We investigate an underlying mathematical model and algorithms for optimizing the performance of a class of distributed systems over the Internet. Such a system consists of a large number of clients who communicate with each other indirectly via a number of intermediate servers. Optimizing the overall performance of such a system then can be formulated as a client-server assignment problem whose aim is to assign the clients to the servers in such a way to satisfy some prespecified requirements on the communication cost and load balancing. We show that 1) the total communication load and load balancing are two opposing metrics, and consequently, their tradeoff is inherent in this class of distributed systems; 2) in general, finding the optimal client-server assignment for some prespecified requirements on the total load and load balancing is NP-hard, and therefore; 3) we propose a heuristic via relaxed convex optimization for finding the approximate solution. Our simulation results indicate that the proposed algorithm produces superior performance than other heuristics, including the popular Normalized Cuts algorithm.
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