Private Information Retrieval on Multigraph-Based Replicated Storage

2025-01-29

AI Summary

This paper investigates private information retrieval (PIR) in multi-graph replicated storage, focusing on an *r*-regular graph model where each group of *r* files is assigned to exactly two servers. To address this heterogeneous replication structure, we propose the first graph-symmetry-based PIR construction and derive tight upper and lower bounds on the PIR capacity. We further establish the first general linear programming upper bound dependent on graph parameters and prove its tightness for even-vertex multipath graphs. Leveraging graph-theoretic modeling, symmetry analysis, and combinatorial design, we obtain explicit closed-form capacity expressions. These results provide a theoretical optimality benchmark for privacy-preserving retrieval in multi-replica storage systems and significantly advance the capacity characterization and constructive design of PIR under non-uniform replication.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We consider the private information retrieval (PIR) problem for a multigraph-based replication system, where each set of $r$ files is stored on two of the servers according to an underlying $r$-multigraph. Our goal is to establish upper and lower bounds on the PIR capacity of the $r$-multigraph. Specifically, we first propose a construction for multigraph-based PIR systems that leverages the symmetry of the underlying graph-based PIR scheme, deriving a capacity lower bound for such multigraphs. Then, we establish a general upper bound using linear programming, expressed as a function of the underlying graph parameters. Our bounds are demonstrated to be tight for PIR systems on multipaths for even number of vertices.

Problem

• Multi-graph Systems
• Efficient Private Information Retrieval
• Privacy Preservation

Innovation

• Multi-Graph Techniques
• Theoretical Efficiency Bounds
• Even Vertex Number Convergence