On the integrality ratio for tree augmentation

• Published in: Operations research letters Vol. 36; no. 4; pp. 399 - 401
• Main Authors: Cheriyan, J., Karloff, H., Khandekar, R., Könemann, J.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-07-2008; Elsevier
• Subjects: 2-edge-connected graph; Applied sciences; Connectivity augmentation; Exact sciences and technology; Integer programming; Integrality ratio; Linear programming; Mathematical programming; Operational research and scientific management; Operational research. Management science; Tree augmentation; Integer programming; Integrality ratio; Linear programming; Tree augmentation; 2-edge-connected graph; Connectivity augmentation; Edge(graph); Tree(graph); Connected graph; HTTP; Packing; Graph connectivity; World wide web; Internet; Non directed graph
• ISSN: 0167-6377; 1872-7468
• DOI: 10.1016/j.orl.2008.01.009

We show that the standard linear programming relaxation for the tree augmentation problem in undirected graphs has an integrality ratio that approaches
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
4
3
.