On the integrality ratio for tree augmentation

Authors:
J. Cheriyan;H. Karloff;R. Khandekar;J. KöNemann
Affiliations:
Department of Comb. & Opt., University of Waterloo, Waterloo ON, Canada N2L 3G1;AT&T Labs-Research, 180 Park Ave., Florham Park, NJ 07932, USA;IBM T.J.Watson Research Center, Yorktown Heights, NY 10598, USA;Department of Comb. & Opt., University of Waterloo, Waterloo ON, Canada N2L 3G1
Venue:
Operations Research Letters
Year:
2008

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Abstract

We show that the standard linear programming relaxation for the tree augmentation problem in undirected graphs has an integrality ratio that approaches 32. This refutes a conjecture of Cheriyan, Jordan, and Ravi [J. Cheriyan, T. Jordan, 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 43.