A (1 + ln 2)-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 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.