Adding regular expressions to graph reachability and pattern queries

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 NP-completeness of graph pattern matching via subgraph isomorphism. (4) The effectiveness, efficiency and scalability of these algorithms are experimentally verified using real-life data and synthetic data.

Capturing topology in graph pattern matching

“…A graph G matches a pattern Q via graph simulation if there exists a binary relation S ⊆ V Q × V , where V Q and V are the set of nodes in Q and G, respectively, such that (1) for each (u, v) ∈ S, u and v have the same label; and (2) for each node u in Q, there exists v in G such that (a) (u, v) ∈ S, and (b) for each edge (u, u ) in Q, there exists an edge (v, v ) in G such that (u , v ) ∈ S. Graph simulation can be determined in quadratic time [24]. Recently this notion has been extended by mapping edges in Q to (bounded) paths in G [19,18], with a cubic-time complexity, to identify matches in, e.g., social networks. Nevertheless, the low complexity comes with a price: (1) simulation and its extensions [19,18] do not preserve the topology of data graphs; in other words, they may match a graph G and a pattern Q with drastically different structures.…”

A trichotomy for regular simple path queries on graphs

“…One might think the intersection of the two paths p 1 and p 2 does not matter, as each loop can be eliminated while preserving the membership of the label in L, according to Lemma 11. In this example this is indeed the case: the path through v 1 , v 2 , v 3 , v 4 , v 6 , v 13 , v 14 , and v 15 belongs to the language L. But Example 4 shows this needs not be the case in general.…”

“…RSPQs, however, are desired in many application scenarios [26,32,6,24,22,39], such as transportation problems, VLSI design, metabolic networks, DNA matching and routing in wireless networks. As a further example, the problem of finding subgraphs matching a graph pattern can be generalized to use regular expressions on pattern edges [14]. Such queries may also enforce the condition that their matched vertices are distinct.…”

Towards Efficient Path Query on Social Network with Hybrid RDF Management

“…From graph analysis perspective, Property path can be viewed as the labelconstraint reachability problem on labeled graph. Though reachability on graph is a further investigated problem, few literatures [1,10] considered its usage in property graph, which is more common in nature. These researches are mainly focus on building reachability indices in advance, which is time or space consuming and not adequate for large-scale data management.…”