The complexity of query evaluation in indefinite temporal constraint databases

We investigate the query evaluation problem for fixed queries over fully dynamic databases where tuples can be inserted or deleted. The task is to design a dynamic data structure that can immediately report the new result of a fixed query after every database update. We consider unions of conjunctive queries (UCQs) and focus on the query evaluation tasks testing (decide whether an input tuple belongs to the query result), enumeration (enumerate, without repetition, all tuples in the query result), and counting (output the number of tuples in the query result). We identify three increasingly restrictive classes of UCQs which we call t-hierarchical, q-hierarchical, and exhaustively q-hierarchical UCQs. Our main results provide the following dichotomies: If the query's homomorphic core is t-hierarchical (q-hierarchical, exhaustively q-hierarchical), then the testing (enumeration, counting) problem can be solved with constant update time and constant testing time (delay, counting time). Otherwise, it cannot be solved with sublinear update time and sublinear testing time (delay, counting time), unless the OV-conjecture and/or the OMv-conjecture fails. We also study the complexity of query evaluation in the dynamic setting in the presence of integrity constraints, and we obtain similar dichotomy results for the special case of small domain constraints (i.e., constraints which state that all values in a particular column of a relation belong to a fixed domain of constant size).

Election databases are the main elements of a recently introduced framework that aims to create bridges between the computational social choice and the data management communities. An election database consists of incomplete information about the preferences of voters, in the form of partial orders, alongside with standard database relations that provide contextual information. Earlier work in computational social choice focused on the computation of possible winners and necessary winners that are determined by the available incomplete information and the voting rule at hand. The presence of the relational context, however, permits the formulation of sophisticated queries about voting rules, candidates, potential winners, issues, and positions on issues. Such queries can be given possible answer semantics and necessary answer semantics on an election database, where the former means that the query is true on some completion of the given partial orders and the latter means that the query is true on every such completion. %In this paper, łooseness = -1 We carry out a systematic investigation of query evaluation on election databases by analyzing how the interaction between the partial preferences, the voting rules and the relational context impacts on the complexity of query evaluation. To this effect, we focus on positional scoring rules and unions of conjunctive queries. We establish a number of results that delineate the complexity of the possible answers and of the necessary answers for different positional scoring rules and for various classes of unions of conjunctive queries. Furthermore, we show that query evaluation is fixed-parameter tractable, where the parameter is the number of candidates in the election.

Preface: Volume 44, Issue 3

On specifying database updates

We present for the first-order theory of atomic Boolean algebras of sets with linear cardinality constraints a quantifier elimination algorithm. In the case of atomic Boolean algebras of sets, this is a new generalization of Boole’s well-known variable elimination method for conjunctions of Boolean equality constraints. We also explain the connection of this new logical result with the evaluation of relational calculus queries on constraint databases that contain Boolean linear cardinality constraints.KeywordsBoolean AlgebraQuery LanguageElimination MethodQuery EvaluationCardinality ConstraintThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The relational calculus (RC) is a concise, declarative query language. However, existing RC query evaluation approaches are inefficient and often deviate from established algorithms based on finite tables used in database management systems. We devise a new translation of an arbitrary RC query into two safe-range queries, for which the finiteness of the query's evaluation result is guaranteed. Assuming an infinite domain, the two queries have the following meaning: The first is closed and characterizes the original query's relative safety, i.e., whether given a fixed database, the original query evaluates to a finite relation. The second safe-range query is equivalent to the original query, if the latter is relatively safe. We compose our translation with other, more standard ones to ultimately obtain two SQL queries. This allows us to use standard database management systems to evaluate arbitrary RC queries. We show that our translation improves the time complexity over existing approaches, which we also empirically confirm in both realistic and synthetic experiments.

Relaxing the assumption that relations are always in First-Normal-Form (1NF) necessitates a reexamination of the fundamentals of relational database theory. In this paper we take a first step towards unifying the various theories of ¬1NF databases. We start by determining an appropriate model to couch our formalisms in. We then define an extended relational calculus as the theoretical basis for our ¬1NF database query language. We define a minimal extended relational algebra and prove its equivalence to the ¬1NF relational calculus. We define a class of ¬1NF relations with certain “good” properties and extend our algebra operators to work within this domain. We prove certain desirable equivalences that hold only if we restrict our language to this domain.

We develop a data integration approach for the efficient evaluation of queries over autonomous source databases. The approach is based on some novel applications and extensions of constraint database techniques. We assume the existence of a global database schema. The contents of each data source are described using a set of constraint tuples over the global schema; each such tuple indicates possible contributions from the source. The "source description catalog" (SDC) of a global relation consists of its associated constraint tuples. Such a method of description is advantageous since it is flexible to add new sources and to modify existing ones. In our framework, to evaluate a conjunctive query over the global schema, a plan generator first identifies relevant data sources by "evaluating" the query against the SDCs using techniques of constraint query evaluation; it then formulates an evaluation plan, consisting of some specialized queries over different paths. The evaluation of a query associated with a path is done by a sequence of partial evaluations at data sources along the path, similar to sideways information passing of Datalog; the partially evaluated queries travel along their associated paths. Our SDC based query planning is efficient since it avoids the NP-complete query rewriting process. We can achieve further optimization using techniques such as emptiness test.

Many different applications in different areas need to deal with both: databases, in order to take into account large amounts of structured data; and quantitative and qualitative temporal constraints about such data. We propose an approach that extends: temporal databases and artificial intelligence temporal reasoning techniques and integrate them in order to face such a need. Regarding temporal reasoning, we consider some results that we proved recently about efficient query answering in the Simple Temporal Problem framework and we extend them in order to deal with partitioned sets of constraints and to support relational database operations. Regarding databases, we extend the relational model in order to consider also qualitative and quantitative temporal constraints both in the data (data expressiveness) and in the queries (query expressiveness). We then propose a modular architecture integrating a relational database with a temporal reasoner. We also consider classes of applications that fit into our approach and consider patient management in a hospital as an example.

Structural joins, i.e., operations that determine all occurrences of parent/child or ancestor/descendant relationships between node sets, are at the heart of XML management systems. To perform these joins, the systems exploit the information about the nested relationships between elements, attributes, and pieces of text in XML documents. Since performing the structural joins is often the most time-consuming phase in query evaluation, the method chosen to model the nested relationships has a considerable impact on the overall effectiveness of any XML management system. In this paper, we discuss four different methods for modeling the nested relationships using relational databases. We also propose a novel modeling method and present the results of our comprehensive performance experiments.

We address the key issues of temporal data modeling and temporal integrity constraints in the temporal extensions to the relational data model in attribute and tuple time stamping. These issues include representation of temporal data, temporal grouping identifiers, primary keys of temporal relations and other forms of temporal integrity constraints. We extend the traditional integrity constraints to the temporal domain. In tackling subtle issues temporality creates, we conceptualize that a temporal integrity constraint has a data and a temporal (time) component. The time component of a temporal integrity constraint limits the attribute values to the lifespan of an object (tuple). We also generalize single state integrity constraints to multi-state temporal integrity constraints and apply them to existential and referential integrity. We provide algorithms for enforcing the two types of temporal integrity constraints.

The need for interoperation and data exchange through the Internet makes XML a dominant standard language. Much work has been done on translating relational data into XML documents and vice versa. However, there is not an integrated method to combine them together as one technology for mass information transmission on the Internet. Furthermore, most XML-enabled database management systems can only translate a few relations into an XML document without data semantics constraints consideration, which is not sufficient for information highway on the Web. This paper presents a methodology, XTOPO, to transmit a relational database on the Internet using XML document as medium. XTOPO facilitates the translation from relational database to XML document and vice versa. XTOPO divides an XML document hierarchical structure into four different topologies—single sub-element (element, sub-element), multiple sub-elements (element, multiple sub-elements), group (element, group of sub-elements), and referral element (element, element—and captures their semantics into classification tables as a knowledge-based repository. The view of a sender company’s information in a relational database is mapped into four topological XML documents according to their data semantics constraints. The intermediate XML documents are integrated into an XML document using DOM (Document Object Model). The XML document instances are loaded into a relational database with generated Object Identity as key. The receiver company translates the XML document back to relational database for processing. The result is a mechanism of mass information transmission on the Internet for an information highway.

Proximity relations in the fuzzy relational database model

An implementation-oriented model to represent uncertain temporal information in databases is proposed. Temporal information is presented to the user as anchored time intervals with optional beginning and end dates. The model accounts for both instants and intervals, and can be applied to uncertain dates by leaving days and months optional, or by using symbolic constraints that present additional time granularities. The model is defined using conventional relational database structures to support ease of deployment and integration to legacy systems with efficient query capabilities. The model is based on experiences with an existing museum database and highlights challenges related to temporal representation of cultural-historical data in practice. The model is compared with temporal representations used in other museum information systems and collections management standards. Possible opportunities to extend the model in the future research include defining a formal algebraic presentation or utilizing an explicit time ontology.

Indexing possibilistic numerical data using Interval B+-trees