New Capacity Bounds for PIR on Graph and Multigraph-Based Replicated Storage

In this paper, we study the problem of private information retrieval (PIR) in both graph-based and multigraph-based replication systems, where each file is stored on exactly two servers, and any pair of servers shares at most $r$ files. We derive upper bounds on the PIR capacity for such systems and construct PIR schemes that approach these bounds. For graph-based systems, we determine the exact PIR capacity for path graphs and improve upon existing results for complete bipartite graphs and complete graphs. For multigraph-based systems, we propose a PIR scheme that leverages the symmetry of the underlying graph-based construction, yielding a capacity lower bound for such multigraphs. Furthermore, we establish several general upper and lower bounds on the PIR capacity of multigraphs, which are tight in certain cases.

@article{kong2025_2504.20888,
  title={ New Capacity Bounds for PIR on Graph and Multigraph-Based Replicated Storage },
  author={ Xiangliang Kong and Shreya Meel and Thomas Jacob Maranzatto and Itzhak Tamo and Sennur Ulukus },
  journal={arXiv preprint arXiv:2504.20888},
  year={ 2025 }
}