An O(mlogn) algorithm for the weighted stable set problem in claw-free graphs with α(G)≤3

In this paper we show how to solve the Maximum Weight Stable Set Problem in a claw-free graph G ( V ,  E ) with α ( G ) ≤ 3 in time O ( | E | log | V | ) . More precisely, in time O ( | E | ) we check whether α ( G ) ≤ 3 or produce a stable set with cardinality at least 4; moreover, if α ( G ) ≤ 3 w...

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Bibliographic Details
Published inMathematical programming Vol. 164; no. 1-2; pp. 157 - 165
Main Authors Nobili, Paolo, Sassano, Antonio
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2017
Subjects
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Theoretical
Claw-free graphs
Algorithms
90C35
Stable set
05C69
05C85
Online AccessGet full text
ISSN0025-5610
1436-4646
DOI10.1007/s10107-016-1080-9

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Summary:In this paper we show how to solve the Maximum Weight Stable Set Problem in a claw-free graph G ( V ,  E ) with α ( G ) ≤ 3 in time O ( | E | log | V | ) . More precisely, in time O ( | E | ) we check whether α ( G ) ≤ 3 or produce a stable set with cardinality at least 4; moreover, if α ( G ) ≤ 3 we produce in time O ( | E | log | V | ) a maximum weight stable set of G . This improves the bound of O ( | E | | V | ) due to Faenza, Oriolo and Stauffer.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-016-1080-9