  We give a dynamic programming solution to find the minimum cost of a diameter
constrained Steiner tree in case of directed graphs. Then we show a simple
reduction from undirected version to the directed version to realize an
algorithm of similar complexity i.e, FPT in number of terminal vertices. Other
natural variants of constrained Steiner trees are defined by imposing
constraints on the min-degree and size of the Steiner tree and some polynomial
time reductions among these problems are proven. To the best of our knowledge,
these fairly simple reductions are not present in the literature prior to our
work.

Data Structures and Algorithms;Discrete Mathematics