An Improved Integrality Gap for Steiner Tree

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.