Some properties and algorithms for the hyper-torus network.

The hyper-torus network based on a three-dimensional hypercube was introduced recently. The hyper-torus $$QT(m,n)$$ performs better than mesh type networks with a similar number of nodes in terms of the network cost. In this paper, we prove that if $$n$$ is even, the bisection width of $$QT(m,n)$$ is $$6n$$ , whereas it is $$6n+2$$ if it is odd. Second, we show that $$QT(m,n)$$ contains a Hamiltonian cycle. In addition, its one-to-all and all-to-all broadcasting algorithms are introduced. All of these broadcasting algorithms are asymptotically optimal. [ABSTRACT FROM AUTHOR]