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In this experimental study we consider Steiner tree approximation algorithms that guarantee a constant approximation ratio smaller than 2. The considered greedy algorithms and approaches based on linear programming involve the incorporation of k-restricted full components for some k ≥ 3. For most of the algorithms, their strongest theoretical approximation bounds are only achieved for k → ∞. However, the running time is also exponentially dependent on k, so only small k are tractable in practice.We investigate different implementation aspects and parameter choices that finally allow us to construct algorithms (somewhat) feasible for practical use. We compare the algorithms against each other, to an exact LP-based algorithm, and to fast and simple 2-approximations. Funded by the German Research Foundation (DFG), project number CH 897/1-1. Preliminary versions of this work appeared as [Chimani and Woste 2011] and [Beyer and Chimani 2014]. 1 arXiv:1409.8318v2 [cs.DS] 9 Dec 2015bound for an approximation ratio is 96/95 ≈ 1.0105 [Chlebík and Chlebíková 2008].The STP has various applications in the fields of VLSI design, routing, network design, computational biology, and computer-aided design. It serves as a basis for generalized problems like prize-collecting and stochastic Steiner trees, Steiner forests, Survivable Network Design problems, discount-augmented problems like Buy-at-Bulk or Rent-or-Buy, and appears as a subproblem in problems like the Steiner packing problem.The versatile applicability of the STP gave rise to a lot of research from virtually all algorithmic points of view: heuristics, metaheuristics, and approximation algorithms [

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