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Empirical Evaluation of Approximation Algorithms for Generalized Graph Coloring and Uniform Quasi-Wideness

Authors Wojciech Nadara, Marcin Pilipczuk, Roman Rabinovich, Felix Reidl, Sebastian Siebertz

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Author Details

Wojciech Nadara
  • Institute of Informatics, University of Warsaw, Poland
Marcin Pilipczuk
  • Institute of Informatics, University of Warsaw, Poland
Roman Rabinovich
  • Lehrstuhl für Logic und Semantik, Technische Universität Berlin, Germany
Felix Reidl
  • Department of Computer Science, Royal Holloway University of London, UK
Sebastian Siebertz
  • Institute of Informatics, University of Warsaw, Poland

Funding

  • Nadara, Wojciech: Supported by the "Recent trends in kernelization: theory and experimental evaluation" project, carried out within the Homing programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund.
  • Pilipczuk, Marcin: Supported by the "Recent trends in kernelization: theory and experimental evaluation" project, carried out within the Homing programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund.
  • Rabinovich, Roman: Supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (ERC Consolidator Grant DISTRUCT, grant agreement No 648527).
  • Siebertz, Sebastian: Supported by the National Science Centre of Poland via POLONEZ grant agreement UMO-2015/19/P/ST6/03998, which has received funding from the European Union’s Horizon 2020 research and innovation programme (Marie Skłodowska-Curie grant agreement No. 665778).

Cite AsGet BibTex

Wojciech Nadara, Marcin Pilipczuk, Roman Rabinovich, Felix Reidl, and Sebastian Siebertz. Empirical Evaluation of Approximation Algorithms for Generalized Graph Coloring and Uniform Quasi-Wideness. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.SEA.2018.14

Abstract

The notions of bounded expansion and nowhere denseness not only offer robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic questions. In this paper we study two structural properties of these graph classes that are of particular importance in this context, namely the property of having bounded generalized coloring numbers and the property of being uniformly quasi-wide. We provide experimental evaluations of several algorithms that approximate these parameters on real-world graphs. On the theoretical side, we provide a new algorithm for uniform quasi-wideness with polynomial size guarantees in graph classes of bounded expansion and show a lower bound indicating that the guarantees of this algorithm are close to optimal in graph classes with fixed excluded minor.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • Empirical Evaluation of Algorithms
  • Sparse Graph Classes
  • Generalized Coloring Numbers
  • Uniform Quasi-Wideness

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