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SPARQL 1.1 offers a type of navigational query for RDF systems, called regular path query (RPQ). A regular path query allows for retrieving node pairs with the paths between them satisfying regular expressions. Regular path queries are always difficult to be evaluated efficiently because of the possible large search space. Thus there has been no scalable and practical solution so far. In this paper, we present Leon+, an in-memory distributed framework, to address the RPQ problem in the context of the knowledge graph. To reduce search space and mitigate mounting communication costs, Leon+ takes advantage of join-ahead pruning via a novel RDF summarization technique together with a path partitioning strategy. We also develop a subtle cost model to devise query plans to achieve high efficiency for complex RPQs. As there has been no available RPQ benchmark, we create micro-benchmarks on both synthetic and real-world datasets. A thorough experimental evaluation is presented between our approach and the state-of-the-art RDF stores. The results show that our approach outperforms 5x faster than the competitors on single RPQ. For query workload, it saves up to 1/2 time and 2/3 communication overheads over the baseline method.

The existing literatures of the query processing on knowledge graphs focus on an exhaustive enumeration of all matches, which is time-consuming. Users are often interested in diversified top-k matches, rather than the entire match set. Motivated by these, this paper formalizes the diversified top-k querying (DTQ) problem in the context of RDF/SPARQL and proposes a diversification function to balance importance and diversity. We first prove that the decision problem of DTQ is NP-complete, and give a baseline algorithm with an approximation ratio of 2. Secondly, an index-based algorithm with the early termination property is proposed. The index is adept in parallel diversified top-k selection in multicore architectures. Using real-world and synthetic data, we experimentally verify that our algorithms are efficient and effective in computing meaningful diversified top-k matches.

As similar queries keep springing up in real query logs, few RDF systems address this problem. In this paper, we propose Leon, a distributed RDF system, which can also deal with multi-query problem. First, we apply a characteristic-set-based partitioning scheme. This scheme (i) supports the fully parallel processing of join within characteristic sets; (ii) minimizes data communication by applying direct transmission of intermediate results instead of broadcasting. Then, Leon revisits the classical problem of multi-query optimization in the context of RDF/SPARQL. In light of the NP-hardness of the multi-query optimization for SPARQL, we propose a heuristic algorithm that partitions the input batch of queries into groups, and discover the common sub-query of multiple SPARQL queries. Our MQO algorithm incorporates with a subtle cost model to generate execution plans.

Masses of large-scale knowledge graphs on various domains have sprung up in recent years. They are no longer able to be managed on a single machine. The distributed RDF systems intervene in the scalability issue using partitioning techniques. However, most of these systems are unaware of query workload and employ static partitioning. As diverse and dynamic workloads keep emerging in the knowledge graph applications, they cannot consistently provide good performance. To address the problem, we propose a workload-aware partitioning framework WISE, which could be deployed on any initial partitioning. It encodes the incoming SPARQL queries in a novel structure called query span and periodically examines the query span to identify the frequent query patterns. The triples of a frequent query pattern are moved to the same partition, aiming at improving the response time in the future. Our experiments on various RDF datasets and workloads indicate that WISE achieves dramatic communication reduction and considerable performance improvement over the baseline method. The migration overhead only accounts for a small portion of the total runtime.

Data cube is the foundation of on-line analytical processing (OLAP), which can provide users with data views from different perspectives and granularities. Heterogeneous information networks consist of multiple types of nodes and edges which represent different semantic relations. With the rapid development of social networks and knowledge graphs, heterogeneous information networks have become increasingly popular. In heterogeneous information networks, cube is the set of aggregate graphs and cube query is required for supporting OLAP. The existing research mainly studies aggregate graph query on homogeneous networks, but only considers the attributes of nodes. To overcome these challenges, this paper investigates cube query problem on heterogeneous information networks. (1) A novel cube model for heterogeneous information networks is proposed, which captures both the attribute and structure semantics. (2) Because the total number of aggregate graphs is huge, computing and storing them cost plenty of time and storage. The problem of partial cube materialization on heterogeneous information networks is investigated. Given a fixed size of memory space, select a subset of aggregate graphs in cube, to minimize the computing cost of the whole cube. This optimization problem is proved to be NP-complete and there is no $$n^{1-{\epsilon }}$$n1-∈ approximation algorithm unless P $$=$$= NP. (3) A greedy algorithm is proposed for partial cube materialization based on two interesting dependencies between aggregate graphs, attribute dependence and path dependence. (4) Experiments on real world data sets show the cube definition is meaningful, and the partial cube materialization algorithm is efficient.

The emerging non-volatile memory (NVM) technologies have attracted much attention due to its advantages over the existing DRAM technology such as non-volatility, byte-addressability and high storage density. These promising features make NVM a promising replacement of DRAM. Although the reading cost of NVM is close to that of DRAM, the writing cost is significantly higher than that of DRAM. Existing algorithms designed on DRAM treat read and write equally and thus are not applicable to NVM. In this paper, we investigate efficient algorithms for subgraph matching, a fundamental problem in graph databases, on NVM. We first give a detailed evaluation on several existing subgraph matching algorithms by experiments and theoretical analysis. Then, we propose our write-limited subgraph matching algorithm based on the analysis. We also extend our algorithm to answer subgraph matching on dynamic graphs. Experiments on an NVM simulator demonstrate a significant improvement in efficiency against the existing algorithms.

Uncertain graph data has been collected, processed and analyzed in a wide range of applications. Under the possible world model, an uncertain graph represents a probability distribution over all its possible worlds. Each possible world is a deterministic graph in which the uncertain graph may be present in practice. To deal with the hardness of computations on uncertain graphs, Parchas et al. first proposed the concept of a degree-based representative possible world. This approach is distinguished from the sampling approach in that it computes on one representative possible world instead of on a large number of possible worlds sampled at random. However, the degree-based representative possible world only tries to preserve vertex degrees. In this paper, we are motivated by the fact that motif structures such as triangles can affect the structural properties of graphs and propose the concept of a triangle-based representative possible world. We also develop an algorithm for finding the triangle-based representative possible world of an uncertain graph. We conducted extensive experimental evaluations and show that the triangle-based representative possible world outperforms the degree-based representative possible world in preserving the structural characteristics of an uncertain graph in expectation.

Frequent subgraph mining has been extensively studied on certain graph data. However, uncertainty is intrinsic in graph data in practice, but there is very few work on mining uncertain graph data. This paper focuses on mining frequent subgraphs over uncertain graph data under the probabilistic semantics. Specifically, a measure called $${\varphi}$$ -frequent probability is introduced to evaluate the degree of recurrence of subgraphs. Given a set of uncertain graphs and two real numbers $${0 < \varphi, \tau < 1}$$ , the goal is to quickly find all subgraphs with $${\varphi}$$ -frequent probability at least ?. Due to the NP-hardness of the problem and to the #P-hardness of computing the $${\varphi}$$ -frequent probability of a subgraph, an approximate mining algorithm is proposed to produce an $${(\varepsilon, \delta)}$$ -approximate set ? of "frequent subgraphs", where $${0 < \varepsilon < \tau}$$ is error tolerance, and 0 < ? < 1 is a confidence bound. The algorithm guarantees that (1) any frequent subgraph S is contained in ? with probability at least ((1 ? ?) /2) s , where s is the number of edges in S; (2) any infrequent subgraph with $${\varphi}$$ -frequent probability less than $${\tau - \varepsilon}$$ is contained in ? with probability at most ?/2. The theoretical analysis shows that to obtain any frequent subgraph with probability at least 1 ? Δ, the input parameter ? of the algorithm must be set to at most $${1 - 2 (1 - \Delta)^{1 / \ell_{\max}}}$$ , where 0 < Δ < 1, and ? max is the maximum number of edges in frequent subgraphs. Extensive experiments on real uncertain graph data verify that the proposed algorithm is practically efficient and has very high approximation quality. Moreover, the difference between the probabilistic semantics and the expected semantics on mining frequent subgraphs over uncertain graph data has been discussed in this paper for the first time.

Frequent subgraph mining has been extensively studied on certain graph data. However, uncertainties are inherently accompanied with graph data in practice, and there is very few work on mining uncertain graph data. This paper investigates frequent subgraph mining on uncertain graphs under probabilistic semantics. Specifically, a measure called φ-frequent probability is introduced to evaluate the degree of recurrence of subgraphs. Given a set of uncertain graphs and two numbers 0 S with probability at least (1 - δ/2)s, where s is the number of edges of S. In addition, it is thoroughly discussed how to set δ to guarantee the overall approximation quality of the algorithm. The extensive experiments on real uncertain graph data verify that the algorithm is efficient and that the mining results have very high quality.

Graph data are subject to uncertainties in many applications due to incompleteness and imprecision of data. Mining uncertain graph data is semantically different from and computationally more challenging than mining exact graph data. This paper investigates the problem of mining frequent subgraph patterns from uncertain graph data. The frequent subgraph pattern mining problem is formalized by designing a new measure called expected support. An approximate mining algorithm is proposed to find an approximate set of frequent subgraph patterns by allowing an error tolerance on the expected supports of the discovered subgraph patterns. The algorithm uses an efficient approximation algorithm to determine whether a subgraph pattern can be output or not. The analytical and experimental results show that the algorithm is very efficient, accurate and scalable for large uncertain graph databases.

In recent years, large amount of data modeled by graphs, namely graph data, have been collected in various domains. Efficiently processing queries on graph databases has attracted a lot of research attentions. Supergraph query is a kind of new and important queries in practice. A supergraph query, q, on a graph database D is to retrieve all graphs in D such that q is a supergraph of them. Because the number of graphs in databases is large and subgraph isomorphism testing is NP-complete, efficiently processing such queries is a big challenge. This paper first proposes an optimal compact method for organizing graph databases. Common subgraphs of the graphs in a database are stored only once in the compact organization of the database, in order to reduce the overall cost of subgraph isomorphism testings from stored graphs to queries during query processing. Then, an exact algorithm and an approximate algorithm for generating significant feature set with optimal order are proposed to construct indices on graph databases. The optimal order on the feature set is to reduce the number of subgraph isomorphism testings during query processing. Based on the compact organization of graph databases, a novel algorithm of testing subgraph isomorphisms from multiple graphs to one graph is presented. Finally, based on all these techniques, a query processing method is proposed. Analytical and experimental results show that the proposed algorithms outper-form the existing similar algorithms by one to two orders of magnitude.