Minimizing message complexity of partially replicated data on hypercubes

Within the framework of distributed and parallel computing, we consider partially replicated data on a hypercube. We address the problem of placing copies on the hypercube in order to minimize message complexity. With realistic restrictions on the read/write ratio and the number of copies, we find the unique optimal configuration of copies. We compute the communication cost of this configuration. The optimal configuration is a linear array satisfying certain properties.