Algorithmic Properties of Sparse Digraphs

Authors Stephan Kreutzer, Irene Muzi, Patrice Ossona de Mendez, Roman Rabinovich, Sebastian Siebertz



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Stephan Kreutzer
  • Technische Universität Berlin, Germany
Irene Muzi
  • University of Warsaw, Poland
Patrice Ossona de Mendez
  • Centre d'Analyse et de Mathématiques Sociales (CNRS, UMR 8557), Paris, France,
  • Computer Science Institute of Charles University (IUUK), Prague, Czech Republic
Roman Rabinovich
  • Technische Universität Berlin, Germany
Sebastian Siebertz
  • Humboldt-Universität zu Berlin, Germany

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Stephan Kreutzer, Irene Muzi, Patrice Ossona de Mendez, Roman Rabinovich, and Sebastian Siebertz. Algorithmic Properties of Sparse Digraphs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.STACS.2019.46

Abstract

The notions of bounded expansion [Nešetřil and Ossona de Mendez, 2008] and nowhere denseness [Nešetřil and Ossona de Mendez, 2011], introduced by Nešetřil and Ossona de Mendez as structural measures for undirected graphs, have been applied very successfully in algorithmic graph theory. We study the corresponding notions of directed bounded expansion and nowhere crownfulness on directed graphs, introduced by Kreutzer and Tazari [Kreutzer and Tazari, 2012]. The classes of directed graphs having those properties are very general classes of sparse directed graphs, as they include, on one hand, all classes of directed graphs whose underlying undirected class has bounded expansion, such as planar, bounded-genus, and H-minor-free graphs, and on the other hand, they also contain classes whose underlying undirected class is not even nowhere dense. We show that many of the algorithmic tools that were developed for undirected bounded expansion classes can, with some care, also be applied in their directed counterparts, and thereby we highlight a rich algorithmic structure theory of directed bounded expansion and nowhere crownful classes.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Fixed parameter tractability
Keywords
  • Directed graphs
  • graph algorithms
  • parameterized complexity
  • approximation

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