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1. Distributed Top-k Subgraph Matching in A Big Graph

   Jianliang Gao, Chuqi Lei ( October 2018 , IEEE International Conference on Big Data)

   Subgraph matching query is to find out the subgraphs of data graph G which match a given query graph Q. Traditional methods can not deal with big data graphs due to their high computational complex. In this paper, we propose a distributed top-k subgraph search method over big graphs. The proposed method is designed at the level of single vertex and all vertices obtain their matching state separately without requiring global graph information. Therefore, it can be easily deployed in distributed platform like Hadoop. The evaluations of running time, number of messages and supersteps show the efficiency and scalability of the proposed method. 

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2. Neural-Answering Logical Queries on Knowledge Graphs

   https://doi.org/10.1145/3447548.3467375  

   Liu, Lihui ; Du, Boxin ; Ji, Heng ; Zhai, ChengXiang ; Tong, Hanghang ( July 2021 , KDD)

   null (Ed.)

   Logical queries constitute an important subset of questions posed in knowledge graph question answering systems. Yet, effectively answering logical queries on large knowledge graphs remains a highly challenging problem. Traditional subgraph matching based methods might suffer from the noise and incompleteness of the underlying knowledge graph, often with a prolonged online response time. Recently, an alternative type of method has emerged whose key idea is to embed knowledge graph entities and the query in an embedding space so that the embedding of answer entities is close to that of the query. Compared with subgraph matching based methods, it can better handle the noisy or missing information in knowledge graph, with a faster online response. Promising as it might be, several fundamental limitations still exist, including the linear transformation assumption for modeling relations and the inability to answer complex queries with multiple variable nodes. In this paper, we propose an embedding based method (NewLook) to address these limitations. Our proposed method offers three major advantages. First (Applicability), it supports four types of logical operations and can answer queries with multiple variable nodes. Second (Effectiveness), the proposed NewLook goes beyond the linear transformation assumption, and thus consistently outperforms the existing methods. Third (Efficiency), compared with subgraph matching based methods, NewLook is at least 3 times faster in answering the queries; compared with the existing embed-ding based methods, NewLook bears a comparable or even faster online response and offline training time. 

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3. Efficient Exact Subgraph Matching via GNN-based Path Dominance Embedding

   Ye, Y ; Lian, X ; Chen, M ( August 2024 , Proceedings of the International Conference on Very Large Data Bases)

   The classic problem of exact subgraph matching returns those subgraphs in a large-scale data graph that are isomorphic to a given query graph, which has gained increasing importance in many real-world applications such as social network analysis, knowledge graph discovery in the Semantic Web, bibliographical network mining, and so on. In this paper, we propose a novel and effective graph neural network (GNN)-based path embedding framework (GNN-PE), which allows efficient exact subgraph matching without introducing false dismissals. Unlike traditional GNN-based graph embeddings that only produce approximate subgraph matching results, in this paper, we carefully devise GNN-based embeddings for paths, such that: if two paths (and 1-hop neighbors of vertices on them) have the subgraph relationship, their corresponding GNN-based embedding vectors will strictly follow the dominance relationship. With such a newly designed property of path dominance embeddings, we are able to propose effective pruning strategies based on path label/dominance embeddings and guarantee no false dismissals for subgraph matching. We build multidimensional indexes over path embedding vectors, and develop an efficient subgraph matching algorithm by traversing indexes over graph partitions in parallel and applying our pruning methods. We also propose a cost-model-based query plan that obtains query paths from the query graph with low query cost. Through extensive experiments, we confirm the efficiency and effectiveness of our proposed GNN-PE approach for exact subgraph matching on both real and synthetic graph data. 

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4. G-Finder: Approximate Attributed Subgraph Matching

   https://doi.org/10.1109/BigData47090.2019.9006525  

   Liu, Lihui ; Du, Boxin ; xu, Jiejun ; Tong, Hanghang ( December 2019 , BigData)

   Subgraph matching is a core primitive across a number of disciplines, ranging from data mining, databases, information retrieval, computer vision to natural language processing. Despite decades of efforts, it is still highly challenging to balance between the matching accuracy and the computational efficiency, especially when the query graph and/or the data graph are large. In this paper, we propose an index-based algorithm (G-FINDER) to find the top-k approximate matching subgraphs. At the heart of the proposed algorithm are two techniques, including (1) a novel auxiliary data structure (LOOKUP-TABLE) in conjunction with a neighborhood expansion method to effectively and efficiently index candidate vertices, and (2) a dynamic filtering and refinement strategy to prune the false candidates at an early stage. The proposed G-FINDER bears some distinctive features, including (1) generality, being able to handle different types of inexact matching (e.g., missing nodes, missing edges, intermediate vertices) on node attributed and/or edge attributed graphs or multigraphs; (2) effectiveness, achieving up to 30% F1-Score improvement over the best known competitor; and (3) efficiency, scaling near-linearly w.r.t. the size of the data graph as well as the query graph. 

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5. FIRST: Fast Interactive Attributed Subgraph Matching

   https://doi.org/10.1145/3097983.3098040  

   Du, Boxin ; Zhang, Si ; Cao, Nan ; Tong, Hanghang ( August 2017 , KDD)

   Attributed subgraph matching is a powerful tool for explorative mining of large attributed networks. In many applications (e.g., network science of teams, intelligence analysis, finance informatics), the user might not know what exactly s/he is looking for, and thus require the user to constantly revise the initial query graph based on what s/he finds from the current matching results. A major bottleneck in such an interactive matching scenario is the efficiency, as simply rerunning the matching algorithm on the revised query graph is computationally prohibitive. In this paper, we propose a family of effective and efficient algorithms (FIRST) to support interactive attributed subgraph matching. There are two key ideas behind the proposed methods. The first is to recast the attributed subgraph matching problem as a cross-network node similarity problem, whose major computation lies in solving a Sylvester equation for the query graph and the underlying data graph. The second key idea is to explore the smoothness between the initial and revised queries, which allows us to solve the new/updated Sylvester equation incrementally, without re-solving it from scratch. Experimental results show that our method can achieve (1) up to 16x speed-up when applying on networks with 6M$+$ nodes; (2) preserving more than 90% accuracy compared with existing methods; and (3) scales linearly with respect to the size of the data graph. 

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