One type of distributed systems is the client/server system consist of clients and servers. In order to improve the performance of such a system, client assignment strategy plays an important role. There are two criteria to evaluate the load on the servers - total load and load balance. The total load increases when the load balance decreases, vice versa. It has been proved that finding the best client assignment is NP-hard. In this paper, we propose a new model for the client assignment problem and design an algorithm based on Semidefinite programming (SDP). Our method has a (relaxed) performance ratio 0.87 when only 2 servers exist. In general case, our method becomes a heuristic, and the ratio of each iteration is 0.87. We are the first one to give these bounds. Our simulation results are compared with the state-of-art client assignment method, and our strategy outperforms it in terms of running time while keeps the load in similar level.
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