Brief Announcement: Treewidth Modulator: Emergency Exit for DFVS

Lokshtanov, Daniel; Ramanujan, M. S.; Saurabh, Saket; Sharma, Roohani; Zehavi, Meirav

doi:10.4230/LIPIcs.ICALP.2018.110

File

LIPIcs.ICALP.2018.110.pdf

Filesize: 390 kB
4 pages

Document Identifiers

DOI: 10.4230/LIPIcs.ICALP.2018.110
URN: urn:nbn:de:0030-drops-91146

Author Details

Daniel Lokshtanov

Department of Informatics, University of Bergen, Norway

M. S. Ramanujan

Algorithms and Complexity Group, TU Wien, Austria

Saket Saurabh

Institute of Mathematical Sciences, HBNI, India and UMI ReLax

Roohani Sharma

Institute of Mathematical Sciences, HBNI, India and UMI ReLax

Meirav Zehavi

Department of Computer Science, Ben-Gurion University, Israel

Cite AsGet BibTex

Daniel Lokshtanov, M. S. Ramanujan, Saket Saurabh, Roohani Sharma, and Meirav Zehavi. Brief Announcement: Treewidth Modulator: Emergency Exit for DFVS. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 110:1-110:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ICALP.2018.110

Abstract

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.

Subject Classification

ACM Subject Classification

Theory of computation → Fixed parameter tractability

Keywords

Polynomial Kernel
Directed Feedback Vertex Set
Treewidth Modulator

Metrics

Access Statistics
Total Accesses (updated on a weekly basis)

0

PDF Downloads

0

Metadata Views

References

F N Abu-Khzam. A kernelization algorithm for d-Hitting Set. JCSS, 76(7):524-531, 2010.
Akanksha Agrawal, Saket Saurabh, Roohani Sharma, and Meirav Zehavi. Kernels for deletion to classes of acyclic digraphs. J. Comput. Syst. Sci., 92:9-21, 2018. URL: http://dx.doi.org/10.1016/j.jcss.2017.07.008.
J Bang-Jensen, A Maddaloni, and S Saurabh. Algorithms and kernels for feedback set problems in generalizations of tournaments. Algorithmica, pages 1-24, 2015.
Benjamin Bergougnoux, Eduard Eiben, Robert Ganian, Sebastian Ordyniak, and M. S. Ramanujan. Towards a polynomial kernel for directed feedback vertex set. In MFCS 2017, 2017. To Appear.
Jianer Chen, Yang Liu, Songjian Lu, Barry O'Sullivan, and Igor Razgon. A fixed-parameter algorithm for the directed feedback vertex set problem. J. ACM, 55(5), 2008. URL: http://dx.doi.org/10.1145/1411509.1411511.
Marek Cygan, Daniel Lokshtanov, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. On the hardness of losing width. Theory Comput. Syst., 54(1):73-82, 2014. URL: http://dx.doi.org/10.1007/s00224-013-9480-1.
M Dom, J Guo, F Hüffner, R Niedermeier, and A Truß. Fixed-parameter tractability results for feedback set problems in tournaments. JDA, 8(1):76-86, 2010. URL: http://dx.doi.org/10.1016/j.jda.2009.08.001.
Rodney G. Downey and Michael R. Fellows. Fixed-parameter intractability. In Proceedings of the Seventh Annual Structure in Complexity Theory Conference, Boston, Massachusetts, USA, June 22-25, 1992, pages 36-49, 1992.
Rodney G. Downey and Michael R. Fellows. Fixed-parameter tractability and completeness I: basic results. SIAM J. Comput., 24(4):873-921, 1995.
Tien-Nam Le, Daniel Lokshtanov, Saket Saurabh, Stéphan Thomassé, and Meirav Zehavi. Subquadratic kernels for implicit 3-hitting set and 3-set packing problems. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, LA, USA, January 7-10, 2018, pages 331-342, 2018.
Matthias Mnich and Erik Jan van Leeuwen. Polynomial kernels for deletion to classes of acyclic digraphs. Discrete Optimization, 25:48-76, 2017. URL: http://dx.doi.org/10.1016/j.disopt.2017.02.002.