Computing Maximum Matchings in Temporal Graphs

Authors George B. Mertzios , Hendrik Molter , Rolf Niedermeier , Viktor Zamaraev , Philipp Zschoche

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Author Details

George B. Mertzios
  • Department of Computer Science, Durham University, UK
Hendrik Molter
  • TU Berlin, Faculty IV, Algorithmics and Computational Complexity, Berlin, Germany
Rolf Niedermeier
  • TU Berlin, Faculty IV, Algorithmics and Computational Complexity, Berlin, Germany
Viktor Zamaraev
  • Department of Computer Science, University of Liverpool, UK
Philipp Zschoche
  • TU Berlin, Faculty IV, Algorithmics and Computational Complexity, Berlin, Germany

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George B. Mertzios, Hendrik Molter, Rolf Niedermeier, Viktor Zamaraev, and Philipp Zschoche. Computing Maximum Matchings in Temporal Graphs. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph G, a temporal graph is represented by assigning a set of integer time-labels to every edge e of G, indicating the discrete time steps at which e is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking into account the dynamic nature of temporal graphs. In our problem, Maximum Temporal Matching, we are looking for the largest possible number of time-labeled edges (simply time-edges) (e,t) such that no vertex is matched more than once within any time window of Δ consecutive time slots, where Δ ∈ ℕ is given. The requirement that a vertex cannot be matched twice in any Δ-window models some necessary "recovery" period that needs to pass for an entity (vertex) after being paired up for some activity with another entity. We prove strong computational hardness results for Maximum Temporal Matching, even for elementary cases. To cope with this computational hardness, we mainly focus on fixed-parameter algorithms with respect to natural parameters, as well as on polynomial-time approximation algorithms.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Approximation algorithms analysis
  • Temporal Graph
  • Link Stream
  • Temporal Line Graph
  • NP-hardness
  • APX-hardness
  • Approximation Algorithm
  • Fixed-parameter Tractability
  • Independent Set


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