Performance and scalability of indexed subgraph query processing methods

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. Specifi- cally, 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

Hybrid algorithms for subgraph pattern queries in graph databases

Numerous methods have been proposed over the years for subgraph query processing, as it is central to graph analytics. Existing work is fragmented into two major categories. Methods in the filter-then-verify (FTV) category first construct an index of the DB graphs. Given a query, the index is used to filter out graphs that cannot contain the query. On the remaining graphs, a subgraph isomorphism algorithm is applied to verify whether each graph indeed contains the query. A second category of algorithms is mainly concerned with optimizing the Subgraph Isomorphism (SI) testing process (an NP-Complete problem) in order to find all occurrences of the query within each DB graph, also known as the matching problem. The current research trend is to totally dismiss FTV methods, because SI methods have been shown to enjoy much shorter query execution times and because of the alleged high costs of managing the DB graph index in FTV methods. Thus, a number of new SI methods are being proposed annually. In the current work, we initially study the performance of the latest SI algorithms over datasets consisting of a large number of graphs. With our study, we evaluate the algorithms’ performance and we provide comparison details with former studies. As a second step, we combine the powerful filtering of a top-performing FTV method, with the various SI methods, which leads to the best practice conclusion that SI and FTV shouldn’t be thought of as disjoint types of solutions, as their union achieves better results than any one of them individually. Specifically, we experimentally analyze and quantify the (positive) impact of including the essence of indexed FTV methods within SI methods, showing that query processing times can be significantly improved at modest additional memory costs. We show that these results hold over a variety of well-known SI methods and across several real and synthetic datasets. As such, hybrids of the type reveal a missing opportunity and a blind spot in related literature and trends

SING: Subgraph search In Non-homogeneous Graphs

<p>Abstract</p> <p>Background</p> <p>Finding the subgraphs of a graph database that are isomorphic to a given query graph has practical applications in several fields, from cheminformatics to image understanding. Since subgraph isomorphism is a computationally hard problem, indexing techniques have been intensively exploited to speed up the process. Such systems filter out those graphs which cannot contain the query, and apply a subgraph isomorphism algorithm to each residual candidate graph. The applicability of such systems is limited to databases of small graphs, because their filtering power degrades on large graphs.</p> <p>Results</p> <p>In this paper, SING (Subgraph search In Non-homogeneous Graphs), a novel indexing system able to cope with large graphs, is presented. The method uses the notion of <it>feature</it>, which can be a small subgraph, subtree or path. Each graph in the database is annotated with the set of all its features. The key point is to make use of feature locality information. This idea is used to both improve the filtering performance and speed up the subgraph isomorphism task.</p> <p>Conclusions</p> <p>Extensive tests on chemical compounds, biological networks and synthetic graphs show that the proposed system outperforms the most popular systems in query time over databases of medium and large graphs. Other specific tests show that the proposed system is effective for single large graphs.</p

Efficient access methods for very large distributed graph databases

Subgraph searching is an essential problem in graph databases, but it is also challenging due to the involved subgraph isomorphism NP-Complete sub-problem. Filter-Then-Verify (FTV) methods mitigate performance overheads by using an index to prune out graphs that do not fit the query in a filtering stage, reducing the number of subgraph isomorphism evaluations in a subsequent verification stage. Subgraph searching has to be applied to very large databases (tens of millions of graphs) in real applications such as molecular substructure searching. Previous surveys have identified the FTV solutions GraphGrepSX (GGSX) and CT-Index as the best ones for large databases (thousands of graphs), however they cannot reach reasonable performance on very large ones (tens of millions graphs). This paper proposes a generic approach for the distributed implementation of FTV solutions. Besides, three previous methods that improve the performance of GGSX and CT-Index are adapted to be executed in clusters. The evaluation shows how the achieved solutions provide a great performance improvement (between 70% and 90% of filtering time reduction) in a centralized configuration and how they may be used to achieve efficient subgraph searching over very large databases in cluster configurationsThis work has been co-funded by the Ministerio de Economía y Competitividad of the Spanish government, and by Mestrelab Research S.L. through the project NEXTCHROM (RTC-2015-3812-2) of the call Retos-Colaboración of the program Programa Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad. The authors wish to thank the financial support provided by Xunta de Galicia under the Project ED431B 2018/28S

A subgraph isomorphism algorithm and its application to biochemical data

BackgroundGraphs can represent biological networks at the molecular, protein, or species level. An important query is to find all matches of a pattern graph to a target graph. Accomplishing this is inherently difficult (NP-complete) and the efficiency of heuristic algorithms for the problem may depend upon the input graphs. The common aim of existing algorithms is to eliminate unsuccessful mappings as early as and as inexpensively as possible.ResultsWe propose a new subgraph isomorphism algorithm which applies a search strategy to significantly reduce the search space without using any complex pruning rules or domain reduction procedures. We compare our method with the most recent and efficient subgraph isomorphism algorithms (VFlib, LAD, and our C++ implementation of FocusSearch which was originally distributed in Modula2) on synthetic, molecules, and interaction networks data. We show a significant reduction in the running time of our approach compared with these other excellent methods and show that our algorithm scales well as memory demands increase.ConclusionsSubgraph isomorphism algorithms are intensively used by biochemical tools. Our analysis gives a comprehensive comparison of different software approaches to subgraph isomorphism highlighting their weaknesses and strengths. This will help researchers make a rational choice among methods depending on their application. We also distribute an open-source package including our system and our own C++ implementation of FocusSearch together with all the used datasets (http://ferrolab.dmi.unict.it/ri.html). In future work, our findings may be extended to approximate subgraph isomorphism algorithms

Indexing query graphs to speedup graph query processing

Subgraph/supergraph queries although central to graph analytics, are costly as they entail the NP-Complete problem of subgraph isomorphism. We present a fresh solution, the novel principle of which is to acquire and utilize knowledge from the results of previously executed queries. Our approach, iGQ, encompasses two component subindexes to identify if a new query is a subgraph/supergraph of previously executed queries and stores related key information. iGQ comes with novel query processing and index space management algorithms, including graph replacement policies. The end result is a system that leads to significant reduction in the number of required subgraph isomorphism tests and speedups in query processing time. iGQ can be incorporated into any sub/supergraph query processing method and help improve performance. In fact, it is the only contribution that can speedup significantly both subgraph and supergraph query processing. We establish the principles of iGQ and formally prove its correctness. We have implemented iGQ and have incorporated it within three popular recent state of the art index-based graph query processing solutions. We evaluated its performance using real-world and synthetic graph datasets with different characteristics, and a number of query workloads, showcasing its benefits

GRAPES-DD: exploiting decision diagrams for index-driven search in biological graph databases

BACKGROUND: Graphs are mathematical structures widely used for expressing relationships among elements when representing biomedical and biological information. On top of these representations, several analyses are performed. A common task is the search of one substructure within one graph, called target. The problem is referred to as one-to-one subgraph search, and it is known to be NP-complete. Heuristics and indexing techniques can be applied to facilitate the search. Indexing techniques are also exploited in the context of searching in a collection of target graphs, referred to as one-to-many subgraph problem. Filter-and-verification methods that use indexing approaches provide a fast pruning of target graphs or parts of them that do not contain the query. The expensive verification phase is then performed only on the subset of promising targets. Indexing strategies extract graph features at a sufficient granularity level for performing a powerful filtering step. Features are memorized in data structures allowing an efficient access. Indexing size, querying time and filtering power are key points for the development of efficient subgraph searching solutions.RESULTS: An existing approach, GRAPES, has been shown to have good performance in terms of speed-up for both one-to-one and one-to-many cases. However, it suffers in the size of the built index. For this reason, we propose GRAPES-DD, a modified version of GRAPES in which the indexing structure has been replaced with a Decision Diagram. Decision Diagrams are a broad class of data structures widely used to encode and manipulate functions efficiently. Experiments on biomedical structures and synthetic graphs have confirmed our expectation showing that GRAPES-DD has substantially reduced the memory utilization compared to GRAPES without worsening the searching time.CONCLUSION: The use of Decision Diagrams for searching in biochemical and biological graphs is completely new and potentially promising thanks to their ability to encode compactly sets by exploiting their structure and regularity, and to manipulate entire sets of elements at once, instead of exploring each single element explicitly. Search strategies based on Decision Diagram makes the indexing for biochemical graphs, and not only, more affordable allowing us to potentially deal with huge and ever growing collections of biochemical and biological structures