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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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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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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