Digraph width measures in parameterized algorithmics

Robert Ganian, Petr Hliněný, Joachim Kneis, Alexander Langer, Jan Obdržálek, Peter Rossmanith
2014 Discrete Applied Mathematics  
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
more » ... eyond 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.
doi:10.1016/j.dam.2013.10.038 fatcat:jw3g26o5gvc7dnk4mhsp2nnmkm