Abstract
In this paper, we consider the task of computing an independent set of maximum weight in a given dclaw 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 𝒪(V(G)^(d+1)⋅(V(G)+E(G))⋅(d1)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 𝒪(V(G)^(d1)²) in the running time. In particular, our result implies a polynomial time d/2approximation algorithm. Furthermore, the wellknown reduction from the weighted kSet Packing Problem to the Maximum Weight Independent Set Problem in k+1claw free graphs provides a (k+1)/2 (1/63,700,992)+εapproximation algorithm for the weighted kSet 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 dClaw Free Graphs}},
booktitle = {38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
pages = {53:153:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771801},
ISSN = {18688969},
year = {2021},
volume = {187},
editor = {Bl\"{a}ser, Markus and Monmege, Benjamin},
publisher = {Schloss Dagstuhl  LeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13698},
URN = {urn:nbn:de:0030drops136982},
doi = {10.4230/LIPIcs.STACS.2021.53},
annote = {Keywords: dClaw free Graphs, independent Set, local Improvement, kSet Packing, weighted}
}
Keywords: 

dClaw free Graphs, independent Set, local Improvement, kSet Packing, weighted 
Collection: 

38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021) 
Issue Date: 

2021 
Date of publication: 

10.03.2021 