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/
Neuwohner, Meike
An Improved Approximation Algorithm for the Maximum Weight Independent Set Problem in d-Claw Free Graphs
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: |
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d-Claw free Graphs, independent Set, local Improvement, k-Set Packing, weighted |
Collection: |
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38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021) |
Issue Date: |
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2021 |
Date of publication: |
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10.03.2021 |