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 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. © 2011 Springer-Verlag.
CITATION STYLE
Cohen, N., & Nutov, Z. (2011). A (1 + ln 2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6845 LNCS, pp. 147–157). https://doi.org/10.1007/978-3-642-22935-0_13
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