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

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

2011-11-29

arxiv.org/abs/1111.6698v2

Computer Science

Data Structures and Algorithms

This paper has been withdrawn due to a crucial error in Lemma 4. In Lemma 4, additional property for $\{Y'_j\}$ is needed to g

Scientific paper

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.

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