  We introduce a neighborhood-based data access model for distributed coded
storage allocation. Storage nodes are connected in a generic network and data
is accessed locally: a user accesses a randomly chosen storage node, which
subsequently queries its neighborhood to recover the data object. We aim at
finding an optimal allocation that minimizes the overall storage budget while
ensuring recovery with probability one. We show that the problem reduces to
finding the fractional dominating set of the underlying network. Furthermore,
we develop a fully distributed algorithm where each storage node communicates
only with its neighborhood in order to find its optimal storage allocation. The
proposed algorithm is based upon the recently proposed proximal center
method--an efficient dual decomposition based on accelerated dual gradient
method. We show that our algorithm achieves a $(1+\epsilon)$-approximation
ratio in $O(d_{\mathrm{max}}^{3/2}/\epsilon)$ iterations and per-node
communications, where $d_{\mathrm{max}}$ is the maximal degree across nodes.
Simulations demonstrate the effectiveness of the algorithm.
