Multistage Vertex Cover

Authors Till Fluschnik , Rolf Niedermeier , Valentin Rohm, Philipp Zschoche

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Author Details

Till Fluschnik
  • Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Germany
Rolf Niedermeier
  • Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Germany
Valentin Rohm
  • Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Germany
Philipp Zschoche
  • Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Germany

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Till Fluschnik, Rolf Niedermeier, Valentin Rohm, and Philipp Zschoche. Multistage Vertex Cover. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Covering all edges of a graph by a small number of vertices, this is the NP-hard Vertex Cover problem, is among the most fundamental algorithmic tasks. Following a recent trend in studying dynamic and temporal graphs, we initiate the study of Multistage Vertex Cover. Herein, having a series of graphs with same vertex set but over time changing edge sets (known as temporal graph consisting of time layers), the goal is to find for each layer of the temporal graph a small vertex cover and to guarantee that the two vertex cover sets between two subsequent layers differ not too much (specified by a given parameter). We show that, different from classic Vertex Cover and some other dynamic or temporal variants of it, Multistage Vertex Cover is computationally hard even in fairly restricted settings. On the positive side, however, we also spot several fixed-parameter tractability results based on some of the most natural parameterizations.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Mathematics of computing → Graph algorithms
  • NP-hardness
  • dynamic graph problems
  • temporal graphs
  • time-evolving networks
  • W[1]-hardness
  • fixed-parameter tractability
  • kernelization


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