LP-relaxations for tree augmentation

Guy Kortsarz, Zeev Nutov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 19th International Workshop, APPROX 2016 and 20th International Workshop, RANDOM 2016
EditorsKlaus Jansen, Claire Mathieu, Jose D. P. Rolim, Chris Umans
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770187
DOIs
StatePublished - 1 Sep 2016
Event19th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2016 and the 20th International Workshop on Randomization and Computation, RANDOM 2016 - Paris, France
Duration: 7 Sep 20169 Sep 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume60
ISSN (Print)1868-8969

Conference

Conference19th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2016 and the 20th International Workshop on Randomization and Computation, RANDOM 2016
Country/TerritoryFrance
CityParis
Period7/09/169/09/16

Keywords

  • Approximation algorithms
  • LP-relaxation
  • Laminar family
  • Tree Augmentation

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