Approximation to the minimum rooted star cover problem

In this paper, we study the following minimum rooted star cover problem: given a complete graph G = (V, E) with a length function l : E -> Z(+) that satisfies the triangle inequality, a designated root vertex r is an element of V, and a length bound D-1 the objective is to find a minimum cardinality set of rooted stars, that covers all vertices in V such that the length of each rooted star is at most D-1 where a rooted star is a subset of E having a common center s is an element of V arid containing the edge (r, s). This problem is NP-complete and we present a constant ratio approximation algorithm for this problem.