Section: New Results

Structure and Tractability of Uncertain Data

A major part of the work conducted in Valda has been to study the connections between tractability and structure in databases, in particular uncertain databases.

In a first line of work, we have investigated incompleteness related to order. In [18], we have introduced a query language for order-incomplete data, based on the positive relational algebra with order-aware accumulation. We have used partial orders to represent order-incomplete data, and studied possible and certain answers for queries in this context, showing these problems are respectively NP-complete and coNP-complete, but identifying tractable cases depending on query operators and the structure of input partial orders. In [16], we consider a different setting where some partial order is known, but actual values are unknown. Our work is the first to propose a principled scheme to derive the value distributions and expected values of unknown items in this setting, with the goal of computing estimated top-$k$ results by interpolating the unknown values from the known ones. We have studied the complexity of this general task, and show tight complexity bounds, proving that the problem is intractable, but can be tractably approximated. We have also isolated structure-based restrictions that allow for a PTIME solution.

In [17], we have investigated parameterizations of both database instances and queries that make query evaluation fixed-parameter tractable in combined complexity, first in a setting without uncertainty. For this, we have introduced a new Datalog fragment with stratified negation, intensional-clique-guarded Datalog (ICG-Datalog), with linear-time evaluation on structures of bounded treewidth for programs of bounded rule size. Our result is shown by compiling to alternating two-way automata, whose semantics is defined via cyclic provenance circuits (cycluits) that can be tractably evaluated. Finally, we move to the probabilistic setting and have shown that probabilistic query evaluation remains intractable in combined complexity under this parameterization.

Finally, a last line of work concerns efficient queries over probabilistic graphs. In a first theoretical work [19], we have studied the combined complexity of conjunctive query evaluation on probabilistic graphs, which can be alternatively phrased as a probabilistic version of the graph homomorphism problem. We have shown that the complexity landscape is surprisingly rich, using a variety of technical tools. In a more practical work [12], we have proposed indexing techniques and algorithms to evaluate source-to-target queries in probabilistic graphs, by exploiting their structure. We have shown that these significantly enhance the accuracy and efficiency of existing query evaluation approaches on probabilistic graphs.