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It has been shown that the peer-to-peer paradigm is more efficient than the traditional client-server model for file sharing among a large number of users. Given a group of leechers who wants to download a single file and a group of seeds who possesses the whole file, the minimum time needed for distributing the file to all users can be calculated based on their bandwidth availabilities. A scheduling algorithm has been developed so that every leecher can obtain the file within this minimum time. Unfortunately, this mechanism is not optimal with regard to the average download time among the peers. In this paper, we study how to reduce the average download time without prolonging the time needed for all leechers to obtain the file from a theoretical perspective. Based on the bandwidth capacities, the seeds and leechers are divided into different groups. We identify the necessary conditions for grouping to bring about benefits. We also study the impact on performance when leechers leave the system before the downloading process is complete. To evaluate our mechanism, we conduct extensive simulations and compare the performance with a BitTorrentlike file sharing algorithm. The results show that our grouping protocol successfully reduces the average download time over a wide range of system configurations.