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Directed Feedback Vertex Set Problem is FPT

Authors Jianer Chen, Yang Liu, Songiian Lu



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DagSemProc.07281.5.pdf
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Jianer Chen
Yang Liu
Songiian Lu

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Jianer Chen, Yang Liu, and Songiian Lu. Directed Feedback Vertex Set Problem is FPT. In Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs. Dagstuhl Seminar Proceedings, Volume 7281, pp. 1-17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2007)
https://doi.org/10.4230/DagSemProc.07281.5

Abstract

To decide if the {sc parameterized feedback vertex set} problem in directed graph is fixed-parameter tractable is a long standing open problem. In this paper, we prove that the {sc parameterized feedback vertex set} in directed graph is fixed-parameter tractable and give the first FPT algorithm of running time $O((1.48k)^kn^{O(1)})$ for it. As the {sc feedback arc set} problem in directed graph can be transformed to a {sc feedback vertex set} problem in directed graph, hence we also show that the {sc parameterized feedback arc set} problem can be solved in time of $O((1.48k)^kn^{O(1)})$.
Keywords
  • Directed feedback vertex set problem
  • parameterized algorithm,

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