A (1+ln2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius

We consider the Tree Augmentation problem: given a graph G=(V,E) with edge-costs and a tree T on V disjoint to E, find a minimum-cost edge-subset F⊆E such that T∪F is 2-edge-connected. Tree Augmentation is equivalent to the problem of finding a minimum-cost edge-cover F⊆E of a laminar set-family. Th...

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Bibliographic Details
Published in:Theoretical computer science Vol. 489-490; pp. 67 - 74
Main Authors: Cohen, Nachshon, Nutov, Zeev
Format: Journal Article
Language:English
Published: Elsevier B.V 10.06.2013
Subjects:
Approximation algorithms
Edge-connectivity
Laminar family
Local replacement
Tree Augmentation
Edge-connectivity
Tree Augmentation
Approximation algorithms
Laminar family
Local replacement
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:We consider the Tree Augmentation problem: given a graph G=(V,E) with edge-costs and a tree T on V disjoint to E, find a minimum-cost edge-subset F⊆E such that T∪F is 2-edge-connected. Tree Augmentation is equivalent to the problem of finding a minimum-cost edge-cover F⊆E of a laminar set-family. The best known approximation ratio for Tree Augmentation is 2, even for trees of radius 2. As laminar families play an important role in network design problems, obtaining a better ratio is a major open problem in connectivity network design. We give a (1+ln2)-approximation algorithm for trees of constant radius. Our algorithm is based on a new decomposition of problem feasible solutions, and on an extension of Steiner Tree technique of Zelikovsky to the Set-Cover problem, which may be of independent interest. •We consider making a tree 2-edge-connected by adding a minimum cost edge set.•We give a (1+ln2)-approximation algorithm for trees of constant radius.•Our algorithm is based on a new decomposition of problem feasible solutions.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2013.04.004