A simplified 1.5-approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2

The Tree Augmentation Problem(TAP) is given a connected graph G = (V, E) and an edge set E on V disjoint to E, find a minimum size subset of edges F ⊆ E such that (V, E ∪ F) is 2-edge-connected. In [5] and [6] a 1.8 and 1.5 approximation were given for the problem. The proof of the 1.5 was cut into two papers, as our proof then was very complex and very long. In the current paper we present a substantially simplified, substantially different, self contained and much shorter proof of the 1.5 ratio. The new ideas in this paper may find future applications. Our paper also corrects a typo from the IPL paper [6] that gave a wrong definition of locking trees