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.STACS.2021.53
URN: urn:nbn:de:0030-drops-136982
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13698/
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Neuwohner, Meike

An Improved Approximation Algorithm for the Maximum Weight Independent Set Problem in d-Claw Free Graphs

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Abstract

In this paper, we consider the task of computing an independent set of maximum weight in a given d-claw free graph G = (V,E) equipped with a positive weight function w:V → ℝ^+. Thereby, d ≥ 2 is considered a constant. The previously best known approximation algorithm for this problem is the local improvement algorithm SquareImp proposed by Berman [Berman, 2000]. It achieves a performance ratio of d/2+ε in time ?(|V(G)|^(d+1)⋅(|V(G)|+|E(G)|)⋅(d-1)²⋅ (d/(2ε)+1)²) for any ε > 0, which has remained unimproved for the last twenty years. By considering a broader class of local improvements, we obtain an approximation ratio of d/2-(1/63,700,992)+ε for any ε > 0 at the cost of an additional factor of ?(|V(G)|^(d-1)²) in the running time. In particular, our result implies a polynomial time d/2-approximation algorithm. Furthermore, the well-known reduction from the weighted k-Set Packing Problem to the Maximum Weight Independent Set Problem in k+1-claw free graphs provides a (k+1)/2 -(1/63,700,992)+ε-approximation algorithm for the weighted k-Set Packing Problem for any ε > 0. This improves on the previously best known approximation guarantee of (k+1)/2 + ε originating from the result of Berman [Berman, 2000].

BibTeX - Entry

@InProceedings{neuwohner:LIPIcs.STACS.2021.53,
  author =	{Neuwohner, Meike},
  title =	{{An Improved Approximation Algorithm for the Maximum Weight Independent Set Problem in d-Claw Free Graphs}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{53:1--53:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13698},
  URN =		{urn:nbn:de:0030-drops-136982},
  doi =		{10.4230/LIPIcs.STACS.2021.53},
  annote =	{Keywords: d-Claw free Graphs, independent Set, local Improvement, k-Set Packing, weighted}
}

Keywords: d-Claw free Graphs, independent Set, local Improvement, k-Set Packing, weighted
Collection: 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)
Issue Date: 2021
Date of publication: 10.03.2021

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