Wannabe bounded treewidth graphs admit a polynomial kernel for DFVS

Daniel Lokshtanov, M. S. Ramanujan, Saket Saurabh, Roohani Sharma, Meirav Zehavi

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

4 Scopus citations

Abstract

In the Directed Feedback Vertex Set (DFVS) problem, given a digraph D and k∈ N, the goal is to check if there exists a set of at most k vertices whose deletion from D leaves a directed acyclic graph. Resolving the existence of a polynomial kernel for DFVS parameterized by the solution size k is a central open problem in Kernelization. In this paper, we give a polynomial kernel for DFVS parameterized by k plus the size of a treewidth- η modulator. Our choice of parameter strictly encompasses previous positive kernelization results on DFVS. Our main result is based on a novel application of the tool of important separators embedded in state-of-the-art machinery such as protrusion decompositions.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings
EditorsZachary Friggstad, Mohammad R. Salavatipour, Jörg-Rüdiger Sack
PublisherSpringer Verlag
Pages523-537
Number of pages15
ISBN (Print)9783030247652
DOIs
StatePublished - 1 Jan 2019
Event16th International Symposium on Algorithms and Data Structures, WADS 2019 - Edmonton, Canada
Duration: 5 Aug 20197 Aug 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11646 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th International Symposium on Algorithms and Data Structures, WADS 2019
Country/TerritoryCanada
CityEdmonton
Period5/08/197/08/19

Keywords

  • DFVS
  • Important separator
  • Kernel
  • Treewidth

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