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

Scalable supergraph search in large graph databases

© 2016 IEEE. 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

B\"uchi Complementation and Size-Change Termination

We compare tools for complementing nondeterministic B\"uchi automata with a recent termination-analysis algorithm. Complementation of B\"uchi automata is a key step in program verification. Early constructions using a Ramsey-based argument have been supplanted by rank-based constructions with exponentially better bounds. In 2001 Lee et al. presented the size-change termination (SCT) problem, along with both a reduction to B\"uchi automata and a Ramsey-based algorithm. The Ramsey-based algorithm was presented as a more practical alternative to the automata-theoretic approach, but strongly resembles the initial complementation constructions for B\"uchi automata. We prove that the SCT algorithm is a specialized realization of the Ramsey-based complementation construction. To do so, we extend the Ramsey-based complementation construction to provide a containment-testing algorithm. Surprisingly, empirical analysis suggests that despite the massive gap in worst-case complexity, Ramsey-based approaches are superior over the domain of SCT problems. Upon further analysis we discover an interesting property of the problem space that both explains this result and provides a chance to improve rank-based tools. With these improvements, we show that theoretical gains in efficiency of the rank-based approach are mirrored in empirical performance

A Scalable Graph-Coarsening Based Index for Dynamic Graph Databases

Graph is a commonly used data structure for modeling complex data such as chemical molecules, images, social networks, and XML documents. This complex data is stored using a set of graphs, known as graph database D. To speed up query answering on graph databases, indexes are commonly used. State-of-the-art graph database indexes do not adapt or scale well to dynamic graph database use; they are static, and their ability to prune possible search responses to meet user needs worsens over time as databases change and grow. Users can re-mine indexes to gain some improvement, but it is time consuming. Users must also tune numerous parameters on an ongoing basis to optimize performance and can inadvertently worsen the query response time if they do not choose parameters wisely. Recently, a one-pass algorithm has been developed to enhance the performance of these indexes in part by using the algorithm to update them regularly. However, there are some drawbacks, most notably the need to make updates as the query workload changes. We propose a new index based on graph-coarsening to speed up query answering time in dynamic graph databases. Our index is parameter-free, query-independent, scalable, small enough to store in the main memory, and is simpler and less costly to maintain for database updates. We conducted an extensive sets of experiments on two types of databases, i.e., chemical and social network databases, to compare our graph-coarsening based index vs. hybrid-indexes as follows. First, we considered no database updates or query workload changes (static graph databases) and compared the indexes according to query vi answering time and index size for different minSup values. Second, we compared the indexes in the case of dynamic graph databases, i.e. when graphs are added to or removed from the database. Third, we compared the indexes with regard to query workload changes. Fourth, we studied the scalability of our index vs. hybrid-indexes. Experimental results show that our index outperforms hybrid-indexes (i.e. indexes updated with one-pass) for query answering time in the case of social network databases, and is comparable with these indexes for frequent and infrequent queries on chemical databases. Our graph-coarsening index can be updated up to 60 times faster in comparison to one-pass on dynamic graph databases. Moreover, our index is independent of the query workload for index update and is up to 15 times better after hybrid indexes are attuned to query workload for social network databases. This work is also published in 26th ACM International Conference on Information and Knowledge Management (CIKM) held in Singapore[18]

Doctor of Philosophy

dissertationServing as a record of what happened during a scientific process, often computational, provenance has become an important piece of computing. The importance of archiving not only data and results but also the lineage of these entities has led to a variety of systems that capture provenance as well as models and schemas for this information. Despite significant work focused on obtaining and modeling provenance, there has been little work on managing and using this information. Using the provenance from past work, it is possible to mine common computational structure or determine differences between executions. Such information can be used to suggest possible completions for partial workflows, summarize a set of approaches, or extend past work in new directions. These applications require infrastructure to support efficient queries and accessible reuse. In order to support knowledge discovery and reuse from provenance information, the management of those data is important. One component of provenance is the specification of the computations; workflows provide structured abstractions of code and are commonly used for complex tasks. Using change-based provenance, it is possible to store large numbers of similar workflows compactly. This storage also allows efficient computation of differences between specifications. However, querying for specific structure across a large collection of workflows is difficult because comparing graphs depends on computing subgraph isomorphism which is NP-Complete. Graph indexing methods identify features that help distinguish graphs of a collection to filter results for a subgraph containment query and reduce the number of subgraph isomorphism computations. For provenance, this work extends these methods to work for more exploratory queries and collections with significant overlap. However, comparing workflow or provenance graphs may not require exact equality; a match between two graphs may allow paired nodes to be similar yet not equivalent. This work presents techniques to better correlate graphs to help summarize collections. Using this infrastructure, provenance can be reused so that users can learn from their own and others' history. Just as textual search has been augmented with suggested completions based on past or common queries, provenance can be used to suggest how computations can be completed or which steps might connect to a given subworkflow. In addition, provenance can help further science by accelerating publication and reuse. By incorporating provenance into publications, authors can more easily integrate their results, and readers can more easily verify and repeat results. However, reusing past computations requires maintaining stronger associations with any input data and underlying code as well as providing paths for migrating old work to new hardware or algorithms. This work presents a framework for maintaining data and code as well as supporting upgrades for workflow computations

Efficient Subgraph Similarity Search on Large Probabilistic Graph Databases

Many studies have been conducted on seeking the efficient solution for subgraph similarity search over certain (deterministic) graphs due to its wide application in many fields, including bioinformatics, social network analysis, and Resource Description Framework (RDF) data management. All these works assume that the underlying data are certain. However, in reality, graphs are often noisy and uncertain due to various factors, such as errors in data extraction, inconsistencies in data integration, and privacy preserving purposes. Therefore, in this paper, we study subgraph similarity search on large probabilistic graph databases. Different from previous works assuming that edges in an uncertain graph are independent of each other, we study the uncertain graphs where edges' occurrences are correlated. We formally prove that subgraph similarity search over probabilistic graphs is #P-complete, thus, we employ a filter-and-verify framework to speed up the search. In the filtering phase,we develop tight lower and upper bounds of subgraph similarity probability based on a probabilistic matrix index, PMI. PMI is composed of discriminative subgraph features associated with tight lower and upper bounds of subgraph isomorphism probability. Based on PMI, we can sort out a large number of probabilistic graphs and maximize the pruning capability. During the verification phase, we develop an efficient sampling algorithm to validate the remaining candidates. The efficiency of our proposed solutions has been verified through extensive experiments.Comment: VLDB201

A list of parameterized problems in bioinformatics

In this report we present a list of problems that originated in bionformatics. Our aim is to collect information on such problems that have been analyzed from the point of view of Parameterized Complexity. For every problem we give its definition and biological motivation together with known complexity results.Postprint (published version