The concept of Pareto frontiers is well-known in economics. Within the database community there exist many different solutions for the specification and calculation of Pareto frontiers, also called Skyline queries in the database context. Slight generalizations like the combination of the Pareto operator with the lexicographical order have been established under the term database preferences. In this paper we present the rPref package which allows to efficiently deal with these concepts within R. With its help, database preferences can be specified in a very similar way as in a state-of-the-art database management system. Our package provides algorithms for an efficient calculation of the Pareto-optimal set and further functionalities for visualizing and analyzing the induced preference order.
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Preferences allow more flexible and personalised queries in database systems. Evaluation of such a query means to select the maximal elements from the respective database w.r.t. to the preference, which is a partial strict-order. We present a point-free calculus of such preferences and exemplify its use in proving algebraic laws about preferences that can be used in query optimisation. We show that this calculus can be mechanised using off-the-shelf automated first-order theorem provers.
Abstract. Preference algebra, an extension of the algebra of database relations, is a well-studied field in the area of personalized databases. It allows modelling user wishes by preference terms; they represent strict partial orders telling which database objects the user prefers over other ones. There are a number of constructors that allow combining simple preferences into quite complex, nested ones. A preference term is then used as a database query, and the results are the maximal objects according to the order it denotes. Depending on the size of the database, this can be computationally expensive. For optimisation, preference queries and the corresponding terms are transformed using a number of algebraic laws. So far, the correctness proofs for such laws have been performed by hand and in a point-wise fashion. We enrich the standard theory of relational databases to an algebraic framework that allows completely point-free reasoning about complex preferences. This black-box view is amenable to a treatment in first-order logic and hence to fully automated proofs using off-the-shelf verification tools. We exemplify the use of the calculus with some non-trivial laws, notably concerning so-called preference prefilters which perform a preselection to speed up the computation of the maximal objects proper.
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