Delaying vs. Deleting

Authors Hendrik Molter , Malte Renken , Philipp Zschoche

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Paths and connectivity problems
  • Mathematics of computing → Network flows
Keywords
  • Temporal Graphs
  • Temporal Paths
  • Disease Spreading
  • Network Flows
  • Parameterized Algorithms
  • NP-hard Problems

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Abstract

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.

Cite As Get BibTex

Hendrik Molter, Malte Renken, and Philipp Zschoche. Temporal Reachability Minimization: Delaying vs. Deleting. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 76:1-76:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.MFCS.2021.76

Author Details

Hendrik Molter
  • Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer Sheva, Israel
  • Faculty IV, Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
Malte Renken
  • Faculty IV, Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
Philipp Zschoche
  • Faculty IV, Algorithmics and Computational Complexity, Technische Universität Berlin, Germany

Funding

  • Molter, Hendrik: Supported by the German Research Foundation (DFG), project MATE (NI 369/17), and by the Israeli Science Foundation (ISF), grant No. 1070/20. The main work was done while affiliated with TU Berlin.
  • Renken, Malte: Supported by the German Research Foundation (DFG), project MATE (NI 369/17).

Acknowledgements

This work was initiated at the research retreat of the Algorithmics and Computational Complexity group of TU Berlin in September 2020 in Zinnowitz.

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