@inproceedings{111014d4382f43b98c8dbdf37e903219,

title = "LP-relaxations for tree augmentation",

abstract = "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 approximation ratio known for TAP is 1.5. In the more general Weighted TAP problem, F should be of minimum weight. Weighted TAP admits several 2-Approximation algorithms w.r.t.To the standard cut-LP relaxation. The problem is equivalent to the problem of covering a laminar set family. Laminar set families play an important role in the design of approximation algorithms for connectivity network design problems. In fact, Weighted TAP is the simplest connectivity network design problem for which a ratio better than 2 is not known. Improving this {"}natural{"} ratio is a major open problem, which may have implications on many other network design problems. It seems that achieving this goal requires finding an LP-relaxation with integrality gap better than 2, which is an old open problem even for TAP. In this paper we introduce two different LP-relaxations, and for each of them give a simple algorithm that computes a feasible solution for TAP of size at most 7/4 times the optimal LP value. This gives some hope to break the ratio 2 for the weighted case.",

keywords = "Approximation algorithms, Laminar family, LP-relaxation, Tree Augmentation",

author = "Guy Kortsarz and Zeev Nutov",

note = "Copyright: Copyright 2017 Elsevier B.V., All rights reserved.; 19th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2016 and the 20th International Workshop on Randomization and Computation, RANDOM 2016 ; Conference date: 07-09-2016 Through 09-09-2016",

year = "2016",

month = sep,

day = "1",

doi = "10.4230/LIPIcs.APPROX-RANDOM.2016.13",

language = "אנגלית",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

editor = "Klaus Jansen and Claire Mathieu and Rolim, {Jose D. P.} and Chris Umans",

booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 19th International Workshop, APPROX 2016 and 20th International Workshop, RANDOM 2016",

address = "גרמניה",

}