@inproceedings{ef1723e6189c4bebb67b31fda515bba1,
title = "Kernels for deletion to classes of acyclic digraphs",
abstract = "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.",
keywords = "Kernelization, Out-forest, Parameterized complexity, Pumpkin",
author = "Akanksha Agrawal and Saket Saurabh and Roohani Sharma and Meirav Zehavi",
note = "Publisher Copyright: {\textcopyright} Akanksha Agrawal, Saket Saurabh, Roohani Sharma, and Meirav Zehavi.; 27th International Symposium on Algorithms and Computation, ISAAC 2016 ; Conference date: 12-12-2016 Through 14-12-2016",
year = "2016",
month = dec,
day = "1",
doi = "https://doi.org/10.4230/LIPIcs.ISAAC.2016.6",
language = "American English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
pages = "6.1--6.12",
editor = "Seok-Hee Hong",
booktitle = "27th International Symposium on Algorithms and Computation, ISAAC 2016",
address = "Germany",
}