A constant-factor approximation for weighted bond cover

The WeightedF-Vertex Deletion for a class F of graphs asks, weighted graph G, for a minimum weight vertex set S such that G−S∈F. The case when F is minor-closed and excludes some graph as a minor has received particular attention but a constant-factor approximation remained elusive for WeightedF-Ver...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 149; p. 103617
Main Authors: Kim, Eun Jung, Lee, Euiwoong, Thilikos, Dimitrios M.
Format: Journal Article
Language:English
Published: Elsevier Inc 01.05.2025
Elsevier
Subjects:
Bonds in graphs
Computer Science
Constant-factor approximation algorithms
Data Structures and Algorithms
Discrete Mathematics
Graph minors
Graph modification problems
Primal-dual method
Constant-factor approximation algorithms
Bonds in graphs
Graph modification problems
Graph minors
Primal-dual method
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary:The WeightedF-Vertex Deletion for a class F of graphs asks, weighted graph G, for a minimum weight vertex set S such that G−S∈F. The case when F is minor-closed and excludes some graph as a minor has received particular attention but a constant-factor approximation remained elusive for WeightedF-Vertex Deletion. Only three cases of minor-closed F are known to admit constant-factor approximations, namely Vertex Cover, Feedback Vertex Set and Diamond Hitting Set. We study the problem for the class F of θc-minor-free graphs, under the equivalent setting of the Weightedc-Bond Cover problem, and present a constant-factor approximation algorithm using the primal-dual method. Besides making an important step in the quest of (dis)proving a constant-factor approximation for WeightedF-Vertex Deletion, our result may be useful as a template for algorithms for other minor-closed families.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2024.103617