Answering Conjunctive Queries under Updates

We consider the task of enumerating and counting answers to $k$-ary conjunctive queries against relational databases that may be updated by inserting or deleting tuples. We exhibit a new notion of q-hierarchical conjunctive queries and show that these can be maintained efficiently in the following sense. During a linear time preprocessing phase, we can build a data structure that enables constant delay enumeration of the query results; and when the database is updated, we can update the data structure and restart the enumeration phase within constant time. For the special case of self-join free conjunctive queries we obtain a dichotomy: if a query is not q-hierarchical, then query enumeration with sublinear$^\ast$ delay and sublinear update time (and arbitrary preprocessing time) is impossible. For answering Boolean conjunctive queries and for the more general problem of counting the number of solutions of k-ary queries we obtain complete dichotomies: if the query's homomorphic core is q-hierarchical, then size of the the query result can be computed in linear time and maintained with constant update time. Otherwise, the size of the query result cannot be maintained with sublinear update time. All our lower bounds rely on the OMv-conjecture, a conjecture on the hardness of online matrix-vector multiplication that has recently emerged in the field of fine-grained complexity to characterise the hardness of dynamic problems. The lower bound for the counting problem additionally relies on the orthogonal vectors conjecture, which in turn is implied by the strong exponential time hypothesis. $^\ast)$ By sublinear we mean $O(n^{1-\varepsilon})$ for some $\varepsilon>0$, where $n$ is the size of the active domain of the current database

Conjunctive Queries with Free Access Patterns under Updates

We study the problem of answering conjunctive queries with free access patterns 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 for such queries. We also give a syntactic characterisation of those queries that admit constant time per single-tuple update and whose output tuples can be enumerated with constant delay given an input tuple. Finally, we chart the complexity trade-off between the preprocessing time, update time and enumeration delay for such queries. For a class of queries, our approach achieves optimal, albeit non-constant, update time and delay. Their optimality is predicated on the Online Matrix-Vector Multiplication conjecture. Our results recover prior work on the dynamic evaluation of conjunctive queries without access patterns.Comment: Extended and polished version. Title changed. Section 4 on the evaluation of arbitrary conjunctive queries with free access patterns is ne

Conjunctive Queries with Free Access Patterns under Updates

We study the problem of answering conjunctive queries with free access patterns 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 for such queries. We also give a syntactic characterisation of those queries that admit constant time per single-tuple update and whose output tuples can be enumerated with constant delay given an input tuple. Finally, we chart the complexity trade-off between the preprocessing time, update time and enumeration delay for such queries. For a class of queries, our approach achieves optimal, albeit non-constant, update time and delay. Their optimality is predicated on the Online Matrix-Vector Multiplication conjecture. Our results recover prior work on the dynamic evaluation of conjunctive queries without access patterns

Fully dynamic evaluation for conjunctive queries with free access patterns

We study the problem of answering conjunctive queries with free access patterns 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 for such queries. It is fully dynamic in the sense that it supports both inserts and deletes of tuples to the input relations. Our approach computes a data structure that supports the enumeration of the output tuples and maintains it under single-tuple updates to the input data. We also give a syntactic characterization of those queries that admit constant time per single-tuple update and whose output tuples can be enumerated with constant delay given an input tuple. Finally, for triangle and hierarchical queries with free access patterns, we chart the complexity trade-offs between the preprocessing time, update time and enumeration delay for such queries. The trade-offs are strongly or weakly Pareto optimal for triangle and a class of hierarchical queries. Their optimality is predicated on the Online Boolean Matrix-Vector Multiplication conjecture

From Causes for Database Queries to Repairs and Model-Based Diagnosis and Back

In this work we establish and investigate connections between causes for query answers in databases, database repairs wrt. denial constraints, and consistency-based diagnosis. The first two are relatively new research areas in databases, and the third one is an established subject in knowledge representation. We show how to obtain database repairs from causes, and the other way around. Causality problems are formulated as diagnosis problems, and the diagnoses provide causes and their responsibilities. The vast body of research on database repairs can be applied to the newer problems of computing actual causes for query answers and their responsibilities. These connections, which are interesting per se, allow us, after a transition -inspired by consistency-based diagnosis- to computational problems on hitting sets and vertex covers in hypergraphs, to obtain several new algorithmic and complexity results for database causality.Comment: To appear in Theory of Computing Systems. By invitation to special issue with extended papers from ICDT 2015 (paper arXiv:1412.4311

Matching Dependencies with Arbitrary Attribute Values: Semantics, Query Answering and Integrity Constraints

Matching dependencies (MDs) were introduced to specify the identification or matching of certain attribute values in pairs of database tuples when some similarity conditions are satisfied. Their enforcement can be seen as a natural generalization of entity resolution. In what we call the "pure case" of MDs, any value from the underlying data domain can be used for the value in common that does the matching. We investigate the semantics and properties of data cleaning through the enforcement of matching dependencies for the pure case. We characterize the intended clean instances and also the "clean answers" to queries as those that are invariant under the cleaning process. The complexity of computing clean instances and clean answers to queries is investigated. Tractable and intractable cases depending on the MDs and queries are identified. Finally, we establish connections with database "repairs" under integrity constraints.Comment: 13 pages, double column, 2 figure