On the membership problem for multivalued dependencies in XML

Like relational databases, to solve the membership problem is essential to design an available algorithm of schema decomposition. In this paper, the membership problem of multivalued dependency in XML is investigated. We first define XML tree and tree tuple etc. in a new way, then based on DTD, we give the concept of multivalued dependency for XML(XMVD), and define its semantics via a relational representation of XML. The definitions of closure, path dependency basis and the closure of paths of multivalued dependencies for XML are also proposed. An algorithm of computing path dependency basis is given. Finally, based on computing path dependency basis, an algorithm of membership problem of XMVD is presented. We also prove the termination and correctness of the two algorithms and analyze the time complexity of them in this paper.