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63
Adding Regular Expressions to Graph Reachability and Pattern Queries
 Frontiers of Computer Science
, 2012
"... Abstract—It is increasingly common to find graphs in which edges bear different types, indicating a variety of relationships. For such graphs we propose a class of reachability queries and a class of graph patterns, in which an edge is specified with a regular expression of a certain form, expressin ..."
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Abstract—It is increasingly common to find graphs in which edges bear different types, indicating a variety of relationships. For such graphs we propose a class of reachability queries and a class of graph patterns, in which an edge is specified with a regular expression of a certain form, expressing the connectivity in a data graph via edges of various types. In addition, we define graph pattern matching based on a revised notion of graph simulation. On graphs in emerging applications such as social networks, we show that these queries are capable of finding more sensible information than their traditional counterparts. Better still, their increased expressive power does not come with extra complexity. Indeed, (1) we investigate their containment and minimization problems, and show that these fundamental problems are in quadratic time for reachability queries and are in cubic time for pattern queries. (2) We develop an algorithm for answering reachability queries, in quadratic time as for their traditional counterpart. (3) We provide two cubictime algorithms for evaluating graph pattern queries based on extended graph simulation, as opposed to the NPcompleteness of graph pattern matching via subgraph isomorphism. (4) The effectiveness, efficiency and scalability of these algorithms are experimentally verified using reallife data and synthetic data. I.
Counting Beyond a Yottabyte, or how SPARQL 1.1 Property Paths will Prevent Adoption of the Standard
"... SPARQL –the standard query language for querying RDF – provides only limited navigational functionalities, although these features are of fundamental importance for graph data formats such as RDF. This has led the W3C to include the property path feature in the upcoming version of the standard, SPAR ..."
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Cited by 26 (2 self)
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SPARQL –the standard query language for querying RDF – provides only limited navigational functionalities, although these features are of fundamental importance for graph data formats such as RDF. This has led the W3C to include the property path feature in the upcoming version of the standard, SPARQL 1.1. We tested several implementations of SPARQL 1.1 handling property path queries, and we observed that their evaluation methods for this class of queries have a poor performance even in some very simple scenarios. To formally explain this fact, we conduct a theoretical study of the computational complexity of property paths evaluation. Our results imply that the poor performance of the tested implementations is not a problem of these particular systems, but of the specification itself. In fact, we show that any implementation that adheres to the SPARQL 1.1 specification (as of November 2011) is doomed to show the same behavior, the key issue being the need for counting solutions imposed by the current specification. We provide several intractability results, that together with our empirical results, provide strong evidence against the current semantics of SPARQL 1.1 property paths. Finally, we put our results in perspective, and propose a natural alternative semantics with tractable evaluation, that we think may lead to a wide adoption of the language by practitioners, developers and theoreticians.
Querying Semantic Web Data with SPARQL
"... The Semantic Web is the initiative of the W3C to make information on the Web readable not only by humans but also by machines. RDF is the data model for Semantic Web data, and SPARQL is the standard query language for this data model. In the last ten years, we have witnessed a constant growth in the ..."
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The Semantic Web is the initiative of the W3C to make information on the Web readable not only by humans but also by machines. RDF is the data model for Semantic Web data, and SPARQL is the standard query language for this data model. In the last ten years, we have witnessed a constant growth in the amount of RDF data available on the Web, which have motivated the theoretical study of some fundamental aspects of SPARQL and the development of efficient mechanisms for implementing this query language. Some of the distinctive features of RDF have made the study and implementation of SPARQL challenging. First, as opposed to usual database applications, the semantics of RDF is open world, making RDF databases inherently incomplete. Thus, one usually obtains partial answers when querying RDF with SPARQL, and the possibility of adding optional information if present is a crucial feature of SPARQL. Second, RDF databases have a graph structure and are interlinked, thus making graph navigational capabilities a necessary component of SPARQL. Last, but not least, SPARQL has to work at Web scale! RDF and SPARQL have attracted interest from the database community. However, we think that this community has much more to say about these technologies, and, in particular, about the fundamental database problems that need to be solved in order to provide solid foundations for the development of these technologies. In this paper, we survey some of the main results about the theory of RDF and SPARQL putting emphasis on some research opportunities for the database community.
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.
Parikh images of grammars: Complexity and applications
 IN LICS
, 2010
"... Parikh’s Theorem states that semilinear sets are effectively equivalent with the Parikh images of regular languages and those of contextfree languages. In this paper, we study the complexity of Parikh’s Theorem over any fixed alphabet size d. We prove various normal form theorems in the case of N ..."
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Cited by 19 (0 self)
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Parikh’s Theorem states that semilinear sets are effectively equivalent with the Parikh images of regular languages and those of contextfree languages. In this paper, we study the complexity of Parikh’s Theorem over any fixed alphabet size d. We prove various normal form theorems in the case of NFAs and CFGs. In particular, the normal form theorems ensure that a union of linear sets with d generators suffice to express such Parikh images, which in the case of NFAs can further be computed in polynomial time. We then apply apply our results to derive: (1) optimal complexity for decision problems concerning Parikh images (e.g. membership, universality, equivalence, and disjointness), (2) a new polynomial fragment of integer programming, (3) an answer to an open question about PAClearnability of semilinear sets, and (4) an optimal algorithm for verifying LTL over discretetimed reversalbounded counter systems.
Regular path queries on graphs with data
 In ICDT’12
"... Graph data models received much attention lately due to applications in social networks, semantic web, biological databases and other areas. Typical query languages for graph databases retrieve their topology, while actual data stored in them is usually queried using standard relational mechanisms. ..."
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Graph data models received much attention lately due to applications in social networks, semantic web, biological databases and other areas. Typical query languages for graph databases retrieve their topology, while actual data stored in them is usually queried using standard relational mechanisms. Our goal is to develop techniques that combine these two modes of querying, and give us query languages that can ask questions about both data and topology. As the basic querying mechanism we consider regular path queries, with the key difference that conditions on paths between nodes now talk not only about labels but also specify how data changes along the path. Paths that combine edge labels with data values are closely related to data words, so for stating conditions in queries, we look at several dataword formalisms developed recently. We show that many of them immediately lead to intractable data complexity for graph queries, with the notable exception of register automata, which can specify many properties of interest, and have NLOGSPACE data and PSPACE combined complexity. As register automata themselves are not easy to use in querying, we define two types of extensions of regular expressions that are more userfriendly, and develop query evaluation techniques for them. For one class, regular expressions with memory, we achieve the same bounds as for automata, and for the other class, regular expressions with equality, we also obtain tractable combined complexity of query evaluation. In addition, we show that results extends to analogs of conjunctive regular path queries.
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.
Relative expressiveness of nested regular expressions
 Proceedings 6th Alberto Mendelzon International Workshop on Foundations of a b c d Management, volume 866 of CEUR Workshop Proceedings
, 2012
"... Abstract. Nested regular expressions (NREs) have been proposed as a powerful formalism for querying RDFS graphs, but not too much investigation on NREs has been pursued in a more general graph database context. In this paper we study the relative expressiveness of NREs by comparing it with the langu ..."
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Abstract. Nested regular expressions (NREs) have been proposed as a powerful formalism for querying RDFS graphs, but not too much investigation on NREs has been pursued in a more general graph database context. In this paper we study the relative expressiveness of NREs by comparing it with the language of conjunctive twoway regular path queries (C2RPQs), which is one of the most widely studied query languages for graph databases. Among other results, we show that NREs and C2RPQs are incomparable in terms of expressive power, but NREs properly extend the language of unions of acyclic C2RPQs. Even more, there is a natural fragment of NREs that coincide in expressive power with the class of unions of acyclic C2RPQs. Our results, plus previous results that show that NREs can be evaluated in linear time in combined complexity, put forward NREs as a query language for graphstructured data that deserves further attention. 1
Querying Graph Patterns
"... Graph data appears in a variety of application domains, and many uses of it, such as querying, matching, and transforming data, naturally result in incompletely specified graph data, i.e., graph patterns. While queries need to be posed against such data, techniques for querying patterns are generall ..."
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Graph data appears in a variety of application domains, and many uses of it, such as querying, matching, and transforming data, naturally result in incompletely specified graph data, i.e., graph patterns. While queries need to be posed against such data, techniques for querying patterns are generally lacking, and properties of such queries are not well understood. Our goal is to study the basics of querying graph patterns. We first identify key features of patterns, such as node and label variables and edges specified by regular expressions, and define a classification of patterns based on them. We then study standard graph queries on graph patterns, and give precise characterizations of both data and combined complexity for each class of patterns. If complexity is high, we do further analysis of features that lead to intractability, as well as lowercomplexity restrictions. We introduce a new automata model for query answering with two modes of acceptance: one captures queries returning nodes, and the other queries returning paths. We study properties of such automata, and the key computational tasks associated with them. Finally, we provide additional restrictions for tractability, and show that some intractable cases can be naturally cast as instances of constraint satisfaction problem.
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.