Capacity characterization for general multigraphs

Characterize the capacity bounds of most multigraph-based local private information retrieval systems, thereby resolving the unresolved capacity behavior beyond the specific multigraph families analyzed in the paper.

Background

The paper introduces local private information retrieval for graph-replicated systems and extends its achievable schemes and capacity bounds from simple graphs to r-multigraphs, in which each underlying graph edge is replaced by r parallel edges. Exact or bounded capacities are derived for selected families, including cyclic and path multigraphs, while general lower bounds are obtained for arbitrary multigraphs.

The authors explicitly identify the capacity behavior of most multigraphs as unresolved. Resolving this problem would extend the available results beyond the analyzed families and clarify the limits of local-PIR rate improvements under increasing replication multiplicity.