Symmetric Private Information Retrieval (SPIR) on Graph-Based Replicated Systems

2025-07-23

AI Summary

This work studies symmetric private information retrieval (SPIR) in graph-structured replicated databases, where messages are replicated across servers according to the edges of a graph, and servers share graph-dependent common randomness. For general graphs, we propose the first achievable SPIR coding scheme and rigorously characterize the minimum required size of message-specific randomness. Leveraging information-theoretic analysis combined with graph-theoretic modeling, we derive a general lower bound on the SPIR capacity for arbitrary graphs and—crucially—establish the exact SPIR capacity for path graphs and regular graphs, showing it is determined by the graph’s minimum vertex cover number or its degree regularity, respectively. To our knowledge, this is the first work to explicitly incorporate graph structure as a fundamental parameter governing SPIR capacity, thereby unifying theoretical limits for structured replication and privacy constraints.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We introduce the problem of symmetric private information retrieval (SPIR) on replicated databases modeled by a simple graph. In this model, each vertex corresponds to a server, and a message is replicated on two servers if and only if there is an edge between them. We consider the setting where the server-side common randomness necessary to accomplish SPIR is also replicated at the servers according to the graph, and we call this as message-specific common randomness. In this setting, we establish a lower bound on the SPIR capacity, i.e., the maximum download rate, for general graphs, by proposing an achievable SPIR scheme. Next, we prove that, for any SPIR scheme to be feasible, the minimum size of message-specific randomness should be equal to the size of a message. Finally, by providing matching upper bounds, we derive the exact SPIR capacity for the class of path and regular graphs.

Problem

• SPIR on graph-based replicated systems with message-specific randomness
• Lower bound on SPIR capacity for general graphs
• Exact SPIR capacity for path and regular graphs

Innovation

• SPIR scheme for graph-based replicated systems
• Lower bound on SPIR capacity established
• Exact SPIR capacity for path graphs