Kernels for deletion to classes of acyclic digraphs

Akanksha Agrawal, Saket Saurabh, Roohani Sharma, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publication27th International Symposium on Algorithms and Computation, ISAAC 2016
EditorsSeok-Hee Hong
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770262
StatePublished - 1 Dec 2016
Externally publishedYes
Event27th International Symposium on Algorithms and Computation, ISAAC 2016 - Sydney, Australia
Duration: 12 Dec 201614 Dec 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference27th International Symposium on Algorithms and Computation, ISAAC 2016


  • Kernelization
  • Out-forest
  • Parameterized complexity
  • Pumpkin

ASJC Scopus subject areas

  • Software


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