Private Information Retrieval for Graph-based Replication with Minimal Subpacketization

2026-01-15

AI Summary

This work addresses the problem of private information retrieval (PIR) in graph-based replicated databases, proposing information-theoretically secure protocols that simultaneously preserve query privacy, minimize file subpacketization overhead, and maximize retrieval rates. The database consists of $K$ files stored across $N$ servers according to a graph structure with $K$ edges. The key contributions include a unit-subpacketization PIR protocol tailored for star graphs, which significantly outperforms existing low-subpacketization schemes, and a general construction based on graph independent set decomposition that applies to arbitrary graphs and extends naturally to multigraphs to further enhance retrieval rates. Theoretical analysis demonstrates that the proposed methods achieve high retrieval rates and optimal subpacketization complexity for star graphs, general graphs, and complete multigraphs alike.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

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 design new minimal-subpacketization schemes for information-theoretic private information retrieval on graph-based replicated databases. In graph-based replication, the system consists of $K$ files replicated across $N$ servers according to a graph with $N$ vertices and $K$ edges. The client wants to retrieve one desired file, while keeping the index of the desired file private from each server via a query-response protocol. We seek PIR protocols that have (a) high rate, which is the ratio of the file-size to the total download cost, and (b) low subpacketization, which acts as a constraint on the size of the files for executing the protocol. We report two new schemes which have unit-subpacketization (which is minimal): (i) for a special class of graphs known as star graphs, and (ii) for general graphs. Our star-graph scheme has a better rate than previously known schemes with low subpacketization for general star graphs. Our scheme for general graphs uses a decomposition of the graph via independent sets. This scheme achieves a rate lower than prior schemes for the complete graph, however it can achieve higher rates than known for some specific graph classes. An extension of our scheme to the case of multigraphs achieves a higher rate than previous schemes for the complete multi-graph.

Problem

• Private Information Retrieval
• Graph-based Replication
• Subpacketization
• Information-theoretic Privacy
• Database Replication

Innovation

• Private Information Retrieval
• Graph-based Replication
• Subpacketization
• Star Graph
• Independent Set Decomposition