Solving equations in the relational algebra

Enumerating all solutions of a relational algebra equation is a natural and powerful operation which, when added as a query language primitive to the nested relational algebra, yields a query language for nested relational databases, equivalent to the well-known powerset algebra. We study \emph{sparse} equations, which are equations with at most polynomially many solutions. We look at their complexity, and compare their expressive power with that of similar notions in the powerset algebra.Comment: Minor revision, accepted for publication in SIAM Journal on Computin

Relational data factorization

Motivated by an analogy with matrix factorization, we introduce the problem of factorizing relational data. In matrix factorization, one is given a matrix and has to factorize it as a product of other matrices. In relational data factorization, the task is to factorize a given relation as a conjunctive query over other relations, i.e., as a combination of natural join operations. Given a conjunctive query and the input relation, the problem is to compute the extensions of the relations used in the query. Thus, relational data factorization is a relational analog of matrix factorization; it is also a form of inverse querying as one has to compute the relations in the query from the result of the query. The result of relational data factorization is neither necessarily unique nor required to be a lossless decomposition of the original relation. Therefore, constraints can be imposed on the desired factorization and a scoring function is used to determine its quality (often similarity to the original data). Relational data factorization is thus a constraint satisfaction and optimization problem. We show how answer set programming can be used for solving relational data factorization problems.Algorithms and the Foundations of Software technolog