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Recently, there has been an increasing interest in content sharing on peer-to-peer (P2P) networks. Since such a system employs a flooding mechanism for queries and because each peer returns many search results, the systems response to a query creates heavy traffic. Therefore, we propose a new and more efficient query processing method for top-k queries on P2P networks. We focus on the fact that users usually need search results only with a higher score. Our method reduces the reply traffic by controlling the number of query replies. Moreover, we evaluate the proposed method by simulation studies.