@inproceedings{583f91057e954a54ba14e84986fff9a4,
title = "Turbocharging Heuristics for Weak Coloring Numbers",
abstract = "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.",
keywords = "Structural sparsity, fixed-parameter tractability, parameterized algorithms, parameterized complexity",
author = "Alexander Dobler and Manuel Sorge and Ana{\"i}s Villedieu",
note = "Publisher Copyright: {\textcopyright} 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.; 30th Annual European Symposium on Algorithms, ESA 2022 ; Conference date: 05-09-2022 Through 09-09-2022",
year = "2022",
month = sep,
day = "1",
doi = "10.4230/LIPIcs.ESA.2022.44",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Shiri Chechik and Gonzalo Navarro and Eva Rotenberg and Grzegorz Herman",
booktitle = "30th Annual European Symposium on Algorithms, ESA 2022",
address = "Germany",
}