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 - http://www.scopus.com/inward/record.url?scp=85049775731&partnerID=8YFLogxK

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 -