Temporal vertex cover with a sliding time window

Akrida, E.C.; Mertzios, G.B.; Spirakis, P.G.; Zamaraev, V.

Abstract

Modern, inherently dynamic systems are usually characterized by a network structure, i.e. an underlying graph topology, which is subject to discrete changes over time. Given a static underlying graph G, a temporal graph can be represented via an assignment of a set of integer time-labels to every edge of G, indicating the discrete time steps when this edge is active. While most of the recent theoretical research on temporal graphs has focused on the notion of a temporal path and other "path-related" temporal notions, only few attempts have been made to investigate "non-path" temporal graph problems. In this paper, motivated by applications in sensor and in transportation networks, we introduce and study two natural temporal extensions of the classical problem Vertex Cover. In our first problem, Temporal Vertex Cover, the aim is to cover every edge at least once during the lifetime of the temporal graph, where an edge can only be covered by one of its endpoints at a time step when it is active. In our second, more pragmatic variation Sliding Window Temporal Vertex Cover, we are also given a natural number Delta, and our aim is to cover every edge at least once at every Delta consecutive time steps. In both cases we wish to minimize the total number of "vertex appearances" that are needed to cover the whole graph. We present a thorough investigation of the computational complexity and approximability of these two temporal covering problems. In particular, we provide strong hardness results, complemented by various approximation and exact algorithms. Some of our algorithms are polynomial-time, while others are asymptotically almost optimal under the Exponential Time Hypothesis (ETH) and other plausible complexity assumptions.

Citation

Akrida, E., Mertzios, G., Spirakis, P., & Zamaraev, V. (2018, July). Temporal vertex cover with a sliding time window. Presented at 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)., Prague, Czech Republic

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018).
• Start Date: Jul 9, 2018
• End Date: Jul 13, 2018
• Acceptance Date: Apr 16, 2018
• Online Publication Date: Jul 4, 2018
• Publication Date: Jul 13, 2018
• Deposit Date: Apr 27, 2018
• Publicly Available Date: Apr 30, 2018
• Publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
• Volume: 107
• Pages: 148:1-148:14
• Series Title: Leibniz international proceedings in informatics (LIPICS)
• Series ISSN: 1868-8969
• Book Title: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) : Prague, Czech Republic, July 9-13, 2018 ; proceedings.
• ISBN: 978-3-95977-076-7
• DOI: https://doi.org/10.4230/lipics.icalp.2018.148
• Keywords: Temporal networks, temporal vertex cover, APX-hard, approximation algorithm, Exponential Time Hypothesis
• Public URL: https://durham-repository.worktribe.com/output/1144863
• Publisher URL: https://iuuk.mff.cuni.cz/~icalp2018/