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

Authors:
Nachshon Cohen;Zeev Nutov
Affiliations:
The Open University of Israel;The Open University of Israel
Venue:
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Year:
2011

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Abstract

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 minimumcost 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 network design. We give a (1 + ln 2)-approximation algorithm for trees of constant radius. Our algorithm is based on a new decomposition of problem solutions, which may be of independent interest.