Answering UCQs under updates and in the presence of integrity constraints

TL;DR

This paper studies dynamic algorithms for evaluating unions of conjunctive queries (UCQs) over databases that undergo updates, providing complexity dichotomies based on query classes and considering integrity constraints.

Contribution

It introduces new classes of UCQs and establishes complexity dichotomies for query testing, enumeration, and counting under database updates and constraints.

Findings

Constant-time updates and query testing for t-hierarchical UCQs.

Sublinear update and testing times are unlikely for non-hierarchical UCQs.

Complexity results extend to databases with small domain constraints.

Abstract

We investigate the query evaluation problem for fixed queries over fully dynamic databases where tuples can be inserted or deleted. The task is to design a dynamic data structure that can immediately report the new result of a fixed query after every database update. We consider unions of conjunctive queries (UCQs) and focus on the query evaluation tasks testing (decide whether an input tuple belongs to the query result), enumeration (enumerate, without repetition, all tuples in the query result), and counting (output the number of tuples in the query result). We identify three increasingly restrictive classes of UCQs which we call t-hierarchical, q-hierarchical, and exhaustively q-hierarchical UCQs. Our main results provide the following dichotomies: If the query's homomorphic core is t-hierarchical (q-hierarchical, exhaustively q-hierarchical), then the testing (enumeration, counting) problem can be solved with constant update time and constant testing time (delay, counting time). Otherwise, it cannot be solved with sublinear update time and sublinear testing time (delay, counting time), unless the OV-conjecture and/or the OMv-conjecture fails. We also study the complexity of query evaluation in the dynamic setting in the presence of integrity constraints, and we obtain according dichotomy results for the special case of small domain constraints (i.e., constraints which state that all values in a particular column of a relation belong to a fixed domain of constant size).