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19
Query Languages for Graph Databases
 SIGMOD Record
, 2012
"... Query languages for graph databases started to be investigated some 25 years ago. With much current data, such as linked data on the Web and social network data, being graphstructured, there has been a recent resurgence in interest in graph query languages. We provide a brief survey of many of the ..."
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Query languages for graph databases started to be investigated some 25 years ago. With much current data, such as linked data on the Web and social network data, being graphstructured, there has been a recent resurgence in interest in graph query languages. We provide a brief survey of many of the graph query languages that have been proposed, focussing on the core functionality provided in these languages. We also consider issues such as expressive power and the computational complexity of query evaluation. 1.
Querying graph databases with XPath
, 2013
"... General Terms XPath plays a prominent role as an XML navigational language due to several factors, including its ability to express queries of interest, its close connection to yardstick database query languages (e.g., firstorder logic), and the low complexity of query evaluation for many fragments ..."
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General Terms XPath plays a prominent role as an XML navigational language due to several factors, including its ability to express queries of interest, its close connection to yardstick database query languages (e.g., firstorder logic), and the low complexity of query evaluation for many fragments. Another common database model — graph databases — also requires a heavy use of navigation in queries; yet it largely adopts a different approach to querying, relying on reachability patterns expressed with regular constraints. Our goal here is to investigate the behavior and applicability of XPathlike languages for querying graph databases, concentrating on their expressiveness and complexity of query evaluation. We are particularly interested in a model of graph data that combines navigation through graphs with querying data held in the nodes, such as, for example, in a social network scenario. As navigational languages, we use analogs of core and regular XPath and augment them with various tests on data values. We relate these languages to firstorder logic, its transitive closure extensions, and finitevariable fragments thereof, proving several capture results. In addition, we describe their relative expressive power. We then show that they behave very well computationally: they have a lowdegree polynomial combined complexity, which becomes linear for several fragments. Furthermore, we introduce new types of tests for XPath languages that let them capture firstorder logic with data comparisons and prove that the low complexity bounds continue to apply to such extended languages. Therefore, XPathlike languages seem to be very wellsuited to query graphs.
Graph Logics with Rational Relations and the Generalized Intersection Problem
"... Abstract—We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular ..."
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Abstract—We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular languages and relations, but they often need to be extended by rational relations such as subword (factor) or subsequence. Evaluating formulae in such extended graph logics boils down to checking nonemptiness of the intersection of rational relations with regular or recognizable relations (or, more generally, to the generalized intersection problem, asking whether some projections of a regular relation have a nonempty intersection with a given rational relation). We prove that for several basic and commonly used rational relations, the intersection problem with regular relations is either undecidable (e.g., for subword or suffix, and some generalizations), or decidable with nonmultiplyrecursive complexity (e.g., for subsequence and its generalizations). These results are used to rule out many classes of graph logics that freely combine regular and rational relations, as well as to provide the simplest problem related to verifying lossy channel systems that has nonmultiplyrecursive complexity. We then prove a dichotomy result for logics combining regular conditions on individual paths and rational relations on paths, by showing that the syntactic form of formulae classifies them into either efficiently checkable or undecidable cases. We also give examples of rational relations for which such logics are decidable even without syntactic restrictions. I.
TriAL for RDF: Adapting Graph Query Languages for RDF Data
"... Querying RDF data is viewed as one of the main applications of graph query languages, and yet the standard model of graph databases – essentially labeled graphs – is different from the triplesbased model of RDF. While encodings of RDF databases into graph data exist, we show that even the most natu ..."
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Querying RDF data is viewed as one of the main applications of graph query languages, and yet the standard model of graph databases – essentially labeled graphs – is different from the triplesbased model of RDF. While encodings of RDF databases into graph data exist, we show that even the most natural ones are bound to lose somefunctionalitywhenused inconjunctionwith graph query languages. The solution is to work directly with triples, but then many properties taken for granted in the graphdatabasecontext(e.g., reachability)losetheir natural meaning. Our goal is to introduce languages that work directly over triples and are closed, i.e., they produce sets of triples, ratherthan graphs. Our basiclanguageis called TriAL, or Triple Algebra: it guarantees closure properties by replacing the product with a family of join operations. We extend TriAL with recursion, and explain why such an extension is more intricate for triples than for graphs. We present a declarative language, namely a fragment of datalog, capturing the recursive algebra. For both languages, the combined complexity of query evaluation is given by lowdegree polynomials. We compare our languages with relational languages, such as finitevariable logics, and previously studied graph query languages such as adaptations of XPath, regular path queries, and nested regular expressions; many of these languages are subsumed by the recursive triple algebra. We also provide examples of the usefulness of TriAL in querying graph, RDF, and social networks data.
GRAPH LOGICS WITH RATIONAL RELATIONS
"... Abstract. We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular ..."
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Abstract. We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular languages and relations, but they often need to be extended by rational relations such as subword or subsequence. Evaluating formulae in such extended graph logics boils down to checking nonemptiness of the intersection of rational relations with regular or recognizable relations (or, more generally, to the generalized intersection problem, asking whether some projections of a regular relation have a nonempty intersection with a given rational relation). We prove that for several basic and commonly used rational relations, the intersection problem with regular relations is either undecidable (e.g., for subword or suffix, and some generalizations), or decidable with nonprimitiverecursive complexity (e.g., for subsequence and its generalizations). These results are used to rule out many classes of graph logics that freely combine regular and rational relations, as well as to provide the simplest problem related to verifying lossy channel systems that has nonprimitiverecursive complexity. We then prove a dichotomy result for logics combining regular conditions on individual paths and rational relations on paths, by showing that the syntactic form of formulae classifies them into either efficiently checkable or undecidable cases. We also give examples of rational relations for which such logics are decidable even without syntactic restrictions.
Regular Expressions for Data Words
"... Abstract. In data words, each position carries not only a letter form a finite alphabet, as the usual words do, but also a data value coming from an infinite domain. There has been a renewed interest in them due to applications in querying and reasoning about data models with complex structural prop ..."
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Abstract. In data words, each position carries not only a letter form a finite alphabet, as the usual words do, but also a data value coming from an infinite domain. There has been a renewed interest in them due to applications in querying and reasoning about data models with complex structural properties, notably XML, and more recently, graph databases. Logical formalisms designed for querying such data often require concise and easily understandable presentations of regular languages over data words. Our goal, therefore, is to define and study regular expressions for data words. As the automaton model, we take register automata, which are a natural analog of NFAs for data words. We first equip standard regular expressions with limited memory, and show that they capture the class of data words defined by register automata. The complexity of the main decision problems for these expressions (nonemptiness, membership) also turns out to be the same as for register automata. We then look at a subclass of these regular expressions that can define many properties of interest in applications of data words, and show that the main decision problems can be solved efficiently for it. 1
Containment of Data Graph Queries
"... The graph database model is currently one of the most popular paradigms for storing data, used in applications such as social networks, biological databases and the Semantic Web. Despite the popularity of this model, the development of graph database management systems is still in its infancy, and ..."
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The graph database model is currently one of the most popular paradigms for storing data, used in applications such as social networks, biological databases and the Semantic Web. Despite the popularity of this model, the development of graph database management systems is still in its infancy, and there are several fundamental issues regarding graph databases that are not fully understood. Indeed, while graph query languages that concentrate on topological properties are now well developed, not much is known about languages that can query both the topology of graphs and their underlying data. Our goal is to conduct a detailed study of static analysis problems for such languages. In this paper we consider the containment problem for several recently proposed classes of queries that manipulate both topology and data: regular queries with memory, regular queries with data tests, and graph XPath. Our results show that the problem is in general undecidable for all of these classes. However, by allowing only positive data comparisons we find natural fragments that enjoy much better static analysis properties: the containment problem is decidable, and its computational complexity ranges from PSPACEcomplete to EXPSPACEcomplete. We also propose extensions of regular queries with an inverse operator, and study query evaluation and query containment for them.
2013. A Trichotomy for Regular Simple Path Queries on Graphs
 In Symposium on Principles of Database Systems (PODS). ACM
"... Regular path queries (RPQs) select nodes connected by some path in a graph. The edge labels of such a path have to form a word that matches a given regular expression. We investigate the evaluation of RPQs with an additional constraint that prevents multiple traversals of the same nodes. Those regu ..."
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Regular path queries (RPQs) select nodes connected by some path in a graph. The edge labels of such a path have to form a word that matches a given regular expression. We investigate the evaluation of RPQs with an additional constraint that prevents multiple traversals of the same nodes. Those regular simple path queries (RSPQs) find several applications in practice, yet they quickly become intractable, even for basic languages such as (aa) ∗ or a∗ba∗. In this paper, we establish a comprehensive classification of regular languages with respect to the complexity of the corresponding regular simple path query problem. More precisely, we identify the fragment that is maximal in the following sense: regular simple path queries can be evaluated in polynomial time for every regular languageL that belongs to this fragment and evaluation is NPcomplete for languages outside this fragment. We thus fully characterize the frontier between tractability and intractability for RSPQs, and we refine our results to show the following trichotomy: Evaluations of RSPQs is eitherAC0,NLcomplete orNPcomplete in data complexity, depending on the regular language L. The fragment identified also admits a simple characterization in terms of regular expressions. Finally, we also discuss the complexity of the following decision problem: decide, given a language L, whether finding a regular simple path for L is tractable. We consider several alternative representations of L: DFAs, NFAs or regular expressions, and prove that this problem is NLcomplete for the first representation and PSPACEcomplete for the other two. As a conclusion we extend our results from edgelabeled graphs to vertexlabeled graphs and vertexedge labeled graphs. 1.
Querying incomplete graphs with data
"... Graph databases underlie several modern applications such as social networks and the Semantic Web. In those scenarios, integrating and exchanging data is very common, which leads to proliferation of incomplete graph data. However, the well developed models of incompleteness of data do not apply to g ..."
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Graph databases underlie several modern applications such as social networks and the Semantic Web. In those scenarios, integrating and exchanging data is very common, which leads to proliferation of incomplete graph data. However, the well developed models of incompleteness of data do not apply to graph data.
Expressive Path Queries on Graphs with Data
"... Abstract. Graph data models have recently become popular owing to their applications, e.g., in social networks, semantic web. Typical navigational query languages over graph databases — such as Conjunctive Regular Path Queries (CRPQs) — cannot express relevant properties of the interaction between ..."
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Abstract. Graph data models have recently become popular owing to their applications, e.g., in social networks, semantic web. Typical navigational query languages over graph databases — such as Conjunctive Regular Path Queries (CRPQs) — cannot express relevant properties of the interaction between the underlying data and the topology. Two languages have been recently proposed to overcome this problem: walk logic (WL) and regular expressions with memory (REM). In this paper, we begin by investigating fundamental properties of WL and REM, i.e., complexity of evaluation problems and expressive power. We first show that the data complexity of WL is nonelementary, which rules out its practicality. On the other hand, while REM has low data complexity, we point out that many natural data/topology properties of graphs expressible in WL cannot be expressed in REM. To this end, we propose register logic, an extension of REM, which we show to be able to express many natural graph properties expressible in WL, while at the same time preserving the elementariness of data complexity of REMs. It is also incomparable in expressive power against WL. 1