You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Resource Description Framework (RDF) has been widely used to represent information on the web, while SPARQL is a standard query language to manipulate RDF data. Given a SPARQL query, there often exist many joins which are the bottlenecks of efficiency of query processing. Besides, the real RDF datasets often reveal strong data sparsity, which indicates that a resource often only relates to a few resources even the number of total resources is large. In this paper, we propose a sparse matrix-based (SM-based) SPARQL query processing approach over RDF datasets which con- siders both join optimization and data sparsity. Firstly, we present a SM-based storage for RDF datasets to lift the storage efficiency, where valid edges are stored only, and then introduce a predicate- based hash index on the storage. Secondly, we develop a scalable SM-based join algorithm for SPARQL query processing. Finally, we analyze the overall cost by accumulating all intermediate results and design a query plan generated algorithm. Besides, we extend our SM-based join algorithm on GPU for parallelizing SPARQL query processing. We have evaluated our approach compared with the state-of-the-art RDF engines over benchmark RDF datasets and the experimental results show that our proposal can significantly improve SPARQL query processing with high scalability.

Cited Abstract(s):
[1]: RDF data are used to model knowledge in various areas such as life sciences, Semantic Web, bioinformatics, and social graphs. The size of real RDF data reaches billions of triples. This calls for a framework for efficiently processing RDF data. The core function of processing RDF data is subgraph pattern matching. There have been two completely different directions for supporting efficient subgraph pattern matching. One direction is to develop specialized RDF query processing engines exploiting the properties of RDF data for the last decade, while the other direction is to develop efficient subgraph isomorphism algorithms for general, labeled graphs for over 30 years. Although both directions have a similar goal (i.e., finding subgraphs in data graphs for a given query graph), they have been independently researched without clear reason. We argue that a subgraph isomorphism algorithm can be easily modified to handle the graph homomorphism, which is the RDF pattern matching semantics, by just removing the injectivity constraint. In this paper, based on the state-of-the-art subgraph isomorphism algorithm, we propose an in-memory solution, TurboHOM++, which is tamed for the RDF processing, and we compare it with the representative RDF processing engines for several RDF benchmarks in a server machine where billions of triples can be loaded in memory. In order to speed up TurboHOM++, we also provide a simple yet effective transformation and a series of optimization techniques. Extensive experiments using several RDF benchmarks show that TurboHOM++ consistently and significantly outperforms the representative RDF engines. Specifically, TurboHOM++ outperforms its competitors by up to five orders of magnitude.

[2]: The proliferation of semantic data on the Web requires RDF database systems to constantly improve their scalability and transactional efficiency. At the same time, users are increasingly interested in investigating or visualizing large collections of online data by performing complex analytic queries. This paper introduces a novel database system for RDF data management called dipLODocus[RDF], which supports both transactional and analytical queries efficiently. dipLODocus[RDF] takes advantage of a new hybrid storage model for RDF data based on recurring graph patterns. In this paper, we describe the general architecture of our system and compare its performance to state-of-the-art solutions for both transactional and analytic workloads.

[3]: Given a query graph q and a data graph g, the subgraph isomorphism search finds all occurrences of q in g and is considered one of the most fundamental query types for many real applications. While this problem belongs to NP-hard, many algorithms have been proposed to solve it in a reasonable time for real datasets. However, a recent study has shown, through an extensive benchmark with various real datasets, that all existing algorithms have serious problems in their matching order selection. Furthermore, all algorithms blindly permutate all possible mappings for query vertices, often leading to useless computations. In this paper, we present an efficient and robust subgraph search solution, called TurboISO, which is turbo-charged with two novel concepts, candidate region exploration and the combine and permute strategy (in short, Comb Perm). The candidate region exploration identifies on-the-fly candidate subgraphs (i.e, candidate regions), which contain embeddings, and computes a robust matching order for each candidate region explored. The Comb Perm strategy exploits the novel concept of the neighborhood equivalence class (NEC). Each query vertex in the same NEC has identically matching data vertices. During subgraph isomorphism search, Comb Perm generates only combinations for each NEC instead of permutating all possible enumerations. Thus, if a chosen combination is determined to not contribute to a complete solution, all possible permutations for that combination will be safely pruned. Extensive experiments with many real datasets show that TurboISO consistently and significantly outperforms all competitors by up to several orders of magnitude.

[4]: We address efficient processing of SPARQL queries over RDF datasets. The proposed techniques, incorporated into the gStore system, handle, in a uniform and scalable manner, SPARQL queries with wildcards and aggregate operators over dynamic RDF datasets. Our approach is graph based. We store RDF data as a large graph and also represent a SPARQL query as a query graph. Thus, the query answering problem is converted into a subgraph matching problem. To achieve efficient and scalable query processing, we develop an index, together with effective pruning rules and efficient search algorithms. We propose techniques that use this infrastructure to answer aggregation queries. We also propose an effective maintenance algorithm to handle online updates over RDF repositories. Extensive experiments confirm the efficiency and effectiveness of our solutions.

[5]: RDF is a standard for the conceptual description of knowledge , and SPARQL is the query language conceived to query RDF data. The RDF data is cherished and exploited by various domains such as life sciences, Semantic Web, social network, etc. Further, its integration at Web-scale compels RDF management engines to deal with complex queries in terms of both size and structure. In this paper, we propose AMbER (Attributed Multigraph Based Engine for RDF querying), a novel RDF query engine specifically designed to optimize the computation of complex queries. AMbER leverages subgraph matching techniques and extends them to tackle the SPARQL query problem. First of all RDF data is represented as a multigraph, and then novel indexing structures are established to efficiently access the information from the multigraph. Finally a SPARQL query is represented as a multigraph, and the SPARQL querying problem is reduced to the subgraph homomorphism problem. AMbER exploits structural properties of the query multigraph as well as the proposed indexes, in order to tackle the problem of subgraph homomorphism. The performance of AMbER, in comparison with state-of-the-art systems, has been extensively evaluated over several RDF benchmarks. The advantages of employing AMbER for complex SPARQL queries have been experimentally validated.

[6]: Due to the increasing use of RDF data, efficient processing of SPARQL queries over RDF datasets has become an important issue. However, existing solutions suffer from two limitations: 1) they cannot answer SPARQL queries with wildcards in a scalable manner; and 2) they cannot handle frequent updates in RDF repositories efficiently. Thus, most of them have to reprocess the dataset from scratch. In this paper, we propose a graph-based approach to store and query RDF data. Rather than mapping RDF triples into a relational database as most existing methods do, we store RDF data as a large graph. A SPARQL query is then converted into a corresponding subgraph matching query. In order to speed up query processing, we develop a novel index, together with some effective pruning rules and efficient search algorithms. Our method can answer exact SPARQL queries and queries with wildcards in a uniform manner. We also propose an effective maintenance algorithm to handle online updates over RDF repositories. Extensive experiments confirm the efficiency and effectiveness of our solution.
Recently, a number of graph-based approaches were proposed to store RDF triples in graph models, such as gStore [6] [4] , dipLODocus @math [2] , Turbo @math and AMBER [5] . These graph-based approaches typically see SPARQL query processing as subgraph matching, which help reserve and query semantic information. gStore [6] [4] maps all predicates and predicate values to binary bit strings which are then organized as a VS*-tree. Since every layer of VS*-tree is a summary of the whole RDF graph, gStore has capacity to process SPARQL query efficiently. dipLODocus @math starts by a mixed storage considering both graph structure of RDF data and requirement of data analysis, in order to find molecule clusters and help accelerate queries through clustering related data. Turbo @math [1] develops TurboISO [3] by transforming RDF graphs into normal data graphs while AMBER [5] represents RDF data and SPARQL query as multigraphs.