The need for graph computations is evident in a multitude of use cases. To support computations on large-scale graphs, several parallel systems have been developed. However, existing graph systems require users to recast algorithms into new models, which makes parallel graph computations as a privilege to experienced users only. Moreover, real world applications often require much more complex graph processing workflows than previously evaluated. In response to these challenges, the thesis presents GRAPE, a distributed graph computation system, shipped with various applications for social network analysis, social media marketing and functional dependencies on graphs. Firstly, the thesis presents the foundation of GRAPE. The principled approach of GRAPE is based on partial evaluation and incremental computation. Sequential graph algorithms can be plugged into GRAPE with minor changes, and get parallelized as a whole. The termination and correctness are guaranteed under a monotonic condition. Secondly, as an application on GRAPE, the thesis proposes graph-pattern association rules (GPARs) for social media marketing. GPARs help users discover regularities between entities in social graphs and identify potential customers by exploring social influence. The thesis studies the problem of discovering top-k diversified GPARs and the problem of identifying potential customers with GPARs. Although both are NP- hard, parallel scalable algorithms on GRAPE are developed, which guarantee a polynomial speedup over sequential algorithms with the increase of processors. Thirdly, the thesis proposes quantified graph patterns (QGPs), an extension of graph patterns by supporting simple counting quantifiers on edges. QGPs naturally express universal and existential quantification, numeric and ratio aggregates, as well as negation. The thesis proves that the matching problem of QGPs remains NP-complete in the absence of negation, and is DP-complete for general QGPs. In addition, the thesis introduces quantified graph association rules defined with QGPs, to identify potential customers in social media marketing. Finally, to address the issue of data consistency, the thesis proposes a class of functional dependencies for graphs, referred to as GFDs. GFDs capture both attribute-value dependencies and topological structures of entities. The satisfiability and implication problems for GFDs are studied and proved to be coNP-complete and NP-complete, respectively. The thesis also proves that the validation problem for GFDs is coNP- complete. The parallel algorithms developed on GRAPE verify that GFDs provide an effective approach to detecting inconsistencies in knowledge and social graphs.

Triangle enumeration is an important element in graph analysis, and because of this it is a topic that has been studied extensively. Although the formulation is simple, for large networks the computation becomes challenging as we have to deal with memory limitation and efficiency. Many algorithms have been proposed to overcome these problems. Some use distributed computing, where the computation is distributed among many machines in a cluster. However, this approach has a high cost in terms of hardware resources and energy. In this thesis we studied triangle counting/listing algorithms for both directed and undirected graphs, and searched for methods to do the computation on a single machine. Through detailed analysis, we found some ways to improve the efficiency of the computation. Programs that implement the algorithms were built and tested on large networks with up to almost a billion nodes. The results were then analysed and discussed. / Graduate

<div>Graph-structured data is pervasive. Modeling large-scale network-structured datasets require graph processing and management systems such as graph databases. Further, the analysis of graph-structured data often necessitates bulk downloads/uploads from/to the cloud or edge nodes. Unfortunately, experience has shown that malicious actors can compromise the confidentiality of highly-sensitive data stored in the cloud or shared nodes, even in an encrypted form. For particular use cases —multi-modal knowledge graphs, electronic health records, finance— network-structured datasets can be highly sensitive and require auditability, authentication, integrity protection, and privacy-preserving computation in a controlled and trusted environment, i.e., the traditional cloud computation is not suitable for these use cases. Similarly, many modern applications utilize a "shared, replicated database" approach to provide accountability and traceability. Those applications often suffer from significant privacy issues because every node in the network can access a copy of relevant contract code and data to guarantee the integrity of transactions and reach consensus, even in the presence of malicious actors.</div><div><br></div><div>This dissertation proposes breaking from the traditional cloud computation model, and instead ship certified pre-approved trusted code closer to the data to protect graph-structured data confidentiality. Further, our technique runs in a controlled environment in a trusted data owner node and provides proof of correct code execution. This computation can be audited in the future and provides the building block to automate a variety of real use cases that require preserving data ownership. This project utilizes trusted execution environments (TEEs) but does not rely solely on TEE's architecture to provide privacy for data and code. We thoughtfully examine the drawbacks of using trusted execution environments in cloud environments. Similarly, we analyze the privacy challenges exposed by the use of blockchain technologies to provide accountability and traceability.</div><div><br></div><div>First, we propose AGAPECert, an Auditable, Generalized, Automated, Privacy-Enabling, Certification framework capable of performing auditable computation on private graph-structured data and reporting real-time aggregate certification status without disclosing underlying private graph-structured data. AGAPECert utilizes a novel mix of trusted execution environments, blockchain technologies, and a real-time graph-based API standard to provide automated, oblivious, and auditable certification. This dissertation includes the invention of two core concepts that provide accountability, data provenance, and automation for the certification process: Oblivious Smart Contracts and Private Automated Certifications. Second, we contribute an auditable and integrity-preserving graph processing model called AuditGraph.io. AuditGraph.io utilizes a unique block-based layout and a multi-modal knowledge graph, potentially improving access locality, encryption, and integrity of highly-sensitive graph-structured data. Third, we contribute a unique data store and compute engine that facilitates the analysis and presentation of graph-structured data, i.e., TruenoDB. TruenoDB offers better throughput than the state-of-the-art. Finally, this dissertation proposes integrity-preserving streaming frameworks at the edge of the network with a personalized graph-based object lookup.</div>