scholarly journals Parameterized Algorithms for Generalizations of Directed Feedback Vertex Set

2019 ◽  
pp. 249-261
Author(s):  
Alexander Göke ◽  
Dániel Marx ◽  
Matthias Mnich
Keyword(s):  
Parameterized Algorithms ◽  
Feedback Vertex Set ◽  
Vertex Set ◽  
Directed Feedback Vertex Set

scholarly journals On Directed Feedback Vertex Set Parameterized by Treewidth

2018 ◽  
pp. 65-78 ◽  
Author(s):  
Marthe Bonamy ◽  
Łukasz Kowalik ◽  
Jesper Nederlof ◽  
Michał Pilipczuk ◽  
Arkadiusz Socała ◽  
...  
Keyword(s):  
Feedback Vertex Set ◽  
Vertex Set ◽  
Directed Feedback Vertex Set

A fixed-parameter algorithm for the directed feedback vertex set problem

2008 ◽  
Vol 55 (5) ◽  
pp. 1-19 ◽  
Author(s):  
Jianer Chen ◽  
Yang Liu ◽  
Songjian Lu ◽  
Barry O'sullivan ◽  
Igor Razgon
Keyword(s):  
Feedback Vertex Set ◽  
Fixed Parameter ◽  
Vertex Set ◽  
Feedback Vertex Set Problem ◽  
Fixed Parameter Algorithm ◽  
Directed Feedback Vertex Set

scholarly journals Generalized Feedback Vertex Set Problems on Bounded-Treewidth Graphs: Chordality is the Key to Single-Exponential Parameterized Algorithms

Algorithmica ◽  
2019 ◽  
Vol 81 (10) ◽  
pp. 3890-3935
Author(s):  
Édouard Bonnet ◽  
Nick Brettell ◽  
O-joung Kwon ◽  
Dániel Marx
Keyword(s):  
Parameterized Algorithms ◽  
Feedback Vertex Set ◽  
Bounded Treewidth ◽  
Vertex Set ◽  
Single Exponential

scholarly journals Towards a Polynomial Kernel for Directed Feedback Vertex Set

Algorithmica ◽  
2020 ◽  
Author(s):  
Benjamin Bergougnoux ◽  
Eduard Eiben ◽  
Robert Ganian ◽  
Sebastian Ordyniak ◽  
M. S. Ramanujan
Keyword(s):  
Undirected Graph ◽  
Polynomial Kernel ◽  
Directed Cycle ◽  
Feedback Vertex Set ◽  
Open Problems ◽  
Fixed Parameter Tractable ◽  
Parameterized Algorithmics ◽  
Fixed Parameter ◽  
Vertex Set ◽  
Directed Feedback Vertex Set

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 et al. (J ACM 55(5):177–186, 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. Since this problem has remained open in spite of the best efforts of a number of prominent researchers and pioneers in the field, a natural step forward is to study the kernelization complexity of DFVS parameterized by a natural larger parameter. 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.

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