Improved Steiner tree algorithms for bounded treewidth

We propose a new algorithm that solves the Steiner tree problem on graphs with vertex set V to optimality in O(Btw+22⋅tw⋅|V|) time, where tw is the graphʼs treewidth and the Bell number Bk is the number of partitions of a k-element set. This is a linear-time algorithm for graphs with fixed treewidth and a polynomial algorithm for tw∈O(log|V|/loglog|V|).