On Digraph Width Measures in Parameterized Algorithmics

Abstract

AbstractIn contrast to undirected width measures (such as tree-width or clique-width), which have provided many important algorithmic applications, analogous measures for digraphs such as DAG-width 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 DAG-depth. 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.KeywordsModel CheckHamiltonian CycleHamiltonian PathLinear Temporal LogicWidth MeasureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.