On Digraph Width Measures in Parameterized Algorithmics

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Authors

GANIAN Robert HLINĚNÝ Petr OBDRŽÁLEK Jan LANGER Alexander KNEIS Joachim ROSSMANITH Peter

Year of publication 2009
Type Article in Proceedings
Conference IWPEC 2009: International Workshop on Parameterized and Exact Computation, Lecture Notes in Computer Science
MU Faculty or unit

Faculty of Informatics

Citation
Web
Doi http://dx.doi.org/10.1007/978-3-642-11269-0_15
Field Informatics
Keywords digraph; DAG-width; bi-rank-width; parameterized complexity
Description In contrast to undirected width measures (such as treewidth or clique-width), which have provided many important algorithmic applications, analogous measures for digraphs such as DAGwidth or Kelly-width do not seem so successful. Several recent papers, e.g. those of Kreutzer-Ordyniak, Dankelmann-Gutin-Kim, or Lampis-Kaouri-Mitsou, have given some evidence for this. We support this direction by showing that many quite different problems remain hard even on graph classes that are restricted very beyond simply having small DAG-width. To this end, we introduce new measures K-width and DAGdepth. On the positive side, we also note that taking Kanté's directed generalization of rank-width as a parameter makes many problems fixed parameter tractable.
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