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Towards Classifying the Polynomial-Time Solvability of Temporal Betweenness Centrality

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Graph-Theoretic Concepts in Computer Science (WG 2021)

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Abstract

In static graphs, the betweenness centrality of a graph vertex measures how many times this vertex is part of a shortest path between any two graph vertices. Betweenness centrality is efficiently computable and it is a fundamental tool in network science. Continuing and extending previous work, we study the efficient computability of betweenness centrality in temporal graphs (graphs with fixed vertex set but time-varying arc sets). Unlike in the static case, there are numerous natural notions of being a “shortest” temporal path (walk). Depending on which notion is used, it was already observed that the problem is #P-hard in some cases while polynomial-time solvable in others. In this conceptual work, we contribute towards classifying what a “shortest path (walk) concept” has to fulfill in order to gain polynomial-time computability of temporal betweenness centrality.

M. Rymar—Partially supported by the DFG, project MATE (NI 369/17).

H. Molter—Supported by the DFG, project MATE (NI 369/17), and by the ISF, grant No. 1070/20. Main part of this work was done while affiliated with TU Berlin.

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Notes

  1. 1.

    In fact, all optimal temporal path concepts (we are aware of) where path counting and computing the betweenness centrality can be done in polynomial time have this property, ensuring that optimal walks are indeed paths.

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Authors and Affiliations

  1. TU Berlin, Algorithmics and Computational Complexity, Berlin, Germany

    Maciej Rymar, Hendrik Molter, André Nichterlein & Rolf Niedermeier

  2. Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Hendrik Molter

Authors
  1. Maciej Rymar
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  2. Hendrik Molter
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  3. André Nichterlein
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  4. Rolf Niedermeier
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Correspondence to Hendrik Molter .

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Editors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Łukasz Kowalik

  2. University of Warsaw, Warsaw, Poland

    Michał Pilipczuk

  3. Warsaw University of Technology, Warsaw, Poland

    Paweł Rzążewski

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Rymar, M., Molter, H., Nichterlein, A., Niedermeier, R. (2021). Towards Classifying the Polynomial-Time Solvability of Temporal Betweenness Centrality. In: Kowalik, Ł., Pilipczuk, M., Rzążewski, P. (eds) Graph-Theoretic Concepts in Computer Science. WG 2021. Lecture Notes in Computer Science(), vol 12911. Springer, Cham. https://doi.org/10.1007/978-3-030-86838-3_17

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  • DOI: https://doi.org/10.1007/978-3-030-86838-3_17

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