An LP 7/4-approximation for the Tree Augmentation Problem

In the Tree Augmentation Problem (TAP) the goal is to augment a tree T by a minimum size edge set F from a given edge set E such that T ∪ F is 2-edge-connected. The best known approximation ratio for the problem is 1.5 [5, 12]. Several paper analysed integrality gaps of LP and SDP relaxations for the problem. In [13] is given a simple LP with gap 1.5 for the case when every edge in E connects two leaves of T . Recently, Cheriyan and Gao [1] showed that a certain SDP relaxation obtained by the Lasserre lift-and-project method has integrality gap 7/4 + ǫ. Here we show, by a simple and short proof, that a modification of the LP used in [13] has integrality gap 7/4, which is achieved by the combinatorial algorithm of [12].