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Search algorithms have been a widely studied topic in the context of Peer-to-Peer (P2P) networks. Generally speaking, unstructured P2P networks, such as Gnutella, are used for performing arbitrary searches (i.e., the form of a search request is not restricted) and structured networks, such as the ones based on Distributed Hash Table algorithms, are used for performing exact searches (i.e., the form of a search request is restricted). In this paper we study the feasibility of an arbitrary search algorithm in structured P2P networks. Intuitively, structured P2P networks are not well-suited for performing arbitrary searches, but our study shows that this is not the case. According to our simulation results, arbitrary searches can be implemented on top of structured P2P networks in an efficient, incrementally deployable, and scalable manner.