Relaxation of Subgraph Queries Delivering Empty Results

Graph databases with the property graph model are used in multiple domains including social networks, biology, and data integration. They provide schema-flexible storage for data of a different degree of a structure and support complex, expressive queries such as subgraph isomorphism queries. The exibility and expressiveness of graph databases make it difficult for the users to express queries correctly and can lead to unexpected query results, e.g. empty results. Therefore, we propose a relaxation approach for subgraph isomorphism queries that is able to automatically rewrite a graph query, such that the rewritten query is similar to the original query and returns a non-empty result set. In detail, we present relaxation operations applicable to a query, cardinality estimation heuristics, and strategies for prioritizing graph query elements to be relaxed. To determine the similarity between the original query and its relaxed variants, we propose a novel cardinality-based graph edit distance. The feasibility of our approach is shown by using real-world queries from the DBpedia query log

DebEAQ - debugging empty-answer queries on large data graphs

The large volume of freely available graph data sets impedes the users in analyzing them. For this purpose, they usually pose plenty of pattern matching queries and study their answers. Without deep knowledge about the data graph, users can create ‘failing’ queries, which deliver empty answers. Analyzing the causes of these empty answers is a time-consuming and complicated task especially for graph queries. To help users in debugging these ‘failing’ queries, there are two common approaches: one is focusing on discovering missing subgraphs of a data graph, the other one tries to rewrite the queries such that they deliver some results. In this demonstration, we will combine both approaches and give the users an opportunity to discover why empty results were delivered by the requested queries. Therefore, we propose DebEAQ, a debugging tool for pattern matching queries, which allows to compare both approaches and also provides functionality to debug queries manually

Considering User Intention in Differential Graph Queries

Empty answers are a major problem by processing pattern matching queries in graph databases. Especially, there can be multiple reasons why a query failed. To support users in such situations, differential queries can be used that deliver missing parts of a graph query. Multiple heuristics are proposed for differential queries, which reduce the search space. Although they are successful in increasing the performance, they can discard query subgraphs relevant to a user. To address this issue, the authors extend the concept of differential queries and introduce top-k differential queries that calculate the ranking based on users’ preferences and significantly support the users’ understanding of query database management systems. A user assigns relevance weights to elements of a graph query that steer the search and are used for the ranking. In this paper the authors propose different strategies for selection of relevance weights and their propagation. As a result, the search is modelled along the most relevant paths. The authors evaluate their solution and both strategies on the DBpedia data graph

Top-k Differential Queries in Graph Databases

The sheer volume as well as the schema complexity of today’s graph databases impede the users in formulating queries against these databases and often cause queries to “fail” by delivering empty answers. To support users in such situations, the concept of differential queries can be used to bridge the gap between an unexpected result (e.g. an empty result set) and the query intention of users. These queries deliver missing parts of a query graph and, therefore, work with such scenarios that require users to specify a query graph. Based on the discovered information about a missing query subgraph, users may understand which vertices and edges are the reasons for queries that unexpectedly return empty answers, and thus can reformulate the queries if needed. A study showed that the result sets of differential queries are often too large to be manually introspected by users and thus a reduction of the number of results and their ranking is required. To address these issues, we extend the concept of differential queries and introduce top-k differential queries that calculate the ranking based on users’ preferences and therefore significantly support the users’ understanding of query database management systems. The idea consists of assigning relevance weights to vertices or edges of a query graph by users that steer the graph search and are used in the scoring function for top-k differential results. Along with the novel concept of the top-k differential queries, we further propose a strategy for propagating relevance weights and we model the search along the most relevant paths

Why-Query Support in Graph Databases

In the last few decades, database management systems became powerful tools for storing large amount of data and executing complex queries over them. In addition to extended functionality, novel types of databases appear like triple stores, distributed databases, etc. Graph databases implementing the property-graph model belong to this development branch and provide a new way for storing and processing data in the form of a graph with nodes representing some entities and edges describing connections between them. This consideration makes them suitable for keeping data without a rigid schema for use cases like social-network processing or data integration. In addition to a flexible storage, graph databases provide new querying possibilities in the form of path queries, detection of connected components, pattern matching, etc. However, the schema flexibility and graph queries come with additional costs. With limited knowledge about data and little experience in constructing the complex queries, users can create such ones, which deliver unexpected results. Forced to debug queries manually and overwhelmed by the amount of query constraints, users can get frustrated by using graph databases. What is really needed, is to improve usability of graph databases by providing debugging and explaining functionality for such situations. We have to assist users in the discovery of what were the reasons of unexpected results and what can be done in order to fix them. The unexpectedness of result sets can be expressed in terms of their size or content. In the first case, users have to solve the empty-answer, too-many-, or too-few-answers problems. In the second case, users care about the result content and miss some expected answers or wonder about presence of some unexpected ones. Considering the typical problems of receiving no or too many results by querying graph databases, in this thesis we focus on investigating the problems of the first group, whose solutions are usually represented by why-empty, why-so-few, and why-so-many queries. Our objective is to extend graph databases with debugging functionality in the form of why-queries for unexpected query results on the example of pattern matching queries, which are one of general graph-query types. We present a comprehensive analysis of existing debugging tools in the state-of-the-art research and identify their common properties. From them, we formulate the following features of why-queries, which we discuss in this thesis, namely: holistic support of different cardinality-based problems, explanation of unexpected results and query reformulation, comprehensive analysis of explanations, and non-intrusive user integration. To support different cardinality-based problems, we develop methods for explaining no, too few, and too many results. To cover different kinds of explanations, we present two types: subgraph- and modification-based explanations. The first type identifies the reasons of unexpectedness in terms of query subgraphs and delivers differential graphs as answers. The second one reformulates queries in such a way that they produce better results. Considering graph queries to be complex structures with multiple constraints, we investigate different ways of generating explanations starting from the most general one that considers only a query topology through coarse-grained rewriting up to fine-grained modification that allows fine changes of predicates and topology. To provide a comprehensive analysis of explanations, we propose to compare them on three levels including a syntactic description, a content, and a size of a result set. In order to deliver user-aware explanations, we discuss two models for non-intrusive user integration in the generation process. With the techniques proposed in this thesis, we are able to provide fundamentals for debugging of pattern-matching queries, which deliver no, too few, or too many results, in graph databases implementing the property-graph model

Approximating expressive queries on graph-modeled data: The GeX approach

We present the GeX (Graph-eXplorer) approach for the approximate matching of complex queries on graph-modeled data. GeX generalizes existing approaches and provides for a highly expressive graph-based query language that supports queries ranging from keyword-based to structured ones. The GeX query answering model gracefully blends label approximation with structural relaxation, under the primary objective of delivering meaningfully approximated results only. GeX implements ad-hoc data structures that are exploited by a top-k retrieval algorithm which enhances the approximate matching of complex queries. An extensive experimental evaluation on real world datasets demonstrates the efficiency of the GeX query answering

Efficient Data Modelling, Indexing and Processing in Large Datasets

Many devices and applications in social networks and on-line services are producing, storing, and using description, location, and occurrence time of objects. There are various systems to study, model, index, and process a huge amount of data. In this thesis, we study graphs and publish/subscribe systems. Firstly, we study the problem of continuously updating top-k messages with the highest ranks, each of which contains all the requested keywords when the rank of a message calculates based on freshness and distance to query’s location. Since new incoming messages are arriving all the time and the score of existing top-k results are decreasing over time, providing the most recent information needs continuously computing and maintaining the best results. We propose an efficient indexing and matching method using keywords, location, and the most recent top-k results of queries. Secondly, we study the problem of the decomposition of (k,s)-core. As both the user engagement of nodes and the strength of relationships are important, the (k, s)-core model is proposed in the literature to discover strong communities. Nevertheless, the decomposition algorithm regarding (k,s)-core is not yet investigated. We propose (k,s)-core algorithms to decompose a graph into its hierarchical structures considering both user engagement and tie strength. We first present the basic (k,s)-core decomposition methods. Then, we propose the advanced algorithms DES and DEK which index the support of edges to enable higher-level cost-sharing in the peeling process. In addition, effective pruning strategies are applied to DES/DEK to further enhance performance. Moreover, we build a novel index based on the decomposition result and investigate efficient (k,s)-core query algorithm based on our index. Finally, we develop efficient algorithm for maintaining the (k, s)-core index of the dynamic graph where vertices and edges are inserted and deleted. The algorithm, uses pruning strategies by exploiting the lower and upper bounds of the core number. We define a new Smax core and develop an efficient method for updating (k,s) numbers of nodes

Approximation Algorithms for NP-Hard Problems

The workshop was concerned with the most important recent developments in the area of efficient approximation algorithms for NP-hard optimization problems as well as with new techniques for proving intrinsic lower bounds for efficient approximation