LP-relaxations for tree augmentation

Guy Kortsarz, Zeev Nutov

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In the TREE AUGMENTATION problem 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 the problem is 1.5. In the more general WEIGHTED TREE AUGMENTATION problem, F should be of minimum weight. WEIGHTED TREE AUGMENTATION admits several 2-approximation algorithms w.r.t. the standard cut-LP relaxation. Improving this natural ratio is a major open problem, and resolving it may have implications on 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 TREE AUGMENTATION. In this paper we introduce two different LP-relaxations, and for each of them give a simple combinatorial algorithm that computes a feasible solution for TREE AUGMENTATION of size at most 1.75 times the optimal LP value.

Original languageEnglish (US)
Pages (from-to)94-105
Number of pages12
JournalDiscrete Applied Mathematics
Volume239
DOIs
StatePublished - Apr 20 2018

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Approximation algorithm
  • LP-relaxation
  • Laminar family
  • Tree augmentation

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