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Most DHT-based P2P search systems assume implicitly that the participating peers contain multiple objects. The distributed hash table (DHT) is used as a directory to store the keys of these objects for efficient lookup. However, maintaining the DHT and keeping its contents fresh require substantial message and storage overhead. In this paper, we study whether it is possible to do without a directory. We consider a special case of the search problem in which each peer is characterized by a single set of attributes and the peers satisfying a given range or k-nearest-neighbor (KNN) query are looked up. The attribute values may change constantly. For this special search problem, we study the feasibility of interconnecting the peers directly using their attribute values instead of using hash keys. The resultant attribute-based overlay network (AON) thus preserves the attribute semantics in the interconnection. Such a distributed structure can easily support range and KNN queries and accommodate dynamically changing attribute values.