License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.IPEC.2020.13
URN: urn:nbn:de:0030-drops-133163
URL: https://drops.dagstuhl.de/opus/volltexte/2020/13316/
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Garlet Milani, Marcelo

A Polynomial Kernel for Funnel Arc Deletion Set

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LIPIcs-IPEC-2020-13.pdf (0.5 MB)


Abstract

In Directed Feedback Arc Set (DFAS) we search for a set of at most k arcs which intersect every cycle in the input digraph. It is a well-known open problem in parameterized complexity to decide if DFAS admits a kernel of polynomial size. We consider ğ’ž-Arc Deletion Set (ğ’ž-ADS), a variant of DFAS where we want to remove at most k arcs from the input digraph in order to turn it into a digraph of a class ğ’ž. In this work, we choose ğ’ž to be the class of funnels. Funnel-ADS is NP-hard even if the input is a DAG, but is fixed-parameter tractable with respect to k. So far no polynomial kernel for this problem was known. Our main result is a kernel for Funnel-ADS with 𝒪(k⁶) many vertices and 𝒪(k⁷) many arcs, computable in 𝒪(nm) time, where n is the number of vertices and m the number of arcs of the input digraph.

BibTeX - Entry

@InProceedings{garletmilani:LIPIcs:2020:13316,
  author =	{Marcelo Garlet Milani},
  title =	{{A Polynomial Kernel for Funnel Arc Deletion Set}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{13:1--13:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Yixin Cao and Marcin Pilipczuk},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13316},
  URN =		{urn:nbn:de:0030-drops-133163},
  doi =		{10.4230/LIPIcs.IPEC.2020.13},
  annote =	{Keywords: graph editing, directed feedback arc set, parameterized algorithm, kernels, funnels}
}

Keywords: graph editing, directed feedback arc set, parameterized algorithm, kernels, funnels
Collection: 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)
Issue Date: 2020
Date of publication: 04.12.2020


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