On full Steiner trees in unit disk graphs

Given an edge-weighted graph G=(V,E) and a subset R of V, a Steiner tree of G is a tree which spans all the vertices in R. A full Steiner tree is a Steiner tree which has all the vertices of R as its leaves. The full Steiner tree problem is to find a full Steiner tree of G with minimum weight. In this paper we consider the full Steiner tree problem when G is a unit disk graph. We present a 20-approximation algorithm for the full Steiner tree problem in G. As for λ-precise unit disk graphs we present a (10+1λ)-approximation algorithm, where λ is the length of the shortest edge in G