The recent ISO SQL:2023 standard adopts SQL/PGQ (Property Graph Queries), facilitating graph-like querying within relational databases. This advancement, however, underscores a significant gap in how to effectively optimize SQL/PGQ queries within relational database systems. To address this gap, we extend the foundational SPJ (Select-Project-Join) queries to SPJM queries, which include an additional matching operator for representing graph pattern matching in SQL/PGQ. Although SPJM queries can be converted to SPJ queries and optimized using existing relational query optimizers, our analysis shows that such a graph-agnostic method fails to benefit from graph-specific optimization techniques found in the literature. To address this issue, we develop a converged relational-graph optimization framework called RelGo for optimizing SPJM queries, leveraging joint efforts from both relational and graph query optimizations. Using DuckDB as the underlying relational execution engine, our experiments show that RelGo can generate efficient execution plans for SPJM queries. On well-established benchmarks, these plans exhibit an average speedup of 21.90x compared to those produced by the graph-agnostic optimizer.

Abstract Maximum biclique search, which finds the biclique with the maximum number of edges in a bipartite graph, is a fundamental problem with a wide spectrum of applications in different domains, such as E-Commerce, social analysis, web services, and bioinformatics. Unfortunately, due to the difficulty of the problem in graph theory, no practical solution has been proposed to solve the issue in large-scale real-world datasets. Existing techniques for maximum clique search on a general graph cannot be applied because the search objective of maximum biclique search is two-dimensional, i.e., we have to consider the size of both parts of the biclique simultaneously. In this paper, we divide the problem into several subproblems each of which is specified using two parameters. These subproblems are derived in a progressive manner, and in each subproblem, we can restrict the search in a very small part of the original bipartite graph. We prove that a logarithmic number of subproblems is enough to guarantee the algorithm correctness. To minimize the computational cost, we show how to reduce significantly the bipartite graph size for each subproblem while preserving the maximum biclique satisfying certain constraints by exploring the properties of one-hop and two-hop neighbors for each vertex. Furthermore, we study the diversified top-kbiclique search problem which aims to findkmaximal bicliques that cover the most edges in total. The basic idea is to repeatedly find the maximum biclique in the bipartite graph and remove it from the bipartite graphktimes. We design an efficient algorithm that considers to share the computation cost among thekresults, based on the idea of deriving the same subproblems of different results. We further propose two optimizations to accelerate the computation by pruning the search space with size constraint and refining the candidates in a lazy manner. We use several real datasets from various application domains, one of which contains over 300 million vertices and 1.3 billion edges, to demonstrate the high efficiency and scalability of our proposed solution. It is reported that 50% improvement on recall can be achieved after applying our method in Alibaba Group to identify the fraudulent transactions in their e-commerce networks. This further demonstrates the usefulness of our techniques in practice.

Maximum biclique search, which finds the biclique with the maximum number of edges in a bipartite graph, is a fundamental problem with a wide spectrum of applications in different domains, such as E-Commerce, social analysis, web services, and bioinformatics. Unfortunately, due to the difficulty of the problem in graph theory, no practical solution has been proposed to solve the issue in large-scale real-world datasets. Existing techniques for maximum clique search on a general graph cannot be applied because the search objective of maximum biclique search is two-dimensional, i.e., we have to consider the size of both parts of the biclique simultaneously. In this paper, we divide the problem into several subproblems each of which is specified using two parameters. These subproblems are derived in a progressive manner, and in each subproblem we can restrict the search in a very small part of the original bipartite graph. We prove that a logarithmic number of subproblems is enough to guarantee the algorithm correctness. To minimize the computational cost, we show how to reduce significantly the bipartite graph size for each subproblem while preserving the maximum biclique satisfying certain constraints by exploring the properties of one-hop and two-hop neighbors for each vertex. We use several real datasets from various application domains, one of which contains over 300 million vertices and 1.3 billion edges, to demonstrate the high efficiency and scalability of our proposed solution. It is reported that 50% improvement on recall can be achieved after applying our method in Alibaba Group to identify the fraudulent transactions in their e-commerce networks. This further demonstrates the usefulness of our techniques in practice.

Supergraph search is a fundamental problem in graph databases that is widely applied in many application scenarios. Given a graph database and a query-graph, supergraph search retrieves all data-graphs contained in the query-graph from the graph database. Most existing solutions for supergraph search follow the pruning-and-verification framework, which prune false answers based on features in the pruning phase and perform subgraph isomorphism testings on the remaining graphs in the verification phase. However, they are not scalable to handle large-sized data-graphs and query-graphs due to three drawbacks. First, they rely on a frequent subgraph mining algorithm to select features which is expensive and cannot generate large features. Second, they require a costly verification phase. Third, they process features in a fixed order without considering their relationships to the query-graph. In this paper, we address the three drawbacks and propose new indexing and query processing algorithms. In indexing, we select features directly from the data-graphs without expensive frequent subgraph mining. The features form a feature-tree that contains all-sized features and both the cost sharing and pruning power of the features are considered. In query processing, we propose a new algorithm, where the order to process features is query-dependent by considering both the cost sharing and the pruning power. We explore two optimization strategies to further improve the algorithm efficiency. The first strategy applies a lightweight graph compression technique and the second strategy optimizes the inclusion of answers. We further introduce how to efficiently maintain the index incrementally when the graph database is updated dynamically. Moreover, we propose an approximation approach to significantly reduce the computational cost for large data-graphs and/or query-graphs while preserving a high result quality. Finally, we conduct extensive performance studies on two real large datasets to demonstrate the efficiency and effectiveness of our algorithms.

Supergraph search is a fundamental problem in graph databases that is widely applied in many application scenarios. Given a graph database and a query-graph, supergraph search retrieves all data-graphs contained in the query-graph from the graph database. Most existing solutions for supergraph search follow the pruning-and-verification framework, which prunes false answers based on features in the pruning phase and performs subgraph isomorphism testings on the remaining graphs in the verification phase. However, they are not scalable to handle large-sized data-graphs and query-graphs due to three drawbacks. First, they rely on a frequent subgraph mining algorithm to select features which is expensive and cannot generate large features. Second, they require a costly verification phase. Third, they process features in a fixed order without considering their relationship to the query-graph. In this paper, we address the three drawbacks and propose new indexing and query processing algorithms. In indexing, we select features directly from the data-graphs without expensive frequent subgraph mining. The features form a feature-tree that contains all-sized features and both the cost sharing and pruning power of the features are considered. In query processing, we propose a verification-free algorithm, where the order to process features is query-dependent by considering both the cost sharing and the pruning power. We explore two optimization strategies to further improve the algorithm efficiency. The first strategy applies a lightweight graph compression technique and the second strategy optimizes the inclusion of answers. Finally, we conduct extensive performance studies on two real large datasets to demonstrate the high scalability of our algorithms.