Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6874728 | Journal of Computer and System Sciences | 2018 | 13 Pages |
Abstract
Given a digraph D and an integer k, Directed Feedback Vertex Set (DFVS) asks whether there exists a set of vertices S of size at most k such that F=DâS is DAG. Mnich and van Leeuwen [STACS 2016â] 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 light on the kernelization complexity of DFVS, a well-known open problem in Parameterized Complexity. 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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Akanksha Agrawal, Saket Saurabh, Roohani Sharma, Meirav Zehavi,