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Most current semantic Web services (SWS) discovery approaches focus on the matchmaking of services in a specific description language while in practical application the advertised services are often heterogeneous and distributed. This paper proposes a metric space approach to resolve this problem in which all heterogeneous Web services are modeled as metric objects regardless of concrete description languages, and thereby the discovery problem can be treated as similarity search in metric space with a uniform criterion. In the matchmaking process, both the functional semantics and non-functional semantics of the Web services are integrated as selection conditions for similarity query. And two types of similarity queries: range query and an improved nearest neighbor query are combined to produce a sorted result set.