Kernels for Deletion to Classes of Acyclic Digraphs
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.
out-forest
pumpkin
parameterized complexity
kernelization
6:1-6:12
Regular Paper
Akanksha
Agrawal
Akanksha Agrawal
Saket
Saurabh
Saket Saurabh
Roohani
Sharma
Roohani Sharma
Meirav
Zehavi
Meirav Zehavi
10.4230/LIPIcs.ISAAC.2016.6
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