Regular path queries on graphs with data

Abstract

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 data-word 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.

Foundations of Modern Query Languages for Graph Databases

“…On the other hand, they did receive some attention in the theoretical literature. For instance, the base language for regular data path queries was introduced in [Libkin and Vrgoč 2012], and some further extensions allowing first order reasoning over paths [Hellings et al 2013], or unlimited use of variables [Libkin et al 2016;Barceló et al 2015] have also been considered. However, since there is still no clear consensus on the correct language for this task, this seems to be a promising area of future work, both with respect to the theoretical issues, and with respect to the correct techniques for implementing such queries in graph database systems.…”

Expressive Path Queries on Graphs with Data

“…This is the data model adopted by Libkin and Vrgoč [9] in their definition of REMs. In the case of WL [7], the authors adopted graph databases as their data model, i.e., data graphs G = (V, E, κ) such that κ is injective (i.e.…”

“…each node carries a different data value). We shall adopt the general model of [9] since none of our complexity results are affected by the data model: upper bounds hold for data graphs, while all lower bounds are proved in the more restrictive setting of graph databases.…”

“…(b) Regular expressions with memory (REMs) were proposed by Libkin and Vrgoč [9] as a formalism for comparing data values along a single path, while retaining a reasonable complexity for query evaluation. The strength of this language is on the side of efficiency.…”

“…REMs define pairs of nodes in the graph database that are linked by a path satisfying a given condition c. Each such condition c is defined in a formalism inspired by the class of register automata [8], allowing some data values to be stored in the registers and then compared against other data values. The evaluation problem for REMs is Pspace-complete (same than for FO over relational databases), and can be solved in polynomial time in data complexity [9], i.e., assuming queries to be fixed. 4 This shows that the language is, in fact, well-behaved in terms of the complexity of query evaluation.…”