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DOI: 10.4230/LIPIcs.IPEC.2020.13

A Polynomial Kernel for Funnel Arc Deletion Set

Authors: Marcelo Garlet Milani

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

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 𝒞-Arc Deletion Set (𝒞-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 𝒞. In this work, we choose 𝒞 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.

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Marcelo Garlet Milani. A Polynomial Kernel for Funnel Arc Deletion Set. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 13:1-13:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{garletmilani:LIPIcs.IPEC.2020.13,
  author =	{Garlet Milani, Marcelo},
  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 =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.13},
  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}
}

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Documents authored by Garlet Milani, Marcelo

A Polynomial Kernel for Funnel Arc Deletion Set

Abstract

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