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Towards a Polynomial Kernel for Directed Feedback Vertex Set

Authors Benjamin Bergougnoux, Eduard Eiben, Robert Ganian, Sebastian Ordyniak, M. S. Ramanujan

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Benjamin Bergougnoux
Eduard Eiben
Robert Ganian
Sebastian Ordyniak
M. S. Ramanujan

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Benjamin Bergougnoux, Eduard Eiben, Robert Ganian, Sebastian Ordyniak, and M. S. Ramanujan. Towards a Polynomial Kernel for Directed Feedback Vertex Set. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 36:1-36:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.MFCS.2017.36

Abstract

In the Directed Feedback Vertex Set (DFVS) problem, the input is
a directed graph D and an integer k. The objective is to determine
whether there exists a set of at most k vertices intersecting every
directed cycle of D. DFVS was shown to be fixed-parameter tractable when parameterized by solution size by Chen, Liu, Lu, O'Sullivan and
Razgon [JACM 2008]; since then, the existence of a polynomial kernel for this problem has become one of the largest open problems in the area of parameterized algorithmics.

In this paper, we study DFVS parameterized by the feedback vertex
set number of the underlying undirected graph. We provide two main contributions: a polynomial kernel for this problem on general instances, and a linear kernel for the case where the input digraph is embeddable on a surface of bounded genus.

Subject Classification

Keywords
  • parameterized algorithms
  • kernelization
  • (directed) feedback vertex set

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