Temporal Reachability Dominating Sets: Contagion in Temporal Graphs

Kutner, D. C. and Larios-Jones, L. (2023) Temporal Reachability Dominating Sets: Contagion in Temporal Graphs. In: 19th International Symposium on Algorithmics of Wireless Networks (ALGOWIN 2023), Amsterdam, The Netherlands, 7-8 Sept 2023, pp. 101-116. ISBN 9783031488825 (doi: 10.1007/978-3-031-48882-5_8)

Abstract

SARS-CoV-2 was independently introduced to the UK at least 1300 times by June 2020. Given a population with dynamic pairwise connections, we ask if the entire population could be (indirectly) infected by a small group of k initially infected individuals. We formalise this problem as the Temporal Reachability Dominating Set (TaRDiS) problem on temporal graphs. We provide positive and negative parameterized complexity results in four different parameters: the number k of initially infected, the lifetime τ of the graph, the number of locally earliest edges in the graph, and the treewidth of the footprint graph G↓. We additionally introduce and study the MaxMinTaRDiS problem, which can be naturally expressed as scheduling connections between individuals so that a population needs to be infected by at least k individuals to become fully infected. Interestingly, we find a restriction of this problem to correspond exactly to the well-studied Distance-3 Independent Set problem on static graphs.

• Item Type: Conference Proceedings
• Keywords: temporal graphs, temporal reachability, treewidth, polynomial hierarchy.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Larios-Jones, Laura
• Authors: Kutner, D. C., and Larios-Jones, L.
• College/School: College of Science and Engineering > School of Computing Science
• ISSN: 1611-3349
• ISBN: 9783031488825
• Published Online: 03 December 2023
• Copyright Holders: Copyright © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
• First Published: First published in Algorithmics of Wireless Networks. ALGOWIN 2023. Lecture Notes in Computer Science 14061:101-116
• Publisher Policy: Reproduced in accordance with the publisher copyright policy