Arbitrary Conjunctive Queries Research Articles

On the Complexity of Consistent Query Answering in the Presence of Simple Ontologies

Consistent query answering is a standard approach for producing meaningful query answers when data is inconsistent. Recent work on consistent query answering in the presence of ontologies has shown this problem to be intractable in data complexity even for ontologies expressed in lightweight description logics. In order to better understand the source of this intractability, we investigate the complexity of consistent query answering for simple ontologies consisting only of class subsumption and class disjointness axioms. We show that for conjunctive queries with at most one quantified variable, the problem is first-order expressible; for queries with at most two quantified variables, the problem has polynomial data complexity but may not be first-order expressible; and for three quantified variables, the problem may become co-NP-hard in data complexity. For queries having at most two quantified variables, we further identify a necessary and sufficient condition for first-order expressibility. In order to be able to handle arbitrary conjunctive queries, we propose a novel inconsistency-tolerant semantics and show that under this semantics, first-order expressibility is always guaranteed. We conclude by extending our positive results to DL-Lite ontologies without inverse.

Aggregated deletion propagation for counting conjunctive query answers

We investigate the computational complexity of minimizing the source side-effect in order to remove a given number of tuples from the output of a conjunctive query. This is a variant of the well-studied deletion propagation problem, the difference being that we are interested in removing the smallest subset of input tuples to remove a given number of output tuples while deletion propagation focuses on removing a specific output tuple. We call this the Aggregated Deletion Propagation problem. We completely characterize the poly-time solvability of this problem for arbitrary conjunctive queries without self-joins. This includes a poly-time algorithm to decide solvability, as well as an exact structural characterization of NP-hard instances. We also provide a practical algorithm for this problem (a heuristic for NP-hard instances) and evaluate its experimental performance on real and synthetic datasets.

CRSQ-KASE: Key Aggregate Searchable Encryption Supporting Conjunctive Range and Sort Query on Multi-owner Encrypted Data

The existing key aggregate searchable encryption (KASE) schemes allow searches on the encrypted dataset using a single query trapdoor, with a feature to delegate the search rights of multiple files using a constant-size key. However, the limitation of the existing KASE schemes is they only support the exact keyword match $$ (Keyword = Value)$$ search query for a single query keyword. In addition, to perform a conjunctive keyword search using the existing KASE schemes, the user requires to submit different trapdoors for each individual keyword to the server. Considering the existence of numeric keywords, the KASE should support different types of query such as range query$$ (Value_1 \le Keyword \le Value_2) $$, comparison query($$ (Keyword \ge Value)$$ or $$ (Keyword \le Value)$$), and sort query. Therefore, a novel KASE scheme is proposed in this paper that supports the conjunctive range and sort query (i.e., CRSQ-KASE) on the encrypted dataset and enhances the query expressiveness of the existing KASE schemes. The proposed CRSQ-KASE scheme supports search among different keyword fields considering both numeric and non-numeric keywords. The user can search over shared encrypted dataset by giving arbitrary conjunctive queries $$ (Keyword_1 = Value_1\wedge Keyword_2 \le Value_2 \wedge \cdots \wedge Value_{n_1} \le Keyword_n \le Value_{n_2}) $$ using a single trapdoor. Furthermore, in the multi-owner setting, the user can search over multiple users’ documents set using a single query trapdoor. The theoretical, empirical, and security analyses show that the proposed CRSQ-KASE scheme performs better than the existing KASE schemes. To the best of our knowledge, the CRSQ-KASE is the first attempt that efficiently supports multi-dimensional, conjunctive keyword searches on the multi-owner encrypted dataset and gives the sorted search result.

Any-k Algorithms for Exploratory Analysis with Conjunctive Queries.

We recently proposed the notion of any-k queries, together with the KARPET algorithm, for tree-pattern search in labeled graphs. Any-k extends top-k by not requiring a pre-specified value of k. Instead, an any-k algorithm returns as many of the top-ranked results as possible, for a given time budget. Given additional time, it produces the next-highest ranked results quickly as well. It can be stopped anytime, but may have to continue until all results are returned. In the latter case, any-k takes times similar to an algorithm that first produces all results and then sorts them. We summarize KARPET and argue that it can be extended to support any-k exploratory search for arbitrary conjunctive queries.

View selection for real conjunctive queries

Given a query workload, a database and a set of constraints, the view-selection problem is to select views to materialize so that the constraints are satisfied and the views can be used to compute the queries in the workload efficiently. A typical constraint, which we consider in the present work, is to require that the views can be stored in a given amount of disk space. Depending on features of SQL queries (e.g., the DISTINCT keyword) and on whether the database relations on which the queries are applied are sets or bags, the queries may be computed under set semantics, bag-set semantics, or bag semantics. In this paper we study the complexity of the view-selection problem for conjunctive queries and views under these semantics. We show that bag semantics is the “easiest to handle” (we show that in this case the decision version of view selection is in NP), whereas under set and bag-set semantics we assume further restrictions on the query workload (we only allow queries without self-joins in the workload) to achieve the same complexity. Moreover, while under bag and bag-set semantics filtering views (i.e., subgoals that can be dropped from the rewriting without impacting equivalence to the query) are practically not needed, under set semantics filtering views can reduce significantly the query-evaluation costs. We show that under set semantics the decision version of the view-selection problem remains in NP only if filtering views are not allowed in the rewritings. Finally, we investigate whether the cgalg algorithm for view selection introduced in Chirkova and Genesereth (Linearly bounded reformulations of conjunctive databases, pp. 987–1001, 2000) is suitable in our setting. We prove that this algorithm is sound for all cases we examine here, and that it is complete under bag semantics for workloads of arbitrary conjunctive queries and under bag-set semantics for workloads of conjunctive queries without self-joins.

Implementation of a Prolog-INGRES interface

This report describes a working prototype of a Prolog-INGRES interface based on external semantic query simplification. Semantic query simplification employs integrity constraints enforced in a database system for reducing the number of tuple variables and terms in a relational query. This type of query simplifier is useful in providing very high level user interfaces to existing database systems. The system employes a graph theoretic approach to simplify arbitrary conjunctive queries with inequalities. One very interesting feature of the system is to provide meaningful error messages in case of an empty query result resulting from contradiction. In addition to data, rules are stored in the database as well and are retrieved automatically if the Prolog program references them but they are not defined in the Prolog rulebase.