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Nowhere Crownful Classes of Directed Graphs

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  • First Online:
Encyclopedia of Algorithms

  • 240 Accesses

Years and Authors of Summarized Original Work

  • 2012; Kreutzer, Tazari

Problem Definition

Many common computational problems on directed graphs are computationally intractable; they are NP-complete and sometimes even harder. Examples include domination problems such as directed dominating set, Kernel, directed Steiner networks, directed disjoint paths, and many other problems.

For undirected graphs, there is an extensive structure theory available to help dealing with this computational intractability. In particular, there is a well-developed hierarchy of classes of undirected graphs and a rich set of algorithmic tools which allow to solve hard computational problems on these classes of graphs. Most notably in this context are classes of graphs of bounded tree width, planar graphs or graphs embeddable on any other fixed surface, classes excluding a fixed minor, and many other graph classes. This theory is closely related to parameterized complexity theory.

For directed graphs, to date,...

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Recommended Reading

  1. Ganian R, Hlinený P, Kneis J, Langer A, Obdrzálek J, Rossmanith P (2009) On digraph width measures in parameterized algorithmics. In: International workshop in parameterized and exact computation (IWPEC), Copenhagen, pp 185–197

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  2. Grohe M, Kreutzer S, Siebertz S (2013) Characterisations of nowhere dense graphs. In: Foundations of software technology and theoretical computer science (FSTTCS 2013), Guwahati, pp 21–40

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  3. Grohe M, Kreutzer S, Siebertz S (2014) Deciding first-order properties of nowhere dense graphs. In: 46th annual symposium on the theory of computing (STOC), New York

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  4. Johnson T, Robertson N, Seymour PD, Thomas R (2001) Directed tree-width. J Comb Theory Ser B 82(1):138–154

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  5. Kreutzer S, Tazari S (2012) Directed nowhere dense classes of graphs. In: Proceedings of the 23rd ACM-SIAM symposium on discrete algorithms (SODA), Kyoto, pp 1552–1562

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  6. Nešetřil J, Ossona de Mendez P (2008) Grad and classes with bounded expansion I–III. Eur J Comb 29. Series of 3 papers appearing in volumes (3) and (4)

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Author information

Authors and Affiliations

  1. Chair for Logic and Semantics, Technical University, Sekr TEL 7-3, Ernst-Reuter Platz 7, 10587 Berlin, Berlin, Germany

    Stephan Kreutzer

Authors
  1. Stephan Kreutzer
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Corresponding author

Correspondence to Stephan Kreutzer .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Kreutzer, S. (2016). Nowhere Crownful Classes of Directed Graphs. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_694

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