Some Approximation Results in Multicasting

The approximability characteristics of the constrained Steiner tree (CST) problem and some if its special cases are considered here. APX is the class of problems for which it is possible to have polynomial time heuristics that guarantee a constant approximation bound. We first show that two special cases of CST, height-constrained spanning tree and height-constrained Steiner tree with unit-weight edges, cannot be in APX. This implies that CST cannot be in APX either. We then show that a more restricted special case of CST, height-constrained spanning tree with edge weights 1 or 2, cannot have a polynomial time approximation scheme unless P=NP.