Abstract—To study data dependencies over heterogeneous data in dataspaces, we define a general dependency form, namely comparable dependencies (CDs), which specifies constraints on comparable attributes. It covers the semantics of a broad class of dependencies in databases, including functional dependencies (FDs), metric functional dependencies (MFDs), and matching dependencies (MDs). As we illustrated, comparable dependencies are useful in real practice of dataspaces, e.g., semantic query optimization. Due to the heterogeneous data in dataspaces, the first question, known as the validation problem, is to determine whether a dependency (almost) holds in a data instance. Unfortunately, as we proved, the validation problem with certain error or confidence guarantee is generally hard. In fact, the confidence validation problem is also NP-hard to approximate to within any constant factor. Nevertheless, we develop several approaches for efficient approximation computation, including greedy and randomized approaches with an approximation bound on the maximum number of violations that an object may introduce. Finally, through an extensive experimental evaluation on real data, we verify the superiority of our methods. I
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