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Publisher DOI: 10.4230/LIPIcs.ICALP.2020.59
arXiv ID: 2003.05267
Title: Hitting long directed cycles is fixed-parameter tractable
Language: English
Authors: Göke, Alexander 
Marx, Dániel 
Mnich, Matthias  
Keywords: directed graphs; directed feedback vertex set; circumference
Issue Date: 2020
Publisher: Schloss Dagstuhl Leibniz-Zentrum für Informatik
Source: International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Abstract (english): 
In the Directed Long Cycle Hitting Set problem we are given a directed graph G, and the task is to find a set S of at most k vertices/arcs such that G − S has no cycle of length longer than `. We show that the problem can be solved in time 2O(`6+`k3 log k+k5 log k log `) · nO(1), that is, it is fixed-parameter tractable (FPT) parameterized by k and `. This algorithm can be seen as a far-reaching generalization of the fixed-parameter tractability of Mixed Graph Feedback Vertex Set [Bonsma and Lokshtanov WADS 2011], which is already a common generalization of the fixed-parameter tractability of (undirected) Feedback Vertex Set and the Directed Feedback Vertex Set problems, two classic results in parameterized algorithms. The algorithm requires significant insights into the structure of graphs without directed cycles of length longer than and can be seen as an exact version of the approximation algorithm following from the Erdős-Pósa property for long cycles in directed graphs proved by Kreutzer and Kawarabayashi [STOC 2015]. © Alexander Göke, Dániel Marx, and Matthias Mnich; licensed under Creative Commons License CC-BY 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020).
Conference: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) 
DOI: 10.15480/882.2883
ISBN: 978-3-95977-138-2
Institute: Algorithmen und Komplexität E-11 
Document Type: Chapter/Article (Proceedings)
Project: Kernelisierung für große Datenmengen 
Multivariate Algorithmen für Scheduling mit hoher Multiplizität 
License: CC BY 3.0 (Attribution) CC BY 3.0 (Attribution)
Part of Series: Leibniz international proceedings in informatics (LIPIcs) 
Volume number: 168
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This item is licensed under a Creative Commons License Creative Commons