Abstract
Watermarking allows robust and unobtrusive insertion of information in a digital document. Very recently, techniques have been proposed for watermarking relational databases or XML documents, where information insertion must preserve a specific measure on data (e.g. mean and variance of numerical attributes.)In this paper we investigate the problem of watermarking databases or XML while preserving a set of parametric queries in a specified language, up to an acceptable distortion.We first observe that unrestricted databases can not be watermarked while preserving trivial parametric queries. We then exhibit query languages and classes of structures that allow guaranteed watermarking capacity, namely 1) local query languages on structures with bounded degree Gaifman graph, and 2) monadic second-order queries on trees or tree-like structures. We relate these results to an important topic in computational learning theory, the VC-dimension. We finally consider incremental aspects of query-preserving watermarking.
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