A promising approach for obtaining improved approximation algorithms for Steiner tree is to use the bidirected cut relaxation (BCR). The integrality gap of this relaxation is at least $36/31$, and it has long been conjectured that its true value is very close to this lower bound. However, the best upper bound for general graphs was an almost trivial $2$. We improve this bound to $3/2$ by a fast combinatorial algorithm based on the primal-dual schema.

翻译：一个有望获得斯坦纳树改进近似算法的途径是使用双向割松弛（BCR）。该松弛的整性间隙至少为$36/31$，且长期以来的猜想认为其真实值非常接近这一下界。然而，对于一般图，最佳上界此前仅为几乎平凡的$2$。我们通过一种基于原始对偶框架的快速组合算法，将该上界改进至$3/2$。