Threshold queries are an important class of queries that only require computing or counting answers up to a specified threshold value. To the best of our knowledge, threshold queries have been largely disregarded in the research literature, which is surprising considering how common they are in practice. In this paper, we present a deep theoretical analysis of threshold query evaluation and show that thresholds can be used to significantly improve the asymptotic bounds of state-of-the-art query evaluation algorithms. We also empirically show that threshold queries are significant in practice. In surprising contrast to conventional wisdom, we found important scenarios in real-world data sets in which users are interested in computing the results of queries up to a certain threshold, independent of a ranking function that orders the query results.

We investigate graph transformations, defined using Datalog-like rules based on acyclic conjunctive two-way regular path queries (acyclic C2RPQs), and we study two fundamental static analysis problems: type checking and equivalence of transformations in the presence of graph schemas. Additionally, we investigate the problem of target schema elicitation, which aims to construct a schema that closely captures all outputs of a transformation over graphs conforming to the input schema. We show all these problems are in EXPTIME by reducing them to C2RPQ containment modulo schema; we also provide matching lower bounds. We use cycle reversing to reduce query containment to the problem of unrestricted (finite or infinite) satisfiability of C2RPQs modulo a theory expressed in a description logic.

Property graphs have reached a high level of maturity, witnessed by multiple robust graph database systems as well as the ongoing ISO standardization effort aiming at creating a new standard Graph Query Language (GQL). Yet, despite documented demand, schema support is limited both in existing systems and in the first version of the GQL Standard. It is anticipated that the second version of the GQL Standard will include a rich DDL. Aiming to inspire the development of GQL and enhance the capabilities of graph database systems, we propose PG-Schema, a simple yet powerful formalism for specifying property graph schemas. It features PG-Schema with flexible type definitions supporting multi-inheritance, as well as expressive constraints based on the recently proposed PG-Keys formalism. We provide the formal syntax and semantics of PG-Schema, which meet principled design requirements grounded in contemporary property graph management scenarios, and offer a detailed comparison of its features with those of existing schema languages and graph database systems.

We investigate the problem of constructing a shape graph that describes the structure of a given graph database. We employ the framework of grammatical inference, where the objective is to find an inference algorithm that is both sound, i.e., always producing a schema that validates the input graph, and complete, i.e., able to produce any schema, within a given class of schemas, provided that a sufficiently informative input graph is presented. We identify a number of fundamental limitations that preclude feasible inference. We present inference algorithms based on natural approaches that allow to infer schemas that we argue to be of practical importance.

Threshold queries are an important class of queries that only require computing or counting answers up to a specified threshold value. To the best of our knowledge, threshold queries have been largely disregarded in the research literature, which is surprising considering how common they are in practice. In this paper, we present a deep theoretical analysis of threshold query evaluation and show that thresholds can be used to significantly improve the asymptotic bounds of state-of-the-art query evaluation algorithms. We also empirically show that threshold queries are significant in practice. In surprising contrast to conventional wisdom, we found important scenarios in real-world data sets in which users are interested in computing the results of queries up to a certain threshold, independent of a ranking function that orders the query results.

We report on a community effort between industry and academia to shape the future of property graph constraints. The standardization for a property graph query language is currently underway through the ISO Graph Query Language (GQL) project. Our position is that this project should pay close attention to schemas and constraints, and should focus next on key constraints. The main purposes of keys are enforcing data integrity and allowing the referencing and identifying of objects. Motivated by use cases from our industry partners, we argue that key constraints should be able to have different modes, which are combinations of basic restriction that require the key to be exclusive, mandatory, and singleton. Moreover, keys should be applicable to nodes, edges, and properties since these all can represent valid real-life entities. Our result is PG-Keys, a flexible and powerful framework for defining key constraints, which fulfills the above goals. PG-Keys is a design by the Linked Data Benchmark Council's Property Graph Schema Working Group, consisting of members from industry, academia, and ISO GQL standards group, intending to bring the best of all worlds to property graph practitioners. PG-Keys aims to guide the evolution of the standardization efforts towards making systems more useful, powerful, and expressive.

We study the problem of containment of shape expression schemas ShEx for RDF graphs. We identify a subclass of ShEx that has a natural graphical representation in the form of shape graphs and whose semantics is captured with a tractable notion of embedding of an RDF graph in a shape graph. When applied to pairs of shape graphs, an embedding is a sufficient condition for containment, and for a practical subclass of deterministic shape graphs, it is also a necessary one, thus yielding a subclass with tractable containment. Containment for general shape graphs is EXP-complete. Finally, we show that containment for arbitrary ShEx is decidable.

We investigate the problem of aligning two RDF databases, an essential problem in understanding the evolution of ontologies. Our approaches address three fundamental challenges: 1) the use of "blank" (null) names, 2) ontology changes in which different names are used to identify the same entity, and 3) small changes in the data values as well as small changes in the graph structure of the RDF database. We propose approaches inspired by the classical notion of graph bisimulation and extend them to capture the natural metrics of edit distance on the data values and the graph structure. We evaluate our methods on three evolving curated data sets. Overall, our results show that the proposed methods perform well and are scalable.

We investigate the problem of learning join queries from user examples. The user is presented with a set of candidate tuples and is asked to label them as positive or negative examples, depending on whether or not she would like the tuples as part of the join result. The goal is to quickly infer an arbitrary n -ary join predicate across an arbitrary number m of relations while keeping the number of user interactions as minimal as possible. We assume no prior knowledge of the integrity constraints across the involved relations. Inferring the join predicate across multiple relations when the referential constraints are unknown may occur in several applications, such as data integration, reverse engineering of database queries, and schema inference. In such scenarios, the number of tuples involved in the join is typically large. We introduce a set of strategies that let us inspect the search space and aggressively prune what we call uninformative tuples, and we directly present to the user the informative ones—that is, those that allow the user to quickly find the goal query she has in mind. In this article, we focus on the inference of joins with equality predicates and also allow disjunctive join predicates and projection in the queries. We precisely characterize the frontier between tractability and intractability for the following problems of interest in these settings: consistency checking, learnability, and deciding the informativeness of a tuple. Next, we propose several strategies for presenting tuples to the user in a given order that allows minimization of the number of interactions. We show the efficiency of our approach through an experimental study on both benchmark and synthetic datasets.

We study the problem of bounded repairability of a given restriction tree language R into a target tree language T . More precisely, we say that R is bounded repairable with respect to T if there exists a bound on the number of standard tree editing operations necessary to apply to any tree in R to obtain a tree in T . We consider a number of possible specifications for tree languages: bottom-up tree automata (on curry encoding of unranked trees) that capture the class of XML schemas and document type definitions (DTDs). We also consider a special case when the restriction language R is universal (i.e., contains all trees over a given alphabet). We give an effective characterization of bounded repairability between pairs of tree languages represented with automata. This characterization introduces two tools—synopsis trees and a coverage relation between them—allowing one to reason about tree languages that undergo a bounded number of editing operations. We then employ this characterization to provide upper bounds to the complexity of deciding bounded repairability and show that these bounds are tight. In particular, when the input tree languages are specified with arbitrary bottom-up automata, the problem is coNExp-complete. The problem remains coNExp-complete even if we use deterministic nonrecursive DTDs to specify the input languages. The complexity of the problem can be reduced if we assume that the alphabet, the set of node labels, is fixed: the problem becomes PS pace -complete for nonrecursive DTDs and coNP-complete for deterministic nonrecursive DTDs. Finally, when the restriction tree language R is universal, we show that the bounded repairability problem becomes E xp -complete if the target language is specified by an arbitrary bottom-up tree automaton and becomes tractable (P-complete, in fact) when a deterministic bottom-up automaton is used.

Graph data abstractions are often assumed to be intuitive, but experience shows that they are not equally understandable or usable in practice. In this vision and challenges paper, we examine the human-centricity of contemporary graph data abstractions through four lenses: researchability, usability, teachability, and societal impact. Drawing on diverse real-world use cases, ranging from clinical data and collaborative knowledge bases to biological and pangenomic graphs, we distill insights from database research, human-computer interaction, and education. Based on this analysis, we identify open research challenges that must be addressed to make graph abstractions easier to study, use, learn, and reason about.

Typically, a (Boolean) query is a finite formula that defines a possibly infinite set of database instances that satisfy it (positive examples), and implicitly, the set of instances that do not satisfy the query (negative examples). We investigate the following natural question: for a given class of queries, is it possible to characterize every query with a finite set of positive and negative examples that no other query is consistent with. We study this question for twig queries and XML databases. We show that while twig queries are characterizable, they generally require exponential sets of examples. Consequently, we focus on a practical subclass of anchored twig queries and show that not only are they characterizable but also with polynomially-sized sets of examples. This result is obtained with the use of generalization operations on twig queries, whose application to an anchored twig query yields a properly contained and minimally different query. Our results illustrate further interesting and strong connections between the structure and the semantics of anchored twig queries that the class of arbitrary twig queries does not enjoy. Finally, we show that the class of unions of twig queries is not characterizable.

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Specifying join predicates may become a cumbersome task in many situations e.g., when the relations to be joined come from disparate data sources, when the values of the attributes carry little or no knowledge of metadata, or simply when the user is unfamiliar with querying formalisms. Such task is recurrent in many traditional data management applications, such as data integration, constraint inference, and database denormalization, but it is also becoming pivotal in novel crowdsourcing applications. We present Jim (Join Inference Machine), a system for interactive join specification tasks, where the user infers an n -ary join predicate by selecting tuples that are part of the join result via Boolean membership queries. The user can label tuples as positive or negative, while the system allows to identify and gray out the uninformative tuples i.e., those that do not add any information to the final learning goal. The tool also guides the user to reach her join inference goal with a minimal number of interactions.

We consider the problem of repairing unranked trees (e.g., XML documents) satisfying a given restriction specification R (e.g., a DTD) into unranked trees satisfying a given target specification T. Specifically, we focus on the question of whether one can get from any tree in a regular language R to some tree in another regular language T with a finite, uniformly bounded, number of edit operations (i.e., deletions and insertions of nodes). We give effective characterizations of the pairs of specifications R and T for which such a uniform bound exists, and we study the complexity of the problem under different representations of the regular tree languages (e.g., non-deterministic stepwise automata, deterministic stepwise automata, DTDs). Finally, we point out some connections with the analogous problem for regular languages of words, which was previously studied in [6].

We investigate the problem of learning XML queries, path queries and twig queries, from examples given by the user. A learning algorithm takes on the input a set of XML documents with nodes annotated by the user and returns a query that selects the nodes in a manner consistent with the annotation. We study two learning settings that differ with the types of annotations. In the first setting the user may only indicate required nodes that the query must select (i.e., positive examples). In the second, more general, setting, the user may also indicate forbidden nodes that the query must not select (i.e., negative examples). The query may or may not select any node with no annotation.

Deterministic regular expressions are widely used in XML processing. For instance, all regular expressions in DTDs and XML Schemas are required to be deterministic. In this paper we show that determinism of a regular expression e can be tested in linear time. The best known algorithms, based on the Glushkov automaton, require O(σ|e|) time, where σ is the number of distinct symbols in e. We further show that matching a word w against an expression e can be achieved in combined linear time O(|e|+|w|), for a wide range of deterministic regular expressions: (i) star-free (for multiple input words), (ii) bounded-occurrence, i.e., expressions in which each symbol appears a bounded number of times, and (iii) bounded plus-depth, i.e., expressions in which the nesting depth of alternating plus (union) and concatenation symbols is bounded. Our algorithms use a new structural decomposition of the parse tree of e. For matching arbitrary deterministic regular expressions we present an O(|e| + |w|log log|e|) time algorithm.

We study the problem of update translation for views on XML documents. More precisely, given an XML view definition and a user defined view update program, find a source update program that translates the view update without side effects on the view. Additionally, we require the translation to be defined on all possible source documents; this corresponds to Hegner's notion of uniform translation. The existence of such translation would allow to update XML views without the need of materialization.

A consistent query answer in a possibly inconsistent database is an answer which is true in every (minimal) repair of the database. We present here a practical framework for computing consistent query answers for large, possibly inconsistent relational databases. We consider relational algebra queries without projection, and denial constraints. Because our framework handles union queries, we can effectively (and efficiently) extract indefinite disjunctive information from an inconsistent database. We describe a number of novel optimization techniques applicable in this context and summarize experimental results that validate our approach.