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Turbocharging Heuristics for Weak Coloring Numbers

Authors Alexander Dobler, Manuel Sorge, Anaïs Villedieu

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Author Details

Alexander Dobler
  • TU Wien, Austria
Manuel Sorge
  • TU Wien, Austria
Anaïs Villedieu
  • TU Wien, Austria


We thank Nadara et al. [Wojciech Nadara et al., 2019] for publishing their code, some small parts of which we reused in our implementations.

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Alexander Dobler, Manuel Sorge, and Anaïs Villedieu. Turbocharging Heuristics for Weak Coloring Numbers. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 44:1-44:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Structural sparsity
  • parameterized algorithms
  • parameterized complexity
  • fixed-parameter tractability


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