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As Time Goes By: Reflections on Treewidth for Temporal Graphs

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Treewidth, Kernels, and Algorithms

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12160))

Abstract

Treewidth is arguably the most important structural graph parameter leading to algorithmically beneficial graph decompositions. Triggered by a strongly growing interest in temporal networks (graphs where edge sets change over time), we discuss fresh algorithmic views on temporal tree decompositions and temporal treewidth. We review and explain some of the recent work together with some encountered pitfalls, and we point out challenges for future research.

Dedicated to Hans L. Bodlaender on the occasion of his 60th birthday.

The inclined reader, besides hopefully discovering interesting science, is also invited to enjoy a few quotes from a famous movie scattered around our text; the paper title is partially taken from the theme song of this movie.

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Notes

  1. 1.

    Also known as time-varying graphs, evolving graphs, link streams, or dynamic graphs where no changes on the vertex set are allowed.

  2. 2.

    In the Gaifman graph of a structure, there is one vertex for each element in the universe and two vertices have an edge if and only if the corresponding elements occur together in the same relation.

  3. 3.

    A \(\varDelta \)-time window is a set of \(\varDelta \) consecutive time steps.

  4. 4.

    To the best of our knowledge, the concept of a “\(\varDelta \)-slice parameter” was introduced by Himmel et al. [51] to define a temporal version of degeneracy. It was later also used by Bentert et al. [7].

  5. 5.

    Note that there are different definitions of static expansion that are typically tailored to the applications they are used in.

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Acknowledgments

HM and MR acknowledge support by DFG, project MATE (NI 369/17). TF acknowledges support by DFG, project TORE (NI 369/18).

We thank Mark de Berg, Anne-Sophie Himmel, Frank Kammer, Sándor Kisfaludi-Bak, Erik Jan van Leeuwen, and George B. Mertzios for their constructive feedback which helped us to improve the presentation of the paper.

We further thank Bernard Mans and Luke Mathieson for helpful discussions concerning the issues presented in Sect. 5.3.

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Authors and Affiliations

  1. Faculty IV, Algorithmics and Computational Complexity, Technische Universität Berlin, Berlin, Germany

    Till Fluschnik, Hendrik Molter, Rolf Niedermeier, Malte Renken & Philipp Zschoche

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  1. Till Fluschnik
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Correspondence to Malte Renken .

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Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Fedor V. Fomin

  2. Humboldt-University, Berlin, Germany

    Stefan Kratsch

  3. Utrecht University, Utrecht, The Netherlands

    Erik Jan van Leeuwen

A Temporal Graph Problem Zoo

A Temporal Graph Problem Zoo

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Fluschnik, T., Molter, H., Niedermeier, R., Renken, M., Zschoche, P. (2020). As Time Goes By: Reflections on Treewidth for Temporal Graphs. In: Fomin, F.V., Kratsch, S., van Leeuwen, E.J. (eds) Treewidth, Kernels, and Algorithms. Lecture Notes in Computer Science(), vol 12160. Springer, Cham. https://doi.org/10.1007/978-3-030-42071-0_6

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