eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-12-07
6:1
6:12
10.4230/LIPIcs.ISAAC.2016.6
article
Kernels for Deletion to Classes of Acyclic Digraphs
Agrawal, Akanksha
Saurabh, Saket
Sharma, Roohani
Zehavi, Meirav
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(k^3) to O(k^2) and of Pumpkin Vertex Deletion Set from O(k^18) to O(k^3). We also prove that the former kernel size is tight under certain complexity theoretic assumptions.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol064-isaac2016/LIPIcs.ISAAC.2016.6/LIPIcs.ISAAC.2016.6.pdf
out-forest
pumpkin
parameterized complexity
kernelization