Application of the hamiltonian circuit latin square to the parallel routing algorithm on 2-circulant networks

Abstract

Double-loop and 2-circulant networks are widely used in the design and implementation of local area networks and parallel processing architectures. In this paper, we investigate the routing of a message on circulant networks, that is a key to the performance of this network. We would like to transmit 2k packets from a source node to a destination node simultaneously along paths on G(n; ±s1,±s2, ...,±sk), where the ith packet will traverse along the ith path (1 ≤ i ≤ 2k). In oder for all packets to arrive at the destination node quickly and securely, the ith path must be node-disjoint from all other paths. For construction of these paths, employing the Hamiltonian Circuit Latin Square(HCLS), a special class of (n × n) matrices, we present O(n2) parallel routing algorithm on circulant networks. © Springer-Verlag 2004.