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Many next-generation Internet architectures propose advanced packet processing functions in the data path of the network. Such "services" are typically performed on some nodes along the path of a packet. We present a novel decentralized algorithm that can determine an allocation of services to network nodes. The algorithm can obtain globally optimal solutions for a single service and approximate solutions for two or more services. In our simulation results, we validate the correctness of the algorithm, quantify the quality of the approximations, and compare the results to those of a centralized algorithm. Our results show that the proposed algorithm presents an effective solution to the service placement problem that can be implemented in a realistic network.