Optimal file sharing in distributed networks

Given a distributed network of processors represented by an undirected graph G=(V, E) and a file size k, the problem of distributing an arbitrary file w of k bits among all nodes of the network G is considered. Memory devices are to be assigned to the node of G such that, by accessing the memory of its own and of its adjacent nodes, each node can reconstruct the contents of w. The objective is to minimize the total size memory in the network. A file distribution scheme that realizes this objective for k≫log Δ_G, where Δ_G, stands for the maximum degree in G, is presented. For this range of k, the total size of memory required by the suggested scheme approaches an integer programming lower bound on that size