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arXiv · 2501.17845

Private Information Retrieval on Multigraph-Based Replicated Storage

Shreya Meel·Xiangliang Kong·Thomas Jacob Maranzatto·Itzhak Tamo·Sennur Ulukus
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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.

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Shreya Meel, Xiangliang Kong, Thomas Jacob Maranzatto, Itzhak Tamo, Sennur Ulukus. 2025-01-29. Private Information Retrieval on Multigraph-Based Replicated Storage. https://arxiv.org/abs/2501.17845

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