Adding regular expressions to graph reachability and pattern queries

Abstract

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.

Foundations of Modern Query Languages for Graph Databases

“…Then an answer to Q over G under the simulation-based semantics is any simulation S between Q and G. As shown in the literature, simulation-based semantics is computationally lighter for certain problems [Henzinger et al 1995;Fan et al 2011] and is more versatile when handling large graphs that might contain incomplete information [Fan et al 2010a;Fan 2012;Fan et al 2010b]. …”

Event pattern matching over graph streams

“…If the current signature value is within the size of an integer, the new edge factor is multiplied into it; otherwise a new signature integer value is initiated (lines 6-7). Similarly, the algorithm goes through each vertex and calculates the degree factors (lines [8][9][10][11][12]. For clarity, we omit the step in 1. for each ← 0…”

“…Ma et al [17] find that the simulation itself in [9,8] often fails to capture the topology of query graphs, yielding false matches or too large a match relation. They rectify this problem by adding constraints dual simulation and locality [17].…”

“…Unlike this work, we do not allow mismatches or edge-path matches. A recent approach to cope with the intractability of SI, which is the closest to ours, is via simulation [19,13,9,8,17]. Specifically, [9] extends simulation [13] to allow bounds on the number of hops in patterns, while [8] has regular expressions as edge constraints.…”

“…1.1, simulation and dual simulation are well-established and extensively studied semantics for subgraph matching (e.g., [19,13,9,8,17]). Intuitively, simulation means that a subgraph of simulates , in that there is a binary match relation pairing a vertex of with a vertex in , such that they have the same label, and every outgoing edge ( , ′ ) from in has a matching edge ( , ′ ) in , where ′ and ′ also match according to .…”