TY - GEN
T1 - Turbocharging Heuristics for Weak Coloring Numbers
AU - Dobler, Alexander
AU - Sorge, Manuel
AU - Villedieu, Anaïs
N1 - Funding Information:
Funding Alexander Dobler: Supported by the Vienna Science and Technology Fund (WWTF) under grant ICT19-035. Manuel Sorge: Supported by the Alexander von Humboldt Foundation. Anaïs Villedieu: Supported by the Austrian Science Fund (FWF) under grant P31119.
Publisher Copyright:
© 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.
PY - 2022/9/1
Y1 - 2022/9/1
N2 - 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.
AB - 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.
KW - Structural sparsity
KW - fixed-parameter tractability
KW - parameterized algorithms
KW - parameterized complexity
UR - http://www.scopus.com/inward/record.url?scp=85137575712&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ESA.2022.44
DO - 10.4230/LIPIcs.ESA.2022.44
M3 - Conference contribution
AN - SCOPUS:85137575712
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 30th Annual European Symposium on Algorithms, ESA 2022
A2 - Chechik, Shiri
A2 - Navarro, Gonzalo
A2 - Rotenberg, Eva
A2 - Herman, Grzegorz
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 30th Annual European Symposium on Algorithms, ESA 2022
Y2 - 5 September 2022 through 9 September 2022
ER -