License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2023.62
URN: urn:nbn:de:0030-drops-185965
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Lampis, Michael ; Melissinos, Nikolaos ; Vasilakis, Manolis

Parameterized Max Min Feedback Vertex Set

LIPIcs-MFCS-2023-62.pdf (0.7 MB)


Given a graph G and an integer k, Max Min FVS asks whether there exists a minimal set of vertices of size at least k whose deletion destroys all cycles. We present several results that improve upon the state of the art of the parameterized complexity of this problem with respect to both structural and natural parameters.
Using standard DP techniques, we first present an algorithm of time tw^O(tw) n^O(1), significantly generalizing a recent algorithm of Gaikwad et al. of time vc^O(vc) n^O(1), where tw, vc denote the input graph’s treewidth and vertex cover respectively. Subsequently, we show that both of these algorithms are essentially optimal, since a vc^o(vc) n^O(1) algorithm would refute the ETH.
With respect to the natural parameter k, the aforementioned recent work by Gaikwad et al. claimed an FPT branching algorithm with complexity 10^k n^O(1). We point out that this algorithm is incorrect and present a branching algorithm of complexity 9.34^k n^O(1).

BibTeX - Entry

  author =	{Lampis, Michael and Melissinos, Nikolaos and Vasilakis, Manolis},
  title =	{{Parameterized Max Min Feedback Vertex Set}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{62:1--62:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-185965},
  doi =		{10.4230/LIPIcs.MFCS.2023.62},
  annote =	{Keywords: ETH, Feedback vertex set, Parameterized algorithms, Treewidth}

Keywords: ETH, Feedback vertex set, Parameterized algorithms, Treewidth
Collection: 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)
Issue Date: 2023
Date of publication: 21.08.2023

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