The Tree Augmentation Problem (TAP) is as follows: given a connected graph G = (V, ε) and an edge set E on V, find a minimum size subset of edges F ⊆ E such that (V, ε cup F) is 2-edge-connected. In the conference version [Even et al. 2001] was sketched a 1.5-approximation algorithm for the problem. Since a full proof was very complex and long, the journal version was cut into two parts. The first part [Even et al. 2009] only proved ratio 1.8. An attempt to simplify the second part produced an error in Even et al. . Here we give a correct, different, and self-contained proof of the ratio 1.5 that is also substantially simpler and shorter than the previous proofs.
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- Edge connectivity
- Laminar set family
- Tree Augmentation