# GDSP: A Graphical Perspective on the Distributed Storage Systems

## TL;DR

This paper generalizes the classical distributed storage problem to arbitrary hyper-graphs and multiple files, analyzing minimum-storage codes for these extended models to improve understanding of storage efficiency in complex network structures.

## Contribution

It introduces the graphical distributed storage problem (GDSP) and advances the analysis of minimum-storage codes for arbitrary graphs and hyper-graphs with multiple files.

## Key findings

- Progress in analyzing minimum-storage codes for arbitrary graphs.
- Extension of classical models to multiple files and hyper-graphs.
- Enhanced understanding of storage optimization in complex network topologies.

## Abstract

The classical distributed storage problem can be modeled by a k-uniform {\it complete} hyper-graph where vertices represent servers and hyper-edges represent users. Hence each hyper-edge should be able to recover the full file using only the memories of the vertices associated with it. This paper considers the generalization of this problem to {\it arbitrary} hyper-graphs and to the case of multiple files, where each user is only interested in one, a problem we will refer to as the graphical distributed storage problem (GDSP). Specifically, we make progress in the analysis of minimum-storage codes for two main subproblems of the GDSP which extend the classical model in two independent directions: the case of an arbitrary graph with multiple files, and the case of an arbitrary hyper-graph with a single file.