On Vertex Cover Problems in Distributed Systems

Ileri, Can Umut; Ural, Aybars; Dağdeviren, Orhan; Kavalci, Vedat

doi:10.4018/978-1-4666-9964-9.ch001

Cited by 4 publications

(2 citation statements)

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“…TVC and ∆-TVC naturally generalize the applications of the static problem Vertex Cover to more dynamic inputs, especially in the areas of wireless ad hoc networks, as well as network security and scheduling. In the case of a static graph, the vertex cover can contain trusted vertices which have the ability to monitor/surveil all transmissions [25,37] or all link failures [26] between any pair of vertices through the edges of the graph. In the temporal setting, it makes sense to monitor the transmissions and to check for link failures within every sliding time window of an appropriate length ∆ (which is exactly modeled by ∆-TVC).…”

Section: Definition 1 (Temporal Graph)mentioning

confidence: 99%

The Complexity of Temporal Vertex Cover in Small-Degree Graphs

Hamm¹,

Klobas²,

Mertzios³

et al. 2022

Preprint

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Temporal graphs naturally model graphs whose underlying topology changes over time. Recently, the problems Temporal Vertex Cover (or TVC) and Sliding-Window Temporal Vertex Cover (or ∆-TVC for time-windows of a fixed-length ∆) have been established as natural extensions of the classic problem Vertex Cover on static graphs with connections to areas such as surveillance in sensor networks.In this paper we initiate a systematic study of the complexity of TVC and ∆-TVC on sparse graphs. Our main result shows that for every ∆ ≥ 2, ∆-TVC is NP-hard even when the underlying topology is described by a path or a cycle. This resolves an open problem from literature and shows a surprising contrast between ∆-TVC and TVC for which we provide a polynomial-time algorithm in the same setting. To circumvent this hardness, we present a number of exact and approximation algorithms for temporal graphs whose underlying topologies are given by a path, that have bounded vertex degree in every time step, or that admit a small-sized temporal vertex cover.

show abstract

Section: Definition 1 (Temporal Graph)mentioning

confidence: 99%

The Complexity of Temporal Vertex Cover in Small-Degree Graphs

Hamm¹,

Klobas²,

Mertzios³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…TVC and ∆-TVC naturally generalize the applications of the static problem VERTEX COVER to more dynamic inputs, especially in the areas of wireless ad hoc networks, as well as network security and scheduling. In the case of a static graph, the vertex cover can contain trusted vertices which have the ability to monitor/surveil all transmissions (Ileri et al 2016;Richter, Helmert, and Gretton 2007) or all link failures (Kavalci, Ural, and Dagdeviren 2014) between any pair of vertices through the edges of the graph. In the temporal setting, it makes sense to monitor the transmissions and to check for link failures within every sliding time window of an appropriate length ∆ (which is exactly modeled by ∆-TVC).…”

Section: Introductionmentioning

confidence: 99%

The Complexity of Temporal Vertex Cover in Small-Degree Graphs

Hamm

Klobas

Mertzios

et al. 2022

AAAI

View full text Add to dashboard Cite

Temporal graphs naturally model graphs whose underlying topology changes over time. Recently, the problems Temporal Vertex Cover (or TVC) and Sliding-Window Temporal Vertex Cover (or Delta-TVC for time-windows of a fixed-length Delta) have been established as natural extensions of the classic Vertex Cover problem on static graphs with connections to areas such as surveillance in sensor networks. In this paper we initiate a systematic study of the complexity of TVC and Delta-TVC on sparse graphs. Our main result shows that for every Delta geq 2, Delta-TVC is NP-hard even when the underlying topology is described by a path or a cycle. This resolves an open problem from literature and shows a surprising contrast between Delta-TVC and TVC for which we provide a polynomial-time algorithm in the same setting. To circumvent this hardness, we present a number of exact and approximation algorithms for temporal graphs whose underlying topologies are given by a path, that have bounded vertex degree in every time step, or that admit a small-sized temporal vertex cover.

show abstract