In this paper, we introduce a model of a distributed storage system that is locally recoverable from any single server failure. 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 connectable to only some, and not all other, nodes. This may happen for reasons such as physical separation, inhomogeneity in storage platforms, and so forth. We estimate the storage capacity of both undirected and directed networks under this model and propose some constructive schemes. From a coding theory point of view, we show that this model is approximately dual of the well-studied index coding problem. Furthermore, in this paper, we extend the above model to handle multiple server failures. Among other results, we provide an upper bound on the minimum pairwise distance of a set of words that can be stored in a graph with the local repair guarantee. The well-known impossibility bounds on the distance of locally recoverable codes follow from our result.
Bibliographical noteFunding Information:
This work was supported in part by the National Science Foundation CAREER Award under Grant CCF 1453121. Parts of this work were presented in the 2014 IEEE International Symposium on Information Theory  and in the 2014 Allerton Conference . The authors thank A. Agarwal, A. G. Dimakis and K. Shanmugam for useful references. They also thank B. Saha for pointing out the constructive nature of Thm. 12.
- Locally repairable codes
- distributed storage
- graph capacity
- index coding