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Distributed interactive applications (DIAs) are networked systems that allow multiple participants at different locations to interact with each other. Wide spreads of client locations in large-scale DIAs often require geographical distribution of servers to meet the latency requirements of the applications. In the distributed server architecture, the network latencies involved in the interactions between clients are directly affected by how the clients are assigned to the servers. In this paper, we focus on the problem of assigning clients to appropriate servers in DIAs to enhance their interactivity. We formulate the problem as a combinational optimization problem and prove that it is NP-complete. Then, we propose several heuristic algorithms for fast computation of good client assignments and theoretically analyze their approximation ratios. The proposed algorithms are also experimentally evaluated with real Internet latency data. The results show that the proposed algorithms are efficient and effective in reducing the interaction time between clients, and our proposed Distributed-Modify-Assignment adapts well to the dynamics of client participation and network conditions. For the special case of tree network topologies, we develop a polynomial-time algorithm to compute the optimal client assignment.