TY - GEN
T1 - Kernels for deletion to classes of acyclic digraphs
AU - Agrawal, Akanksha
AU - Saurabh, Saket
AU - Sharma, Roohani
AU - Zehavi, Meirav
N1 - Funding Information:
The research leading to these results received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreements no. 306992 (S. Saurabh). Part of this work was done while M. Zehavi was visiting the Simons Institute for the Theory of Computing.
Publisher Copyright:
© Akanksha Agrawal, Saket Saurabh, Roohani Sharma, and Meirav Zehavi.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - In the DIRECTED FEEDBACK VERTEX SET (DFVS) problem, we are given a digraph D on n vertices and a positive integer k and the objective is to check whether there exists a set of vertices S of size at most k such that F = D - S is a directed acyclic digraph. In a recent paper, Mnich and van Leeuwen [STACS 2016 ] considered the kernelization complexity of DFVS with an additional restriction on F, namely that F must be an out-forest (OUT-FOREST VERTEX DELETION SET), an out-tree (OUT-TREE VERTEX DELETION SET), or a (directed) pumpkin (PUMPKIN VERTEX DELETION SET). Their objective was to shed some light on the kernelization complexity of the DFVS problem, a well known open problem in the area of Parameterized Complexity. In this article, we improve the kernel sizes of OUT-FOREST VERTEX DELETION SET from O(k3) to O(k2) and of PUMPKIN VERTEX DELETION SET from O(k18) to O(k3). We also prove that the former kernel size is tight under certain complexity theoretic assumptions.
AB - In the DIRECTED FEEDBACK VERTEX SET (DFVS) problem, we are given a digraph D on n vertices and a positive integer k and the objective is to check whether there exists a set of vertices S of size at most k such that F = D - S is a directed acyclic digraph. In a recent paper, Mnich and van Leeuwen [STACS 2016 ] considered the kernelization complexity of DFVS with an additional restriction on F, namely that F must be an out-forest (OUT-FOREST VERTEX DELETION SET), an out-tree (OUT-TREE VERTEX DELETION SET), or a (directed) pumpkin (PUMPKIN VERTEX DELETION SET). Their objective was to shed some light on the kernelization complexity of the DFVS problem, a well known open problem in the area of Parameterized Complexity. In this article, we improve the kernel sizes of OUT-FOREST VERTEX DELETION SET from O(k3) to O(k2) and of PUMPKIN VERTEX DELETION SET from O(k18) to O(k3). We also prove that the former kernel size is tight under certain complexity theoretic assumptions.
KW - Kernelization
KW - Out-forest
KW - Parameterized complexity
KW - Pumpkin
UR - http://www.scopus.com/inward/record.url?scp=85010817981&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ISAAC.2016.6
DO - 10.4230/LIPIcs.ISAAC.2016.6
M3 - Conference contribution
AN - SCOPUS:85010817981
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 6.1-6.12
BT - 27th International Symposium on Algorithms and Computation, ISAAC 2016
A2 - Hong, Seok-Hee
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 27th International Symposium on Algorithms and Computation, ISAAC 2016
Y2 - 12 December 2016 through 14 December 2016
ER -