Seeded Graph Matching: Efficient Algorithms and Theoretical Guarantees

In this paper, a new information theoretic framework for graph matching is introduced. Using this framework, the graph isomorphism and seeded graph matching problems are studied. The maximum degree algorithm for graph isomorphism is analyzed and sufficient conditions for successful matching are rederived using type analysis. Furthermore, a new seeded matching algorithm with polynomial time complexity is introduced. The algorithm uses `typicality matching' and techniques from point-to-point communications for reliable matching. Assuming an Erdos-Renyi model on the correlated graph pair, it is shown that successful matching is guaranteed when the number of seeds grows logarithmically with the number of vertices in the graphs. The logarithmic coefficient is shown to be inversely proportional to the mutual information between the edge variables in the two graphs

Privacy, Access Control, and Integrity for Large Graph Databases

Graph data are extensively utilized in social networks, collaboration networks, geo-social networks, and communication networks. Their growing usage in cyberspaces poses daunting security and privacy challenges. Data publication requires privacy-protection mechanisms to guard against information breaches. In addition, access control mechanisms can be used to allow controlled sharing of data. Provision of privacy-protection, access control, and data integrity for graph data require a holistic approach for data management and secure query processing. This thesis presents such an approach. In particular, the thesis addresses two notable challenges for graph databases, which are: i) how to ensure users\u27 privacy in published graph data under an access control policy enforcement, and ii) how to verify the integrity and query results of graph datasets. To address the first challenge, a privacy-protection framework under role-based access control (RBAC) policy constraints is proposed. The design of such a framework poses a trade-off problem, which is proved to be NP-complete. Novel heuristic solutions are provided to solve the constraint problem. To the best of our knowledge, this is the first scheme that studies the trade-off between RBAC policy constraints and privacy-protection for graph data. To address the second challenge, a cryptographic security model based on Hash Message Authentic Codes (HMACs) is proposed. The model ensures integrity and completeness verification of data and query results under both two-party and third-party data distribution environments. Unique solutions based on HMACs for integrity verification of graph data are developed and detailed security analysis is provided for the proposed schemes. Extensive experimental evaluations are conducted to illustrate the performance of proposed algorithms