Generating all the Steiner trees and computing Steiner intervals for a fixed number of terminals

In this work we present an enumeration algorithm for the generation of all Steiner trees containing a given set W of terminals of an unweighted graph G such that |W|=k, for a fixed positive integer k. The enumeration is performed within O(n) delay, where n=|V(G)| consequence of the algorithm is that the Steiner interval and the strong Steiner interval of a subset W⊆V(G) can be computed in polynomial time, provided that the size of W is bounded by a constant.