Parameterised Algorithms for Deletion to Classes of DAGs

Akanksha Agrawal, Saket Saurabh, Roohani Sharma, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 such that F = D − S is an acyclic digraph. In a recent paper, Mnich and van Leeuwen [STACS 2016] studied the kernelization complexity of DFVS with an additional restriction on F—namely that F must be an out-forest, an out-tree, or a (directed) pumpkin—with an objective of shedding some light on the kernelization complexity of the DFVS problem, a well known open problem in the area. The vertex deletion problems corresponding to obtaining an out-forest, an out-tree, or a (directed) pumpkin are Out-forest/Out-tree/Pumpkin Vertex Deletion Set, respectively. They showed that Out-forest/Out-tree/Pumpkin Vertex Deletion Set admit polynomial kernels. Another open problem regarding DFVS is that, does DFVS admit an algorithm with running time 2 O ( k )nO ( 1 )? We complement the kernelization programme of Mnich and van Leeuwen by designing fast FPT algorithms for the above mentioned problems. In particular, we design an algorithm for Out-forest Vertex Deletion Set that runs in time O(2.73 2 knO ( 1 )) and algorithms for Pumpkin/Out-tree Vertex Deletion Set that runs in time O(2.56 2 knO ( 1 )). As a corollary of our FPT algorithms and the recent result of Fomin et al. [STOC 2016] which gives a relation between FPT algorithms and exact algorithms, we get exact algorithms for Out-forest/Out-tree/Pumpkin Vertex Deletion Set that run in time O(1.63 3 nnO ( 1 )) , O(1.60 9 nnO ( 1 )) and O(1.60 9 nnO ( 1 )) , respectively.

Original languageEnglish
Pages (from-to)1880-1909
Number of pages30
JournalTheory of Computing Systems
Issue number8
StatePublished - 1 Nov 2018


  • Bounded search trees
  • Fixed parameter tractability
  • Out-forest
  • Out-tree
  • Pumpkin
  • branching

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics


Dive into the research topics of 'Parameterised Algorithms for Deletion to Classes of DAGs'. Together they form a unique fingerprint.

Cite this