On the Integrality Gap of the Directed-Component Relaxation for Steiner Tree

Mohammad Taghi Hajiaghayi; Shi Li

On the Integrality Gap of the Directed-Component Relaxation for Steiner Tree

Data Structures and Algorithms 2011-12-06 v2

Authors: Mohammad Taghi Hajiaghayi , Shi Li

Abstract

In this note, we show that the integrality gap of the $k$ -Directed-Component- Relaxation( $k$ -DCR) LP for the Steiner tree problem, introduced by Byrka, Grandoni, Rothvob and Sanita (STOC 2010), is at most $\ln(4)<1.39$ . The proof is constructive: we can efficiently find a Steiner tree whose cost is at most $\ln(4)$ times the cost of the optimal fractional $k$ -restricted Steiner tree given by the $k$ -DCR LP.

Keywords

Steiner tree problem integrality gap directed-component relaxation linear programming approximation algorithms k-DCR constructive proof

Cite

@article{arxiv.1111.6698,
  title  = {On the Integrality Gap of the Directed-Component Relaxation for Steiner Tree},
  author = {Mohammad Taghi Hajiaghayi and Shi Li},
  journal= {arXiv preprint arXiv:1111.6698},
  year   = {2011}
}

Comments

This paper has been withdrawn due to a crucial error in Lemma 4. In Lemma 4, additional property for $\{Y'_j\}$ is needed to guarantee that the family of distributions exists. However, we can not guarantee the condition for every iteration

On the Integrality Gap of the Directed-Component Relaxation for Steiner Tree

Abstract

Keywords

Cite

Comments

Related papers