This paper presents two semi-definite programming (SDP) based methods to solve the Key Player Problem (KPP). The KPP is to identify a set of k nodes (i. e., key players) from a social network of size n such that the number of nodes connected to these k nodes is maximized. The KPP has applications in social diffusion and products adoption as it helps maximizing information diffusion and impact. We first formulate the KPP as an integer program (IP) and then convert it into an SDP formulation, which can be solved efficiently and produce a set of high quality candidate solutions. We develop an IP-based algorithm and a stochastic search (greedy) algorithm to find the final solution for the KPP. We compare our algorithms with existing methods in small and large networks with different network structures, including random graph, scale-free network, and community-based scale-free network (CSN). Computational results show that our algorithms are more efficient in solving the KPP in all networks. In addition, we examine how the network structure influences the nodes coverage. It is found that CSNs allow the highest nodes coverage due to their community and scale-free structure.