A parallel routing algorithm on recursive cube of rings networks employing Hamiltonian circuit Latin square

Recursive cube of rings (RCR) networks [Y. Sun, P. Cheung, X. Lin, Recursive cube of rings: a new topology for interconnection networks, IEEE Trans. Parallel Dist. Syst. 11 (3) (2000) 275-286] can be widely used in the design and implementation of parallel processing architectures. In this paper, we investigate the routing of a message on RCR networks, that is a key to the performance of this network. We would like to transmit k+1 packets from a source node to a destination node simultaneously along paths on RCR networks, the ith packet will traverse along the ith path (1⩽i⩽k+1). In order for all packets to arrive at a destination node quickly and securely, the ith path must be node-disjoint from all other paths. For construction of these paths, employing Hamiltonian circuit Latin square (HCLS), we present O(n2) parallel routing algorithm on RCR networks.