Achievable schemes and limits for local recovery on a graph

Recently, a graph-theoretic model for a single-failure-recoverable distributed storage system was proposed. Unlike the usual local recovery model of codes for distributed storage, this model accounts for the fact that each server or storage node in a network is connectible to only some, and not all other, nodes. Here we provide bounds and constructive schemes for data storage in such networks. We also impose an additional requirement on the codes for such model - a minimum distance guarantee. The model is further generalized for multiple node failures and cooperative repairs.