Diskless computing nodes in cluster supercomputers require massive deployment procedure of operating systems software for their booting. Most previous studies for massive deployment of large files focus on developing flexible and scalable mechanisms in hidden or changeable network topologies, but the topology-optimal deployment has been rarely investigated in fixed open network topologies. In this article, we investigate the topology-optimal deployment method designed for a specific cluster supercomputer with the fat-tree topology. We examine possible deployment approaches and propose the optimal peer-to-peer deployment method. The proposed deployment method minimizes the number of peer-to-peer transmission steps by fully utilizing resources of the fat-tree topology and avoids contention between peer-to-peer communications. Simulation results show that the proposed method completes deployment at least nine times faster than the baseline method.