Turbocharging Heuristics for Weak Coloring Numbers

Alexander Dobler, Manuel Sorge, Anaïs Villedieu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


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.

Original languageEnglish
Title of host publication30th Annual European Symposium on Algorithms, ESA 2022
EditorsShiri Chechik, Gonzalo Navarro, Eva Rotenberg, Grzegorz Herman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772471
StatePublished - 1 Sep 2022
Externally publishedYes
Event30th Annual European Symposium on Algorithms, ESA 2022 - Berlin/Potsdam, Germany
Duration: 5 Sep 20229 Sep 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference30th Annual European Symposium on Algorithms, ESA 2022


  • Structural sparsity
  • fixed-parameter tractability
  • parameterized algorithms
  • parameterized complexity

ASJC Scopus subject areas

  • Software


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