Brief Announcement: Treewidth Modulator: Emergency Exit for DFVS
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.
Polynomial Kernel
Directed Feedback Vertex Set
Treewidth Modulator
Theory of computation~Fixed parameter tractability
110:1-110:4
Brief Announcement
Daniel
Lokshtanov
Daniel Lokshtanov
Department of Informatics, University of Bergen, Norway
M. S.
Ramanujan
M. S. Ramanujan
Algorithms and Complexity Group, TU Wien, Austria
Saket
Saurabh
Saket Saurabh
Institute of Mathematical Sciences, HBNI, India and UMI ReLax
Roohani
Sharma
Roohani Sharma
Institute of Mathematical Sciences, HBNI, India and UMI ReLax
Meirav
Zehavi
Meirav Zehavi
Department of Computer Science, Ben-Gurion University, Israel
10.4230/LIPIcs.ICALP.2018.110
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Daniel Lokshtanov, M.S. Ramanujan, Saket Saurabh, Roohani Sharma, and Meirav Zehavi
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