Private Information Retrieval on Multigraph-Based Replicated Storage

TL;DR

This paper investigates the limits of private information retrieval in multigraph-based storage systems, providing bounds on capacity and demonstrating tightness for specific graph structures.

Contribution

It introduces a multigraph-based PIR scheme leveraging graph symmetry and derives capacity bounds, including a tight bound for multipaths with even vertices.

Findings

Capacity bounds are established for multigraph-based PIR.

The proposed scheme leverages graph symmetry for improved PIR.

Bounds are tight for multipaths with an even number of vertices.

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.