Temporal Vertex Cover with a Sliding Time Window
Eleni C. Akrida, George B. Mertzios, Paul G. Spirakis, Viktor Zamaraev

TL;DR
This paper introduces and analyzes two temporal vertex cover problems on dynamic graphs, focusing on minimizing vertex appearances to cover edges over time, with applications in sensor and transportation networks.
Contribution
It defines two new temporal vertex cover variants, analyzes their computational complexity, and provides approximation and exact algorithms, including some with near-optimal performance under ETH.
Findings
Both problems are computationally hard with strong hardness results.
Polynomial-time algorithms are developed for certain cases.
Some algorithms are nearly optimal assuming ETH.
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 , a temporal graph can be represented via an assignment of a set of integer time-labels to every edge of , 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 both cases we wish to minimize the total number of "vertex appearances" that are needed to "cover" the whole…
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