An Efficient Approximation Algorithm for the Steiner Tree Problem
Chi‐Yeh Chen · 2019
The Steiner tree problem is one of the classic and most fundamental NP-hard problems: given an arbitrary weighted graph, seek a minimum-cost tree spanning a given subset of the vertices (terminals). Byrka et al. proposed a 1.3863+ϵ-approximation algorithm in which the linear program is solved at every iteration after contracting a component. Goemans et al. shown that it is possible to achieve the same approximation guarantee while only solving hypergraphic LP relaxation once. However, optimizing hypergraphic LP relaxation exactly is strongly NP-hard. This article presents an efficient two-phase heuristic in greedy strategy that achieves an approximation ratio of 1.4295.