Hybrid search plan generation for generalized graph pattern matching

Highlights

• Constraints in a graph query are represented uniformly.

• Static information allows considering the graph query's structure.

• Dynamic information allows tailoring to host graph heterogeneities.

• Filtering effects of constraint checks are considered.

Abstract

In recent years, the increased interest in application areas such as social networks has resulted in a rising popularity of graph-based approaches for storing and processing large amounts of interconnected data. To extract useful information from the growing network structures, efficient querying techniques are required.

In this paper, we propose an approach for graph pattern matching that allows a uniform handling of arbitrary constraints over the query vertices. Our technique builds on a previously introduced matching algorithm, which takes concrete host graph information into account to dynamically adapt the employed search plan during query execution. The dynamic algorithm is combined with an existing static approach for search plan generation, resulting in a hybrid technique which we further extend by a more sophisticated handling of filtering effects caused by constraint checks. We evaluate the presented concepts empirically based on an implementation for our graph pattern matching tool, the Story Diagram Interpreter, with queries and data provided by the LDBC Social Network Benchmark. Our results suggest that the hybrid technique may improve search efficiency in several cases, and rarely reduces efficiency.

Introduction

In recent years, the increased interest in application areas such as social networks has resulted in a rising popularity of graph-based approaches for storing and processing large amounts of information [1]. The considered graphs frequently exhibit an inhomogeneous structure, which in the case of social networks can be caused by the diverse behaviour of different users, including extreme outliers such as celebrities. In order to extract useful information from the growing, heterogeneous network structures, efficient querying techniques are required.

In this paper, which is an extension of [2], we focus on queries without nesting or paths of varying length, which corresponds to the problem of graph pattern matching. Existing solutions usually work by iteratively mapping elements from a query specification to elements in a host graph according to a search plan. Since the order in which the individual elements are mapped has a substantial impact on performance, many solutions employ sophisticated strategies for determining good search plans.

The majority of these techniques only considers structural information, that is, typing information and edges between nodes in the graph like relationships between persons in a social network, for guiding the matching process. However, in many realistic application scenarios, nonstructural information also plays an important role. This includes attributes of nodes like the age of a person in the network as well as external data structures such as indices, which are particularly relevant in the context of graph databases or the evaluation of decomposed queries [3]. Hence, a tighter integration of constraints specified over such nonstructural information into the matching process is desirable.

We therefore introduce a unified notion of constraints in a graph query. We then propose a general matching algorithm that is based on an existing dynamic technique [4], which allows the generation of a search plan on the fly as a query is being executed. On the one hand, the dynamic technique allows tailoring the search to heterogeneities in the host graph that cannot be handled by a static search plan. On the other hand, this approach has the drawback of not being able to consider the overall structure of the query, which can lead to shortsighted decisions during the matching process. To address this problem, we combine our adapted approach with a static but model-sensitive technique for search plan generation [5]. In addition to an analysis of its worst-case runtime complexity, the resulting hybrid approach is evaluated empirically using queries and datasets from the LDBC Social Network Benchmark [6]. Our analytical results confirm that the basic version of the hybrid technique has the same worst-case complexity as the considered static approach. However, our empirical results suggest that the hybrid technique may improve search efficiency in several cases, and rarely reduces efficiency.

Compared to [2], we have extended this paper by an analysis of the complexity of our algorithm in conjunction with an analytical evaluation of different strategies for search plan generation, facilitating a comparison to known subgraph isomorphism algorithms. Furthermore, we introduce two new variants of our hybrid approach for search plan generation. We consider these variants in an extended empirical evaluation, which now also includes a completely different static technique for search plan generation introduced in [7] and flat versions of the previously decomposed benchmark queries.

The remainder of the paper is structured as follows: Section 2 briefly introduces the basic notion of graphs, graph morphisms, and graph queries as used in this paper. We then present our generalised algorithm for graph pattern matching in Section 3 and give an overview of an existing static and a dynamic technique for search plan generation. In Section 4, we first integrate these strategies into a hybrid solution. Subsequently, several extensions and modifications of the resulting hybrid approach, such as a more sophisticated consideration of constraint checks during search plan generation, are outlined in Section 5. The developed concepts are evaluated analytically and empirically in Section 6, using a benchmark from the domain of social networks. Section 7 discusses related work and Section 8 concludes the paper.