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Caching and replication of popular data objects contribute significantly to the reduction of the network bandwidth usage and the overall access time to data. Our focus is to improve the efficiency of object replication within a given distributed replication group. Such a group consists of servers that dedicate certain amount of memory for replicating objects requested by their clients. The content replication problem we are solving is defined as follows: Given the request rates for the objects and the server capacities, find the replica allocation that minimizes the access time over all servers and objects. We design a distributed approximation algorithm that solves this problem and prove that it provides a 2-approximation solution. We also show that the communication and computational complexity of the algorithm is polynomial with respect to the number of servers, the number of objects, and the sum of the capacities of all servers. Finally, we perform simulation experiments to investigate the performance of our algorithm. The experiments show that our algorithm outperforms the best existing distributed algorithm that solves the replica placement problem.