On the integrality ratio for tree augmentation

We show that the standard linear programming relaxation for the tree augmentation problem in undirected graphs has an integrality ratio that approaches frac(3, 2). This refutes a conjecture of Cheriyan, Jordán, and Ravi [J. Cheriyan, T. Jordán, R. Ravi, On 2-coverings and 2-packings of laminar families, in: Proceedings, European Symposium on Algorithms, 1999, pp. 510-520. A longer version is on the web: http://www.math.uwaterloo.ca/jcheriyan/publications.html] that the integrality ratio is frac(4, 3). Crown Copyright © 2008.