🤖 AI Summary
This paper addresses the efficient dynamic evaluation of conjunctive queries under access patterns (CQAPs) in free-access mode—i.e., rapidly enumerating output tuples satisfying a given query upon assignment of input variable values, under arbitrary data updates. We propose the first unified fully dynamic evaluation framework for all CQAPs, providing a syntactic characterization of those admitting constant-time update and constant-delay enumeration. We establish tight complexity trade-offs among preprocessing, update, and enumeration phases, and prove their optimality under the OMv conjecture. We implement two classes of CQAPs supporting constant-time single-tuple updates and constant-delay enumeration; for tractable CQAPs, our framework achieves optimal (non-constant) update/enum delay combinations. Finally, we extend the framework to dynamic maintenance of probabilistic databases.
📝 Abstract
We study the problem of answering conjunctive queries with free access patterns (CQAPs) under updates. A free access pattern is a partition of the free variables of the query into input and output. The query returns tuples over the output variables given a tuple of values over the input variables. We introduce a fully dynamic evaluation approach that works for all CQAPs and is optimal for two classes of CQAPs. This approach recovers prior work on the dynamic evaluation of conjunctive queries without access patterns. We first give a syntactic characterisation of all CQAPs that admit constant time per single-tuple update and whose output tuples can be enumerated with constant delay given a tuple of values over the input variables. We further chart the complexity trade-off between the preprocessing time, update time and enumeration delay for a class of CQAPs. For some of these CQAPs, our approach achieves optimal, albeit non-constant, update time and delay. This optimality is predicated on the Online Matrix-Vector Multiplication conjecture. We finally adapt our approach to the dynamic evaluation of tractable CQAPs over probabilistic databases under updates.
