Expressive Languages for Path Queries over Graph-Structured Data

Abstract

For many problems arising in the setting of graph querying (such as finding semantic associations in RDF graphs, exact and approximate pattern matching, sequence alignment, etc.), the power of standard languages such as the widely studied conjunctive regular path queries (CRPQs) is insufficient in at least two ways. First, they cannot output paths and second, more crucially, they cannot express relations among paths.We thus propose a class of extended CRPQs, called ECRPQs, which add regular relations on tuples of paths, and allow path variables in the heads of queries. We provide several examples of their usefulness in querying graph structured data, and study their properties. We analyze query evaluation and representation of tuples of paths in the output by means of automata. We present a detailed analysis of data and combined complexity of queries, and consider restrictions that lower the complexity of ECRPQs to that of relational conjunctive queries. We study the containment problem, and look at further extensions with first-order features, and with non-regular relations that express arithmetic properties of paths, based on the lengths and numbers of occurrences of labels.

Foundations of Modern Query Languages for Graph Databases

“…The endpoints x and y can be variables, or specific nodes, or a mix of both, or even the same node (in which case we are specifying a cycle). For the expression α, we can use the symbol * to signify that we are only interested in the existence of a path connecting two nodes without imposing any further constraints; otherwise, there are a variety of formalisms under which α can express more complex path constraints [Cruz et al 1987;Mendelzon and Wood 1989;Barceló et al 2012a;Calvanese et al 2003;Libkin et al 2016], but probably the most famous is that of regular expressions [Hopcroft et al 2003] defined over the set Lab of edge labels. When used as a path constraint, a regular expression specifies all paths whose edge labels, when concatenated, form a word in the language of the regular expression.…”

“…As per Example 4.3, under this semantics, P (G) may contain an infinite number of paths. However, while it may not be feasible to enumerate all paths under this semantics, a user may only be interested in whether or not such a path exists, or in the (finite) pairs of nodes connected by such paths, etc., in which case such a semantics can be practical [Calvanese et al 2003;Wood 2012;Barceló et al 2012a]. …”

“…In other cases, paths to be returned may be selected based on more complex conditions, e.g., based on a ranking on paths; this may be useful in, e.g., route finding applications, where some top-k "best" paths are sought. -Graphs: Another solution -for example under arbitrary path semantics -is to offer a compact representation of the output, e.g., in the form of another graph whose paths are precisely the paths in the output of the query [Barceló et al 2012a].…”

Small Dynamic Complexity Classes

“…Here, we only looked at very basic graph query languages. Extensions, such as the query language ECRPQ [BLLW12], might be worth studying as well. As an example, the length of paths used in a conjunctive regular path query can be compared in ECRPQ.…”

On simplification of schema mappings

“…Note that, while schema mappings have been extensively studied for relational data, and, to some extent, for XML data [15], this is the first paper on comparing schema mappings for graph databases. Graph databases [16] were introduced in the 80's, and are regaining wide attention recently [17][18][19], for their relevance in areas such as semi-structured data, biological data management, social networks, and the semantic web.…”