Private Information Retrieval on Multigraph-Based Replicated Storage
Information Theory
2025-05-06 v2 Cryptography and Security
Networking and Internet Architecture
Signal Processing
math.IT
Abstract
We consider the private information retrieval (PIR) problem for a multigraph-based replication system, where each set of files is stored on two of the servers according to an underlying -multigraph. Our goal is to establish upper and lower bounds on the PIR capacity of the -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.
Cite
@article{arxiv.2501.17845,
title = {Private Information Retrieval on Multigraph-Based Replicated Storage},
author = {Shreya Meel and Xiangliang Kong and Thomas Jacob Maranzatto and Itzhak Tamo and Sennur Ulukus},
journal= {arXiv preprint arXiv:2501.17845},
year = {2025}
}