Contraction-Based Steiner Tree Approximations in Practice

In this experimental study we consider contraction-based Steiner tree approximations. This class contains the only approximation algorithms that guarantee a constant approximation ratio below 2 and still may be applicable in practice. Despite their vivid evolution in theory, these algorithms have, to our knowledge, never been thoroughly investigated in practice before, which is particularly interesting as most of these algorithms' approximation guarantees only hold when some (constant) parameter k tends to infinity, while the running time is exponentially dependent on this very k. We investigate different implementation aspects and parameter choices which finally allow us to construct algorithms feasible for practical use. Then we compare these algorithms against each other and against state-of-the-art approaches.