TY - GEN
T1 - Brief announcement
T2 - 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
AU - Lokshtanov, Daniel
AU - Ramanujan, M. S.
AU - Saurabh, Saket
AU - Sharma, Roohani
AU - Zehavi, Meirav
N1 - Publisher Copyright:
© 2018 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - 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-η modulator, for any positive integer η. We also give a polynomial kernel for the problem, which we call Vertex Deletion to treewidth-η 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 treewidth1 of D − S is at most η.
AB - 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-η modulator, for any positive integer η. We also give a polynomial kernel for the problem, which we call Vertex Deletion to treewidth-η 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 treewidth1 of D − S is at most η.
KW - Directed feedback vertex set
KW - Polynomial kernel
KW - Treewidth modulator
UR - https://www.scopus.com/pages/publications/85049775731
U2 - 10.4230/LIPIcs.ICALP.2018.110
DO - 10.4230/LIPIcs.ICALP.2018.110
M3 - Conference contribution
AN - SCOPUS:85049775731
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
A2 - Kaklamanis, Christos
A2 - Marx, Daniel
A2 - Chatzigiannakis, Ioannis
A2 - Sannella, Donald
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Y2 - 9 July 2018 through 13 July 2018
ER -