Graph pattern matching is typically defined in terms of subgraph isomorphism, which makes it an np-complete problem. Moreover, it requires bijective functions, which are often too restrictive to characterize patterns in emerging applications. We propose a class of graph patterns, in which an edge denotes the connectivity in a data graph within a predefined number of hops. In addition, we define matching based on a notion of bounded simulation, an extension of graph simulation. We show that with this revision, graph pattern matching can be performed in cubic-time, by providing such an algorithm. We also develop algorithms for incrementally finding matches when data graphs are updated, with performance guarantees for dag patterns. We experimentally verify that these algorithms scale well, and that the revised notion of graph pattern matching allows us to identify communities commonly found in real-world networks.

Graph Pattern Matching.

With the rapid development of information technologies, various big graphs are prevalent in many real applications (e.g., social media and knowledge bases). An important component of these graphs is the network community. Essentially, a community is a group of vertices which are densely connected internally. Community retrieval can be used in many real applications, such as event organization, friend recommendation, and so on. Consequently, how to efficiently find high-quality communities from big graphs is an important research topic in the era of big data. Recently, a large group of research works, called community search, have been proposed. They aim to provide efficient solutions for searching high-quality communities from large networks in real time. Nevertheless, these works focus on different types of graphs and formulate communities in different manners, and thus, it is desirable to have a comprehensive review of these works. In this survey, we conduct a thorough review of existing community search works. Moreover, we analyze and compare the quality of communities under their models, and the performance of different solutions. Furthermore, we point out new research directions. This survey does not only help researchers to have better understanding of existing community search solutions, but also provides practitioners a better judgment on choosing the proper solutions.

A survey of community search over big graphs

RDF knowledge graphs have attracted increasing attentions these years. However, due to the schema-free nature of RDF data, it is very difficult for users to have full knowledge of the underlying schema. Furthermore, the same kind of information can be represented in diverse graph fragments. Hence, it is a huge challenge to formulate complex SPARQL expressions by taking the union of all possible structures.In this paper, we propose an effective framework to access the RDF repository even if users have no full knowledge of the underlying schema. Specifically, given a SPARQL query, the system could return as more answers that match the query based on the semantic similarity as possible. Interestingly, we propose a systematic method to mine diverse semantically equivalent structure patterns. More importantly, incorporating both structural and semantic similarities we are the first to propose a novel similarity measure, semantic graph edit distance. In order to improve the efficiency performance, we apply the semantic summary graph to summarize the knowledge graph, which supports both high-level pruning and drill-down pruning. We also devise an effective lower bound based on the TA-style access to each of the candidate sets. Extensive experiments over real datasets confirm the effectiveness and efficiency of our approach.

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Semantic SPARQL similarity search over RDF knowledge graphs

A graph is a fundamental and general data structure underlying all data applications. Many applications today call for the management and query capabilities directly on graphs. Real time graph streams, as seen in road networks, social and communication networks, and web requests, are such applications. Event pattern matching requires the awareness of graph structures, which is different from traditional complex event processing. It also requires a focus on the dynamicity of the graph, time order constraints in patterns, and online query processing, which deviates significantly from previous work on subgraph matching as well. We study the semantics and efficient online algorithms for this important and intriguing problem, and evaluate our approaches with extensive experiments over real world datasets in four different domains.

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Event pattern matching over graph streams

In the real world, various systems can be modeled using heterogeneous networks which consist of entities of different types. Many problems on such networks can be mapped to an underlying critical problem of discovering top-K subgraphs of entities with rare and surprising associations. Answering such subgraph queries efficiently involves two main challenges: (1) computing all matching subgraphs which satisfy the query and (2) ranking such results based on the rarity and the interestingness of the associations among entities in the subgraphs. Previous work on the matching problem can be harnessed for a naive ranking-after-matching solution. However, for large graphs, subgraph queries may have enormous number of matches, and so it is inefficient to compute all matches when only the top-K matches are desired. In this paper, we address the two challenges of matching and ranking in top-K subgraph discovery as follows. First, we introduce two index structures for the network: topology index, and graph maximum metapath weight index, which are both computed offline. Second, we propose novel top-K mechanisms to exploit these indexes for answering interesting subgraph queries online efficiently. Experimental results on several synthetic datasets and the DBLP and Wikipedia datasets containing thousands of entities show the efficiency and the effectiveness of the proposed approach in computing interesting subgraphs.

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Top-K interesting subgraph discovery in information networks

There exist many graph-based applications including bioinformatics, social science, link analysis, citation analysis, and collaborative work. All need to deal with a large data graph. Given a large data graph, in this paper, we study finding top-k answers for a graph pattern query (kGPM), and in particular, we focus on top-k cyclic graph queries where a graph query is cyclic and can be complex. The capability of supporting kGPM provides much more flexibility for a user to search graphs. And the problem itself is challenging. In this paper, we propose a new framework of processing kGPM with on-the-fly ranked lists based on spanning trees of the cyclic graph query. We observe a multidimensional representation for using multiple ranked lists to answer a given kGPM query. Under this representation, we propose a cost model to estimate the least number of tree answers to be consumed in each ranked list for a given kGPM query. This leads to a query optimization approach for kGPM processing, and a top-k algorithm to process kGPM with the optimal query plan. We conducted extensive performance studies using a synthetic dataset and a real dataset, and we confirm the efficiency of our proposed approach.

Top-k graph pattern matching over large graphs

There exist many graph-based applications including bioinformatics, social science, link analysis, citation analysis, and collaborative work. All need to deal with a large data graph. Given a large data graph, in this paper, we study finding top-k answers for a graph query, and in particular, we focus on top-k cyclic graph queries where a graph query is cyclic and can be complex. The capability of supporting top-k cyclic graph queries over a data graph provides much more flexibility for a user to search graphs. And the problem itself is challenging. After investigating a direct yet infeasible solution, we propose a new twig query approach. In our approach, we first identify a spanning tree of the cyclic graph query, which is used to generate a list of ranked twig answers on-demand. Then we identify the top-k answers for the graph query based on the twig answer list. In order to find the best twig query in solving a given cyclic graph query, cost-based optimization for twig query selection is studied. We conducted extensive performance studies using a real dataset, and we report our findings in this paper.

Xianggang Zeng

Papers

Top-k graph pattern matching over large graphs

Top-K Graph Pattern Matching: A Twig Query Approach