License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2022.44
URN: urn:nbn:de:0030-drops-169820
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Dobler, Alexander ; Sorge, Manuel ; Villedieu, Anaïs

Turbocharging Heuristics for Weak Coloring Numbers

LIPIcs-ESA-2022-44.pdf (1 MB)


Bounded expansion and nowhere-dense classes of graphs capture the theoretical tractability for several important algorithmic problems. These classes of graphs can be characterized by the so-called weak coloring numbers of graphs, which generalize the well-known graph invariant degeneracy (also called k-core number). Being NP-hard, weak-coloring numbers were previously computed on real-world graphs mainly via incremental heuristics. We study whether it is feasible to augment such heuristics with exponential-time subprocedures that kick in when a desired upper bound on the weak coloring number is breached. We provide hardness and tractability results on the corresponding computational subproblems. We implemented several of the resulting algorithms and show them to be competitive with previous approaches on a previously studied set of benchmark instances containing 86 graphs with up to 183831 edges. We obtain improved weak coloring numbers for over half of the instances.

BibTeX - Entry

  author =	{Dobler, Alexander and Sorge, Manuel and Villedieu, Ana\"{i}s},
  title =	{{Turbocharging Heuristics for Weak Coloring Numbers}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{44:1--44:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-169820},
  doi =		{10.4230/LIPIcs.ESA.2022.44},
  annote =	{Keywords: Structural sparsity, parameterized algorithms, parameterized complexity, fixed-parameter tractability}

Keywords: Structural sparsity, parameterized algorithms, parameterized complexity, fixed-parameter tractability
Collection: 30th Annual European Symposium on Algorithms (ESA 2022)
Issue Date: 2022
Date of publication: 01.09.2022
Supplementary Material: Software:

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