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.2022.53
URN: urn:nbn:de:0030-drops-168517
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16851/
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Gong, Mingyang ; Fan, Jing ; Lin, Guohui ; Miyano, Eiji

Approximation Algorithms for Covering Vertices by Long Paths

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LIPIcs-MFCS-2022-53.pdf (0.7 MB)

Abstract

Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least k vertices is considered long. When k ≤ 3, the problem is polynomial time solvable; when k is the total number of vertices, the problem reduces to the Hamiltonian path problem, which is NP-complete. For a fixed k ≥ 4, the problem is NP-hard and the best known approximation algorithm for the weighted set packing problem implies a k-approximation algorithm. To the best of our knowledge, there is no approximation algorithm directly designed for the general problem; when k = 4, the problem admits a 4-approximation algorithm which was presented recently. We propose the first (0.4394 k + O(1))-approximation algorithm for the general problem and an improved 2-approximation algorithm when k = 4. Both algorithms are based on local improvement, and their performance analyses are done via amortization.

BibTeX - Entry

@InProceedings{gong_et_al:LIPIcs.MFCS.2022.53,
  author =	{Gong, Mingyang and Fan, Jing and Lin, Guohui and Miyano, Eiji},
  title =	{{Approximation Algorithms for Covering Vertices by Long Paths}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{53:1--53:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16851},
  URN =		{urn:nbn:de:0030-drops-168517},
  doi =		{10.4230/LIPIcs.MFCS.2022.53},
  annote =	{Keywords: Path cover, k-path, local improvement, amortized analysis, approximation algorithm}
}

Keywords: Path cover, k-path, local improvement, amortized analysis, approximation algorithm
Collection: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)
Issue Date: 2022
Date of publication: 22.08.2022

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