Algorithms of Routing and Matrix Multiplication on Dualcube

Dualcube is an interconnection networks that has hypercube-like structure with the capacity to hold much more nodes than the conventional hypercube with the same number of links per node. The motivation of using dualcube as an interconnection network is to mitigate the problem of increasing the number of links in the large-scale hypercube network while keeps most of the topological properties of the hypercube network. In this paper, we focus on the design of efficient algorithms for routing and numerical operations on dualcube such as prefix computation, vectormatrix and matrix-matrix multiplications. Our results show that the routing and the basic numerical computations can be done on dualcube almost as fast as those on hypercube.