Given an edge-weighted graph G and a node subset R, the Steiner tree problem asks for an R-spanning tree of minimum weight. There are several strong approximation algorithms for this NP-hard problem, but research on their practicality is still in its early stages. In this study, we investigate how the behavior of approximation algorithms changes when applying preprocessing routines first. In particular, the shrunken instances allow us to consider algorithm parameterizations that have been impractical before, shedding new light on the algorithms' respective drawbacks and benefits.
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