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(B tw+2 · tw · |V |) time, where tw is the graph’s 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 |/ log log |V |). While being faster than the previously known algorithms, our thereby used coloring scheme can be extended to give new, improved algorithms for the prize-collecting Steiner tree as well as the k-cardinality tree problems.