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Update management of XML documents is an increasingly important research issue in XML databases, because contents of XML documents evolve as time goes by. Even though, XML databases should be able to effectively process XML queries as well as updates on the documents. We propose a robust node-numbering scheme for XML documents named QRS (quartering-regions scheme). In QRS, reefs (regions expressed by floating-point numbers), a variant of regions, are used for expressing node-numbers. Reefs are almost compatible to regions, and thus they can be used for detecting ancestor-descendant relationship among nodes for the purpose of efficient query processing. Moreover, reefs can cope with updates by utilizing gaps between reefs in terms of floating-point numbers. Consequently, we can avoid node renumbering as much as possible.