On the Tree Augmentation Problem

In the Tree Augmentation problem we are given a tree T = (V, F ) and an additional set E ⊆ V × V of edges, called “links”, with positive integer costs {ce : e ∈ E}. The goal is to augment T by a minimum cost set of links J ⊆ E such that T ∪ J is 2-edge-connected. Let M denote the maximum cost of a link. Recently, Adjiashvili [1] introduced a novel LP for the problem and used it to break the natural 2-approximation barrier for instances when M is a constant. Specifically, his algorithm computes a 1.96418 + approximate solution in time n 2). Using a slightly weaker LP we achieve ratio 12 7 + for arbitrary costs and ratio 1.6 + for unit costs in time 2 2).