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In this paper, we address the problem of cardinality estimation of XPath queries over XML data stored in a distributed, Internet-scale environment such as a large-scale, data sharing system designed to foster innovations in biomedical and health informatics. The cardinality estimate of XPath expressions is useful in XQuery optimization, designing IR-style relevance ranking schemes, and statistical hypothesis testing. We present a novel gossip algorithm called XGossip, which given an XPath query estimates the number of XML documents in the network that contain a match for the query. XGossip is designed to be scalable, decentralized, and robust to failures--properties that are desirable in a large-scale distributed system. XGossip employs a novel divide-and-conquer strategy for load balancing and reducing the bandwidth consumption. We conduct theoretical analysis of XGossip in terms of accuracy of cardinality estimation, message complexity, and bandwidth consumption. We present a comprehensive performance evaluation of XGossip on Amazon EC2 using a heterogeneous collection of XML documents.