Spectral Decomposition for Optimal Graph Index Prediction

Graph databases supporting retrieval based on structural similarity utilize structure indexes. A structure index is a data structure that indexes different structural features of member graphs. These features are typically extracted at insertion time. However, as the extraction of structural features may suffer from combinatorial explosion, the structure index takes long insertion time and large disk space. The member graphs cannot be modified, since even a simple structural modification may require re-extraction of structural features. The depth to which structural features were extracted during insertion, forms a hard limit on query precision, which cannot be changed at query time. In order to address these issues, a new model is introduced that combines the database graph storage and the structure index into one data structure. There is no need to extract structural features at insertion time, no hard limit on query refinement and graph modifications are supported naturally.

Proceedings of the VLDB Endowment, 2015

Graph data management systems have become very popular as graphs are the natural data model for many applications. One of the main problems addressed by these systems is subgraph query processing; i.e., given a query graph, return all graphs that contain the query. The naive method for processing such queries is to perform a subgraph isomorphism test against each graph in the dataset. This obviously does not scale, as subgraph isomorphism is NP-Complete. Thus, many indexing methods have been proposed to reduce the number of candidate graphs that have to underpass the subgraph isomorphism test. In this paper, we identify a set of key factors-parameters, that influence the performance of related methods: namely, the number of nodes per graph, the graph density, the number of distinct labels, the number of graphs in the dataset, and the query graph size. We then conduct comprehensive and systematic experiments that analyze the sensitivity of the various methods on the values of the key parameters. Our aims are twofold: first to derive conclusions about the algorithms' relative performance, and, second, to stress-test all algorithms, deriving insights as to their scalability, and highlight how both performance and scalability depend on the above factors. We choose six wellestablished indexing methods, namely Grapes, CT-Index, GraphGrepSX, gIndex, Tree+∆, and gCode, as representative approaches of the overall design space, including the most recent and best performing methods. We report on their index construction time and index size, and on query processing performance in terms of time and false positive ratio. We employ both real and synthetic datasets. Specifically, four real datasets of different characteristics are used: AIDS, PDBS, PCM, and PPI. In addition, we generate a large number of synthetic graph datasets, empowering us to systematically study the algorithms' performance and scalability versus the aforementioned key parameters.

Lecture Notes in Computer Science

Graph is an important data structure to model complex structural data, such as chemical compounds, proteins, and XML documents. Among many graph data-based applications, sub-graph search is a key problem, which is defined as given a query Q, retrieving all graphs containing Q as a sub-graph in the graph database. Most existing sub-graph search methods try to filter out false positives (graphs that are not possible in the results) as many as possible by indexing some frequent sub-structures in graph database, such as [20, 22, 4, 23]. However, due to ignoring the relationships between sub-structures, these methods still admit a high percentage of false positives. In this paper, we propose a novel concept, Summarization Graph, which is a complete graph and captures most topology information of the original graph, such as sub-structures and their relationships. Based on Summarization Graphs, we convert the filtering problem into retrieving objects with set-valued attributes. Moreover, we build an efficient signature file-based index to improve the filtering process. We prove theoretically that the pruning power of our method is larger than existing structure-based approaches. Finally, we show by extensive experimental study on real and synthetic data sets that the size of candidate set generated by Summarization Graph-based approach is only about 50% of that left by existing graph indexing methods, and the total response time of our method is reduced 2-10 times.

International Journal on Semantic Web and Information Systems, 2015

Querying large data graphs has brought the attention of the research community. Many solutions were pro- posed, such as Oracle Semantic Technologies, Virtuoso, RDF3X, and C-Store, among others. Although such approaches have shown good performance in queries with medium complexity, they perform poorly when the complexity of the queries increases. In this paper, the authors propose the Graph Signature Index, a novel and scalable approach to index and query large data graphs. The idea is that they summarize a graph and instead of executing the query on the original graph, they execute it on the summaries. The authors’ experi- ments with Yago (16M triples) have shown that e.g., a query with 4 levels costs 62 sec using Oracle but it only costs about 0.6 sec with their index. Their index can be implemented on top of any Graph database, but they chose to implement it as an extension to Oracle on top of the SEM_MATCH table function. The paper also introduces disk-based versions of the Trace Equivalence and Bisimilarity algorithms to summarize data graphs, and discusses their complexity and usability for RDF graphs.

… on Management of …, 2005

Graph databases are gaining importance in several emerging applications, especially molecular biology. In many existing approaches, such databases are regarded as a "schemaless" collection of labeled graphs. However, there are often user-defined schemes that help in limiting the search space while answering a query and to deliver meaningful results. Techniques based only on index structures do not exploit such situations. This paper presents our work on a graph database system called GRACE, where a Data Manipulation Language (DML) called Safari is proposed for graph databases and is closely integrated with structural indexes in the DBMS. Users may define schematic structures over a subset of graphs in the database and add them into the database as any other member graphs. The query model in turn can use such member graphs to define its search space in order to deliver more meaningful results. Queries can be composed, so that schemas defining search spaces can be generated dynamically. An augmenting index structure called labeled walk index (LWI) is also proposed that is extensively used for answering structural queries in Safari.

2003

To facilitate queries over semi-structured data, various structural summaries have been proposed. Structural summaries are derived directly from the data and serve as indices for evaluating path expressions on semi-structured or XML data. We introduce the D(k) index, an adaptive structural summary for general graph structured documents. Building on previous work, 1-index and A(k) index, the D(k)-index is also based on the concept of bisimilarity. However, as a generalization of the 1-index and A(k)-index, the D(k) index possesses the adaptive ability to adjust its structure according to the current query load. This dynamism also facilitates efficient update algorithms, which are crucial to practical applications of structural indices, but have not been adequately addressed in previous index proposals. Our experiments show that the D(k) index is a more effective structural summary than previous static ones, as a result of its query load sensitivity. In addition, update operations on the D(k) index can be performed more efficiently than on its predecessors.

… of IASTED Int'l Conf. on …, 2002

This paper addresses the problem of retrieval from graph databases. Graph databases store graph structures in- stead of tables. Typically, graph databases are appli- cable in domains that require storage and retrieval of structural information. One of the main issues in graph databases is retrieval of member graphs based on struc- ture matching. Structure matching of graphs is a known

2017

Graphs are widely used to model complicated structures and link them with each other. Some of such structures are XML documents, social networks, and computer networks. Information and model extraction from graph databases is a graph mining process. Efficient query search in graph databases, known as query processing, is one of the heated debates in the field of graph mining. One of the query processing techniques is sequential search over the whole dataset and isomorphism test on all sub-graphs in the database, which is not an optimal technique as to response time and storage. This problem brought in the issues of indexing graph databases to improve query processing performance. As the method implies, part of the database where the answer is expected to be found there is pruned and the number of needed isomorphism tests decreases. It might not be easy to compare the methods and techniques of graph query techniques as different techniques have different objectives. For instance, similarity search techniques reduce query time, while they cannot compete with exact matching techniques as to accuracy and vice versa. Input data volume might be also effective on query time as with immense datasets, similarity search techniques are more preferred than exact matching techniques. The present study is a survey of graph query processing techniques with emphasis on similarity search and exact matching.

International Journal of Database Management Systems, 2016

Graph databases (GDB) have recently been arisen to overcome the limits of traditional databases for storing and managing data with graph-like structure. Today, they represent a requirementfor many applications that manage graph-like data,like social networks.Most of the techniques, applied to optimize queries in graph databases, have been used in traditional databases, distribution systems,… or they are inspired from graph theory. However, their reuse in graph databases should take care of the main characteristics of graph databases, such as dynamic structure, highly interconnected data, and ability to efficiently access data relationships. In this paper, we survey the query optimization techniques in graph databases. In particular,we focus on the features they have introduced to improve querying graph-like data.

Proceedings of the 21st ACM international conference on Information and knowledge management, 2012

We study a new type of graph queries, which injectively maps its edges to paths of the graphs in a given database, where the length of each path is constrained by a given threshold specified by the weight of the corresponding matching edge. We give important applications of the new graph query and identify new challenges of processing such a query. Then, we devise the cost model of the branchand-bound algorithm framework for processing the graph query, and propose an efficient algorithm to minimize the cost overhead. We also develop three indexing techniques to efficiently answer the queries online. Finally, we verify the efficiency of our proposed indexes with extensive experiments on large real and synthetic datasets.