A Primal Dual Algorithm On 2-Steiner Graphs

Abstract

The Steiner Tree Problem is a fundamental network design problem, where the goal is to connect a subset of terminals of a given network at minimum cost. A major open question regarding this problem, is proving that the integrality gap of a certain linear program relaxation, called the bidirected cut relaxation (BCR), is strictly smaller than 2. In this thesis, we prove that (BCR) has integrality gap at most 5/3 for a subset of instances, which we call 2-Steiner instances, via a primal-dual method.