The Directed Feedback Vertex Set (DFVS) problem takes as input a directed graph G and seeks a smallest vertex set S that hits all cycles in G. This is one of Karp’s 21 -complete problems. Resolving the parameterized complexity status of DFVS was a long-standing open problem until Chen et al. in 2008 showed its fixed-parameter tractability via a -time algorithm, where. Here we show fixed-parameter tractability of two generalizations of DFVS: Find a smallest vertex set S such that every strong component of has size at most s: we give an algorithm solving this problem in time. Find a smallest vertex set S such that every non-trivial strong component of is 1-out-regular: we give an algorithm solving this problem in time. We also solve the corresponding arc versions of these problems by fixed-parameter algorithms.
CITATION STYLE
Göke, A., Marx, D., & Mnich, M. (2019). Parameterized Algorithms for Generalizations of Directed Feedback Vertex Set. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11485 LNCS, pp. 249–261). Springer Verlag. https://doi.org/10.1007/978-3-030-17402-6_21
Mendeley helps you to discover research relevant for your work.