Bisection (Band)Width of Product Networks with Application to Data Centers

The bisection width of interconnection networks has always been important in parallel computing, since it bounds the speed at which information can be moved from one side of a network to another, i.e., the bisection bandwidth. Finding its exact value has proven to be challenging for some network families. For instance, the problem of finding the exact bisection width of the multidimensional torus was posed by Leighton [1, Problem 1.281] and has remained open for almost 20 years. We provide two general results that allow us to obtain upper and lower bounds on the bisection width of any product graph as a function of some properties of its factor graphs. The power of these results is shown by deriving the exact value of the bisection width of the torus, as well as of several d-dimensional classical parallel topologies that can be obtained by the application of the Cartesian product of graphs. We also apply these results to data centers, by obtaining bounds for the bisection bandwidth of the d-dimensional BCube network, a recently proposed topology for data centers.