eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-07-04
110:1
110:4
10.4230/LIPIcs.ICALP.2018.110
article
Brief Announcement: Treewidth Modulator: Emergency Exit for DFVS
Lokshtanov, Daniel
1
Ramanujan, M. S.
2
Saurabh, Saket
3
Sharma, Roohani
3
Zehavi, Meirav
4
Department of Informatics, University of Bergen, Norway
Algorithms and Complexity Group, TU Wien, Austria
Institute of Mathematical Sciences, HBNI, India and UMI ReLax
Department of Computer Science, Ben-Gurion University, Israel
In the Directed Feedback Vertex Set (DFVS) problem, we are given as input a directed graph D and an integer k, and the objective is to check whether there exists a set S of at most k vertices such that F=D-S is a directed acyclic graph (DAG). Determining whether DFVS admits a polynomial kernel (parameterized by the solution size) is one of the most important open problems in parameterized complexity. In this article, we give a polynomial kernel for DFVS parameterized by the solution size plus the size of any treewidth-eta modulator, for any positive integer eta. We also give a polynomial kernel for the problem, which we call Vertex Deletion to treewidth-eta DAG, where given as input a directed graph D and a positive integer k, the objective is to decide whether there exists a set of at most k vertices, say S, such that D-S is a DAG and the treewidth of D-S is at most eta.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol107-icalp2018/LIPIcs.ICALP.2018.110/LIPIcs.ICALP.2018.110.pdf
Polynomial Kernel
Directed Feedback Vertex Set
Treewidth Modulator