Conjunctive Queries Research Articles

Computing A Well-Representative Summary of Conjunctive Query Results

Computing A Well-Representative Summary of Conjunctive Query Results

Output-sensitive Conjunctive Query Evaluation

Output-sensitive Conjunctive Query Evaluation

Complex Event Recognition meets Hierarchical Conjunctive Queries

Complex Event Recognition meets Hierarchical Conjunctive Queries

Languages Generated by Conjunctive Query Fragments of FC[REG

Abstract$${\textsf{FC}}$$ FC is a finite model variant on the theory of concatenation, $${\textsf{FC}[\textsf{REG}]}$$ FC [ REG ] extends $${\textsf{FC}}$$ FC with regular constraints. This paper considers the languages generated by their conjunctive query fragments, and . We compare the expressive power of $${\textsf {FC[REG]-CQ}}$$ FC [ REG ] - CQ to that of various related language generators, such as regular expressions, patterns, and typed patterns. We then consider decision problems for $${\textsf {FC-CQ}}$$ FC - CQ and $${\textsf {FC[REG]-CQ}}$$ FC [ REG ] - CQ , and show that certain static analysis problems (such as equivalence and regularity) are undecidable. While this paper defines $${\textsf {FC-CQ}}$$ FC - CQ based on the logic $${\textsf{FC}}$$ FC , it can equally be understood as synchronized intersections of pattern languages, or as systems of restricted word equations.

Approximately Counting Answers to Conjunctive Queries with Disequalities and Negations

Approximately Counting Answers to Conjunctive Queries with Disequalities and Negations

Tractable Circuits in Database Theory

This work reviews how database theory uses tractable circuit classes from knowledge compilation. We present relevant query evaluation tasks, and notions of tractable circuits. We then show how these tractable circuits can be used to address database tasks. We first focus on Boolean provenance and its applications for aggregation tasks, in particular probabilistic query evaluation. We study these for Monadic Second Order (MSO) queries on trees, and for safe Conjunctive Queries (CQs) and Union of Conjunctive Queries (UCQs). We also study circuit representations of query answers, and their applications to enumeration tasks: both in the Boolean setting (for MSO) and the multivalued setting (for CQs and UCQs).

Controlled query evaluation in description logics through consistent query answering

Controlled Query Evaluation (CQE) is a framework for the protection of confidential data, where a policy given in terms of logic formulae indicates which information must be kept private. Functions called censors filter query answering so that no answers are returned that may lead a user to infer data protected by the policy. The preferred censors, called optimal censors, are the ones that conceal only what is necessary, thus maximizing the returned answers. Typically, given a policy over a data or knowledge base, several optimal censors exist.Our research on CQE is based on the following intuition: confidential data are those that violate the logical assertions specifying the policy, and thus censoring them in query answering is similar to processing queries in the presence of inconsistent data as studied in Consistent Query Answering (CQA). In this paper, we investigate the relationship between CQE and CQA in the context of Description Logic ontologies. We borrow the idea from CQA that query answering is a form of skeptical reasoning that takes into account all possible optimal censors. This approach leads to a revised notion of CQE, which allows us to avoid making an arbitrary choice on the censor to be selected, as done by previous research on the topic.We then study the data complexity of query answering in our CQE framework, for conjunctive queries issued over ontologies specified in the popular Description Logics DL-LiteR and EL⊥. In our analysis, we consider some variants of the censor language, which is the language used by the censor to enforce the policy. Whereas the problem is in general intractable for simple censor languages, we show that for DL-LiteR ontologies it is first-order rewritable, and thus in AC0 in data complexity, for the most expressive censor language we propose.

Relational Algorithms for Top-k Query Evaluation

The evaluation of top-k conjunctive queries, a staple in business analysis, often requires evaluating the conjunctive query prior to filtering the top-k results, leading to a significant computational overhead within Database Management Systems (DBMSs). While efficient algorithms have been proposed, their integration into DBMSs remains arduous. We introduce relational algorithms, a paradigm where each algorithmic step is expressed by a relational operator. This allows the algorithm to be represented as a set of SQL queries, enabling easy deployment across different systems that support SQL. We introduce two novel relational algorithms, level-k and product-k, specifically designed for evaluating top-k conjunctive queries and demonstrate that level-k achieves optimal running time for top-k free-connex queries. Furthermore, these algorithms enable easy translation into an oblivious algorithm for secure query evaluations. The presented algorithms are not only theoretically optimal but also exhibit eminent efficiency in practice. The experiment results show significant improvements, with our rewritten SQL outperforming the baseline by up to 6 orders of magnitude. Moreover, our secure implementations not only achieve substantial speedup compared to the baseline with secure guarantees but even surpass those baselines that have no secure guarantees.

The Weisfeiler-Leman Dimension of Conjunctive Queries

A graph parameter is a function f on graphs with the property that, for any pair of isomorphic graphs G 1 and G 2 , f(G 1 )=f(G 2 ). The Weisfeiler--Leman (WL) dimension of f is the minimum k such that, if G 1 and G 2 are indistinguishable by the k-dimensional WL-algorithm then f(G 1 )=f(G 2 ). The WL-dimension of f is ∞ if no such k exists. We study the WL-dimension of graph parameters characterised by the number of answers from a fixed conjunctive query to the graph. Given a conjunctive query φ, we quantify the WL-dimension of the function that maps every graph G to the number of answers of φ in G. The works of Dvorak (J. Graph Theory 2010), Dell, Grohe, and Rattan (ICALP 2018), and Neuen (ArXiv 2023) have answered this question for full conjunctive queries, which are conjunctive queries without existentially quantified variables. For such queries φ, the WL-dimension is equal to the treewidth of the Gaifman graph of φ. In this work, we give a characterisation that applies to all conjunctive queries. Given any conjunctive query φ, we prove that its WL-dimension is equal to the semantic extension width sew(φ), a novel width measure that can be thought of as a combination of the treewidth of φ and its quantified star size, an invariant introduced by Durand and Mengel (ICDT 2013) describing how the existentially quantified variables of φ are connected with the free variables. Using the recently established equivalence between the WL-algorithm and higher-order Graph Neural Networks (GNNs) due to Morris et al. (AAAI 2019), we obtain as a consequence that the function counting answers to a conjunctive query φ cannot be computed by GNNs of order smaller than sew(φ). The majority of the paper is concerned with establishing a lower bound of the WL-dimension of a query. Given any conjunctive query φ with semantic extension width k, we consider a graph F of treewidth k obtained from the Gaifman graph of φ by repeatedly cloning the vertices corresponding to existentially quantified variables. Using a modification due to Furer (ICALP 2001) of the Cai-Fürer-Immerman construction (Combinatorica 1992), we then obtain a pair of graphs χ(F) and ^χ(F) that are indistinguishable by the (k-1)-dimensional WL-algorithm since F has treewidth k. Finally, in the technical heart of the paper, we show that φ has a different number of answers in χ(F) and ^χ(F). Thus, φ can distinguish two graphs that cannot be distinguished by the (k-1)-dimensional WL-algorithm, so the WL-dimension of φ is at least k.

Counting Answers to Unions of Conjunctive Queries: Natural Tractability Criteria and Meta-Complexity

We study the problem of counting answers to unions of conjunctive queries (UCQs) under structural restrictions on the input query. Concretely, given a class C of UCQs, the problem #UCQ (C) provides as input a UCQ Ψ ∈ C and a database D and the problem is to compute the number of answers of Ψ in D. Chen and Mengel [PODS'16] have shown that for any recursively enumerable class C, the problem #UCQ (C) is either fixed-parameter tractable or hard for one of the parameterised complexity classes W[1] or #W[1]. However, their tractability criterion is unwieldy in the sense that, given any concrete class C of UCQs, it is not easy to determine how hard it is to count answers to queries in C. Moreover, given a single specific UCQ Ψ, it is not easy to determine how hard it is to count answers to Ψ. In this work, we address the question of finding a natural tractability criterion: The combined conjunctive query of a UCQ Ψ=φ 1 ∨ ... ∨ φ l is the conjunctive query ^ Ψ = φ_1 ∧ ... ∧ φ l . We show that under natural closure properties of C, the problem #UCQ (C) is fixed-parameter tractable if and only if the combined conjunctive queries of UCQs in C, and their contracts, have bounded treewidth. A contract of a conjunctive query is an augmented structure, taking into account how the quantified variables are connected to the free variables --- if all variables are free, then a conjunctive query is equal to its contract; in this special case the criterion for fixed-parameter tractability of #UCQ (C) thus simplifies to the combined queries having bounded treewidth. Finally, we give evidence that a closure property on C is necessary for obtaining a natural tractability criterion: We show that even for a single UCQ Ψ, the meta problem of deciding whether #UCQ (Ψ) can be solved in time O(|D| d ) is NP-hard for any fixed d ≥ 1. Moreover, we prove that a known exponential-time algorithm for solving the meta problem is optimal under assumptions from fine-grained complexity theory. As a corollary of our reduction, we also establish that approximating the Weisfeiler-Leman-Dimension of a UCQ is NP-hard.

Conjunctive Queries with Negation and Aggregation: A Linear Time Characterization

In this paper, we study the complexity of evaluating Conjunctive Queries with negation (\cqneg). First, we present an algorithm with linear preprocessing time and constant delay enumeration for a class of CQs with negation called free-connex signed-acyclic queries. We show that no other queries admit such an algorithm subject to lower-bound conjectures. Second, we extend our algorithm to Conjunctive Queries with negation and aggregation over a general semiring, which we call Functional Aggregate Queries with negation (\faqneg). Such an algorithm achieves constant delay enumeration for the same class of queries but with a slightly increased preprocessing time, which includes an inverse Ackermann function. We show that this surprising appearance of the Ackermmann function is probably unavoidable for general semirings but can be removed when the semiring has a specific structure. Finally, we show an application of our results to computing the difference of CQs.

Bag Semantics Conjunctive Query Containment. Four Small Steps Towards Undecidability.

Query Containment Problem (QCP) is one of the most fundamental decision problems in database query processing and optimization. Complexity of QCP for conjunctive queries has been fully understood since 1970s. But, as Chaudhuri and Vardi noticed in their classical 1993 paper this understanding is based on the assumption that query answers are sets of tuples, and it does not transfer to the situation when multi-set (bag) semantics is considered. Now, 30 years later, decidability of QCP for bag semantics remains an open question, one of the most intriguing open questions in database theory. In this paper we show a series of undecidability results for some generalizations of this problem. We show, for example, that the problem whether, for given two boolean conjunctive queries φ s and φ b , and a linear function F, the inequality F(φ s (D)) =< φ b (D) holds for each database instance D, is undecidable.

Combined Approximations for Uniform Operational Consistent Query Answering

Operational consistent query answering (CQA) is a recent framework for CQA based on revised definitions of repairs, which are built by applying a sequence of operations (e.g., fact deletions) starting from an inconsistent database until we reach a database that is consistent w.r.t. the given set of constraints. It has been recently shown that there is an efficient approximation for computing the percentage of repairs that entail a given query when we focus on primary keys, conjunctive queries, and assuming the query is fixed (i.e., in data complexity). However, it has been left open whether such an approximation exists when the query is part of the input (i.e., in combined complexity). We show that this is the case when we focus on self-join-free conjunctive queries of bounded generelized hypertreewidth. We also show that it is unlikely that efficient approximation schemes exist once we give up one of the adopted syntactic restrictions, i.e., self-join-freeness or bounding the generelized hypertreewidth. Towards the desired approximation, we introduce a counting complexity class, called SpanTL, show that each problem in it admits an efficient approximation scheme by using a recent approximability result about tree automata, and then place the problem of interest in SpanTL.

Minimally Factorizing the Provenance of Self-join Free Conjunctive Queries

We consider the problem of finding the minimal-size factorization of the provenance of self-join-free conjunctive queries, i.e.,we want to find a formula that minimizes the number of variable repetitions. This problem is equivalent to solving the fundamental Boolean formula factorization problem for the restricted setting of the provenance formulas of self-join free queries. While general Boolean formula minimization is Σ p 2 -complete, we show that the problem is NP-Complete in our case. Additionally, we identify a large class of queries that can be solved in PTIME, expanding beyond the previously known tractable cases of read-once formulas and hierarchical queries. We describe connections between factorizations, Variable Elimination Orders (VEOs), and minimal query plans. We leverage these insights to create an Integer Linear Program (ILP) that can solve the minimal factorization problem exactly. We also propose a Max-Flow Min-Cut (MFMC) based algorithm that gives an efficient approximate solution. Importantly, we show that both the Linear Programming (LP) relaxation of our ILP, and our MFMC-based algorithm are always correct for all currently known PTIME cases. Thus, we present two unified algorithms (ILP and MFMC) that can both recover all known PTIME cases in PTIME, yet also solve NP-Complete cases either exactly (ILP) or approximately (MFMC), as desired.

Thorough Data Pruning for Join Query in Database System

The improvement of robustness and efficiency for multi-way equijoin query is challenging, no-matter for centralized database systems or distributed database systems. Due to lots of unnecessary data existing during query processing, these two metrics will be seriously reduced. If we can thoroughly prune unnecessary data in advance, the robustness and efficiency will be highly improved. However, the pruning power of current strategies, such as predicate push-down and algebraic equivalence, is limited. We present deepDP, a powerful, generalized, and efficient strategy for data pruning. deepDP builds multiple independent pruning spaces by generating longest transitive closures and applies appropriate data pruning strategy for each pruning space. For thoroughly pruning unnecessary data, deepDP employs <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha \cdot \beta$</tex-math></inline-formula> pruning strategy to clean each pruning space based on a newly designed statistic information-Hollow Range and re-shuffles the elements in all pruned spaces for maximizing robustness and efficiency benefits meanwhile minimizing the invasion. We implement deepDP in PostgreSQL but are not limited to it, and evaluate deepDP on TPC-H, JOB, and our synthesis benchmark–DHR. The experiment results show that compared to traditional data pruning strategy, deepDP can improve multi-way equijoin query on efficiency by 3.5x.

A Gentle Introduction to Controlled Query Evaluation in DL-Lite Ontologies

Controlled query evaluation (CQE) is an approach for confidentiality-preserving query answering where a function called censor alters query answers so that users can never infer data that are protected by a policy given in terms of logic formulae. In this paper, we review some foundational results we have recently found in the context of CQE over Description Logic ontologies. In more detail, we discuss the main characteristics of two notions of censor, CQ censor and GA censor, focusing on the computational complexity of query answering and on the notion of indistinguishability. The latter is a desirable property imposing that a censor always makes a user believe that the underlying data instance might not contain confidential data. As for computational aspects, we characterize the data complexity of answering conjunctive queries for the relevant and practical case of DL-LiteR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {DL-Lite} _{{\\mathcal {R}}}$$\\end{document} ontologies. Since neither CQ censors nor GA censors enjoy both indistinguishability and tractability of query answering in the analyzed setting, we finally recall the notion of IGA censors, a sound approximation of GA censors which instead enjoys both properties, thus paving the way for robust and practical CQE for DL-LiteR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {DL-Lite} _{{\\mathcal {R}}}$$\\end{document} ontologies.

Cardinality Estimation over Knowledge Graphs with Embeddings and Graph Neural Networks

Cardinality Estimation over Knowledge Graphs (KG) is crucial for query optimization, yet remains a challenging task due to the semi-structured nature and complex correlations of data in typical KGs. In this work, we propose GNCE, a novel approach that leverages knowledge graph embeddings and Graph Neural Networks (GNN) to accurately predict the cardinality of conjunctive queries over KGs. GNCE first creates semantically meaningful embeddings for all entities in the KG, which are then used to learn a representation of a query using a GNN to estimate the cardinality of the query. We evaluate GNCE on several KGs in terms of q-Error and demonstrate that it outperforms state-of-the-art approaches based on sampling, summaries, and (machine) learning in terms of estimation accuracy while also having a low execution time and few parameters. Additionally, we show that GNCE performs similarly well on real-world queries and can inductively generalize to unseen entities, making it suitable for use in dynamic query processing scenarios. Our proposed approach has the potential to significantly improve query optimization and related applications that rely on accurate cardinality estimates of conjunctive queries.

Forward Private Verifiable Dynamic Searchable Symmetric Encryption With Efficient Conjunctive Query

Forward Private Verifiable Dynamic Searchable Symmetric Encryption With Efficient Conjunctive Query

Linear Programs with Conjunctive Database Queries

In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions depend on the answer sets of conjunctive queries. We contribute an efficient algorithm for solving programs in a fragment of LP(CQ). The natural approach constructs a linear program having as many variables as there are elements in the answer set of the queries. Our approach constructs a linear program having the same optimal value but fewer variables. This is done by exploiting the structure of the conjunctive queries using generalized hypertree decompositions of small width to factorize elements of the answer set together. We illustrate the various applications of LP(CQ) programs on three examples: optimizing deliveries of resources, minimizing noise for differential privacy, and computing the s-measure of patterns in graphs as needed for data mining.

Conjunctive query answering over unrestricted OWL 2 ontologies

Conjunctive Query (CQ) answering is a primary reasoning task over knowledge bases. However, when considering expressive description logics, query answering can be computationally very expensive; reasoners for CQ answering, although heavily optimized, often sacrifice expressive power of the input ontology or completeness of the computed answers in order to achieve tractability and scalability for the problem. In this work, we present a hybrid query answering architecture that combines various services to provide a CQ answering service for OWL. Specifically, it combines scalable CQ answering services for tractable languages with a CQ answering service for a more expressive language approaching the full OWL 2. If the query can be fully answered by one of the tractable services, then that service is used, to ensure maximum performance. Otherwise, the tractable services are used to compute lower and upper bound approximations. The union of the lower bounds and the intersection of the upper bounds are then compared. If the bounds do not coincide, then the “gap” answers are checked using the “full” service. These techniques led to the development of two new systems: (i) RSAComb, an efficient implementation of a new tractable answering service for RSA (role safety acyclic) (ii) ACQuA, a reference implementation of the proposed hybrid architecture combining RSAComb, PAGOdA, and HermiT to provide a CQ answering service for OWL. Our extensive evaluation shows how the additional computational cost introduced by reasoning over a more expressive language like RSA can still provide a significant improvement compared to relying on a fully-fledged reasoner. Additionally, we show how ACQuA can reliably match the performance of PAGOdA, a state-of-the-art CQ answering system that uses a similar approach, and can significantly improve performance when PAGOdA extensively relies on the underlying fully-fledged reasoner.