Bag Query Containment and Information Theory

The query containment problem is a fundamental algorithmic problem in data management. While this problem is well understood under set semantics, it is by far less understood under bag semantics. In particular, it is a long-standing open question whether or not the conjunctive query containment problem under bag semantics is decidable. We unveil tight connections between information theory and the conjunctive query containment under bag semantics. These connections are established using information inequalities, which are considered to be the laws of information theory. Our first main result asserts that deciding the validity of a generalization of information inequalities is many-one equivalent to the restricted case of conjunctive query containment in which the containing query is acyclic; thus, either both these problems are decidable or both are undecidable. Our second main result identifies a new decidable case of the conjunctive query containment problem under bag semantics. Specifically, we give an exponential-time algorithm for conjunctive query containment under bag semantics, provided the containing query is chordal and admits a simple junction tree.

OnGIS

Geospatial data sources are heterogeneous and backed by different data management technologies. This brings problems in data integration as well as their subsequent interpretation. This article proposes a technique for choosing the relevant data source out of many such sources, given a complex spatial query. Each source is described with a set of prototypical queries that are algorithmically arranged into a lattice. Upon query execution, the lattice is searched for an element matching best the input query. The matching algorithm makes use of the GeoSPARQL query containment enhanced with OWL 2 QL semantics. The technique is implemented in a prototypical system called OnGIS.