Internet is a network of several distributed systems that consists of clients and servers communicating with each other directly or indirectly. In order to improve the performance of such a system, client-server assignment plays an important role. Achieving optimal client-server assignment in internet distributed systems is a great challenge. It is dependent on various factors and can be achieved by various means. Our approach is mainly dependent on two important factors, 1) Total communication load and 2) Load balancing of the servers. In our approach we propose an algorithm that is based on Semidefinite programming, to obtain an approximately optimal solution for the client-server assignment problem. We will show the efficiency of our approach by the simulation experiments compared with the existing client-server assignment.