Approximation algorithms for the k+-star packing problem

Given a target graph G and a set $G$ of $k^{+}$-stars, that is, stars with at least k satellites, a $k^{+}$-star packing of G is a set of vertex-disjoint subgraphs of G with each isomorphic to some element of $G$. The $k^{+}$-star packing problem is to find one such packing that covers as many vertices of G as possible. It is known to be NP-hard for any fixed $k\ge 2$, and has a simple 2-approximation algorithm when $k=2$. In this paper, we present an improved algorithm with a tight approximation ratio of 9/5 for $k=2$, and a $\frac{k+2}{2}$-approximation algorithm for general $k\ge 2$ using the local search approach.