Set-to-Set Disjoint Paths in Tori

Numerous TOP500 supercomputers are based on a torus interconnection network. The torus topology is effectively one of the most popular interconnection networks for massively parallel systems due to its interesting topological properties such as symmetry and simplicity. For instance, the world-famous supercomputers Fujitsu K, IBM Blue Gene/L, IBM Blue Gene/P and Cray XT3 are all torus-based. In this paper, we propose an algorithm that constructs 2n mutually node-disjoint paths from a set S of 2n source nodes to a set D of 2n destination nodes in an n-dimensional k-ary torus T-n,T-k (n >= 1, k >= 3). This algorithm is then formally evaluated. We have proved that the paths selected by the proposed algorithm have lengths at most 2(k + 1) n and can be obtained with a time complexity of O( kn (3) + n (3) log n).