An FPT algorithm in polynomial space for the Directed Steiner Tree problem with Limited number of Diffusing nodes

We provide an FPT exact algorithm running in time O(td⋅dk⋅n⋅(d+k)) and in polynomial space for DSTLD, where td is the number of unordered rooted trees with d unlabelled nodes. Thereby, we also provide the first exact algorithm running in polynomial space and in FPT time with respect to k which returns an optimal solution for DST instead of the optimal cost only.