Solving the SPARQL query containment problem with SpeCS

The query containment problem is a fundamental algorithmic problem in data management. While this problem is well understood under set semantics, it is by far less understood under bag semantics. In particular, it is a long-standing open question whether or not the conjunctive query containment problem under bag semantics is decidable. We unveil tight connections between information theory and the conjunctive query containment under bag semantics. These connections are established using information inequalities, which are considered to be the laws of information theory. Our first main result asserts that deciding the validity of a generalization of information inequalities is many-one equivalent to the restricted case of conjunctive query containment in which the containing query is acyclic; thus, either both these problems are decidable or both are undecidable. Our second main result identifies a new decidable case of the conjunctive query containment problem under bag semantics. Specifically, we give an exponential-time algorithm for conjunctive query containment under bag semantics, provided the containing query is chordal and admits a simple junction tree.

Query containment is one of the building block of query optimization techniques. In the relational world, query containment is a well-studied problem. At the same time it is well-understood that relational queries are not enough to cope with graph-structured data, where one is interested in expressing queries that capture navigation in the graph. This paper contributes a study on the problem of query containment for an expressive class of navigational queries called Extended Property Paths (EPPs). EPPs are more expressive than previous navigational extension of SPARQL (e.g., nested regular expressions) as they allow to express path conjunction and path negation, among others. We attack the problem of EPPs containment and provide complexity bounds.

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.

The query containment is one of the fundamental problems in the context of query processing and optimization. Concerning the answers of queries for databases, three semantics were intensively analyzed. In the first one, called \(set\), both databases and answers of queries for databases are considered sets. In the second one, called \(\textit{bag-set}\), databases are sets, but the answers are bags (multi-sets). In the third one, called \(bag\), both databases and answers are bags.

Caching is important for any system attempting to achieve high performance. The semantic caching is an approach trying to benefit from the certain knowledge of data semantics. The authors expect that this information might enable reuse of semantically close data rather than exactly equal to cached data in the traditional system. However, the major obstacle for extensive application of semantic caching for any data model or query language is the computational complexity of the query containment problem, which is, in general, undecidable. In this article the authors introduce and compare three approximate conservative query matching algorithms for semantic caching of semi-structured queries. The authors then analyze their applicability for distributed query processing. Based on this analysis, the authors outline few scenarios where semantic caching can be beneficial for query processing in a distributed system of heterogeneous semi-structured information resources.

Query containment is the problem of deciding if the answers to a query are included in those of another query for any queried database. This problem is very important for query optimization purposes. In the SPARQL context, it can be equally useful. This problem has recently been investigated theoretically and some query containment solvers are available. Yet, there were no benchmarks to compare theses systems and foster their improvement. In order to experimentally assess implementation strengths and limitations, we provide a first SPARQL containment test benchmark. It has been designed with respect to both the capabilities of existing solvers and the study of typical queries. Some solvers support optional constructs and cycles, while other solvers support projection, union of conjunctive queries and RDF Schemas. No solver currently supports all these features or OWL entailment regimes. The study of query demographics on DBPedia logs shows that the vast majority of queries are acyclic and a significant part of them uses UNION or projection. We thus test available solvers on their domain of applicability on three different benchmark suites. These experiments show that (i) tested solutions are overall functionally correct, (ii) in spite of its complexity, SPARQL query containment is practicable for acyclic queries, (iii) state-of-the-art solvers are at an early stage both in terms of capability and implementation.

We tackle the containment problem for conjunctive queries with negation, which takes two queries q1 and q2 as input and asks if q1 is contained in q2. A general approach for solving this problem consists of considering all completions of q1 (intuitively these completions represent all canonical databases that satisfy q1) and checking if each completion yields the same answer on q2. Since the total number of completions of q1 is exponential in the size of q1, several proposals have aimed at reducing the number (and the size) of the completions checked. In this paper, we propose a unifying framework for comparing algorithms following this general approach and define two kinds of heuristics for exploring the space of completions. Combining these heuristics with both classical kinds of traversals, i.e., depth-first and breadth-first, we obtain four algorithms that we compare experimentally with respect to running time on difficult instances of the containment problem.

Formulation of efficient algorithms to check implication and satisfibality for relational queries is an important research issue. Implication and satisfibality checking can be used to find query containment in semantic cache query processing and other similar applications. Description logic (DL) is a formalism used to model knowledge of a domain in the form of concepts and a rich set of associations between these concepts in the T-Boxes. Reasoning on these knowledge bases can be performed in order to find explicit relation as well as discover implicit relations. Sound and Complete subsumption algorithms exist for reasoning facts represented in Description Logic. The most common reasoning (which can be used for other sort of reasoning, too) is the determination of a subsumption relation between the logical expressions of T-boxes. In this paper, we propose an algorithm to translate relational queries in to description logic ALC(D), so that DL subsumption algorithms can be applied on these translated queries to find query containment. Working of the algorithm is demonstrated with the help of a case study. Conversion of relational query into DL will also help in optimization of cache size for the storage of semantics by eliminating redundant semantics in the cache. Hence, the sound and complete reasoning services of DL can be used for relational query containment.

To benefit from the Cloud platform's unlimited resources, managing and evaluating huge volume of RDF data in a scalable manner has attracted intensive research efforts recently. Progresses have been made on evaluating SPARQL queries with either high-level declarative programming languages, like Pig [1], or a sequence of sophisticated designed MapReduce jobs, both of which tend to answer the query with multiple join operations. However, due to the simplicity of Cloud storage and the coarse organization of RDF data in existing solutions, multiple join operations easily bring significant I/O and network traffic which can severely degrade the system performance. In this work, we first propose EAGRE, an Entity-Aware Graph compREssion technique to form a new representation of RDF data on Cloud platforms, based on which we propose an I/O efficient strategy to evaluate SPARQL queries as quickly as possible, especially queries with specified solution sequence modifiers, e.g., PROJECTION, ORDER BY, etc. We implement a prototype system and conduct extensive experiments over both real and synthetic datasets on an in-house cluster. The experimental results show that our solution can achieve over an order of magnitude of time saving for the SPARQL query evaluation compared to the state-of-art MapReduce-based solutions.

Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for monadic second order logic (respectively first order logic with a reachability predicate) is decidable on such graphs. We unify both models by introducing the notion of stack trees, trees whose nodes are labelled by higher-order stacks, and define the corresponding class of higher-order ground tree rewriting systems. We show that these graphs retain the decidability properties of ground tree rewriting graphs while generalising the pushdown hierarchy of graphs.

In the propositional modal (and algebraic) treatment of two-variable first-order logic equality is modelled by a `diagonal' constant, interpreted in square products of universal frames as the identity (also known as the `diagonal') relation. Here we study the decision problem of products of two arbitrary modal logics equipped with such a diagonal. As the presence or absence of equality in two-variable first-order logic does not influence the complexity of its satisfiability problem, one might expect that adding a diagonal to product logics in general is similarly harmless. We show that this is far from being the case, and there can be quite a big jump in complexity, even from decidable to the highly undecidable. Our undecidable logics can also be viewed as new fragments of first- order logic where adding equality changes a decidable fragment to undecidable. We prove our results by a novel application of counter machine problems. While our formalism apparently cannot force reliable counter machine computations directly, the presence of a unique diagonal in the models makes it possible to encode both lossy and insertion-error computations, for the same sequence of instructions. We show that, given such a pair of faulty computations, it is then possible to reconstruct a reliable run from them.

The number of linked sources and the size of the linked open graph keep growing every day. As a consequence, semantic RDF services are more and more confronted with various big data problems. Query processing in the presence of inferences is one them. For instance, to complete the answer set of SPARQL queries, RDF database systems evaluate semantic RDFS relationships (subPropertyOf, subClassOf) through time-consuming query rewriting algorithms or space-consuming materialization solutions. To reduce the memory footprint and ease the exchange of large datasets, these systems generally apply a dictionary approach for compressing triple sizes by replacing resource identifiers (IRIs), blank nodes and literals with integer values. In this article, we present a structured resource identification scheme using a clever encoding of concepts and property hierarchies for efficiently evaluating the main common RDFS entailment rules while minimizing triple materialization and query rewriting. We will show how this encoding can be computed by a scalable parallel algorithm and directly be implemented over the Apache Spark framework. The efficiency of our encoding scheme is emphasized by an evaluation conducted over both synthetic and real world datasets.

A meta-program, regardless of the nature of the programming language, is a program whose data denotes another (object) program. The importance of meta-programming can be gauged from its large number of applications. These include compilers, interpreters, program analysers, and program transformers. Furthermore, if the object program is a logic or functional program formalizing some knowledge, then the meta-program may be regarded as a meta-reasoner for reasoning about this knowledge. In this chapter, the meta-program is assumed to be a logic program. The object program does not have to be a logic program although much of the work in this chapter assumes this. We have identified three major topics for consideration. These are the theoretical foundations of meta-programming, the suitability of the alternative meta-programming techniques for different applications, and methods for improving the efficiency of meta-programs. As with logic programs generally, meta-programs have declarative and procedural semantics. The theoretical study of meta-programming shows that both aspects of the semantics depend crucially on the manner in which object programs are represented as data in a meta-program. The second theme of the paper is the problem of designing and choosing appropriate ways of specifying important meta-programming problems, including dynamic metaprogramming and problems involving self-application. The third theme concerns efficient implementation of meta-programs. Meta-programming systems require representations with facilities that minimize the overhead of interpreting the object program. In addition, efficiency can be gained by transforming the meta-program, specializing it for the particular object program it is reasoning about. This chapter, which concentrates on these aspects of meta-programming, is not intended to be a survey of the field. A more complete survey of meta-programming for logic programming can be found in [Barklund, 1995]. Many issues in meta-programming have their roots in problems in logic which have been studied for several decades. This chapter emphasizes meta-programming solutions. It is not intended to give a full treatment of the underlying logical problems, though we try to indicate some connections to wider topics in meta-logic. The meta-programs in this chapter are logic programs based on first order logic.

Federated RDF systems allow users to retrieve data from multiple independent sources without needing to have all the data in the same triple store. The performance of these systems can be poor for large and geographically distributed RDF data where network transfer costs are high. This article introduces CBTP-OL and CBTP-Nhop, two novel join algorithms that take advantage of network topology to decrease the cost of processing Basic Graph Pattern (BGP) SPARQL queries in a geographically distributed environment. Federation members are grouped in clusters, based on the network communication cost between the members, and the bulk of the join processing is pushed to the clusters. Our CBTP-OL and CBTL-Nhop algorithms use an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">overlap list</i> and, respectively, an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N-hop overlap list</i> , to efficiently compute join results from triples in different clusters. We implement our algorithms in the OpenRDF Sesame federated framework and use Apache Rya triple store instances as federation members. Experimental evaluation results show the advantages of our approach over existing techniques.

The authors propose a new method for mining sets of patterns for classification, where patterns are represented as SPARQL queries over RDFS. The method contributes to so-called semantic data mining, a data mining approach where domain ontologies are used as background knowledge, and where the new challenge is to mine knowledge encoded in domain ontologies, rather than only purely empirical data. The authors have developed a tool that implements this approach. Using this the authors have conducted an experimental evaluation including comparison of our method to state-of-the-art approaches to classification of semantic data and an experimental study within emerging subfield of meta-learning called semantic meta-mining. The most important research contributions of the paper to the state-of-art are as follows. For pattern mining research or relational learning in general, the paper contributes a new algorithm for discovery of new type of patterns. For Semantic Web research, it theoretically and empirically illustrates how semantic, structured data can be used in traditional machine learning methods through a pattern-based approach for constructing semantic features.