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

TL;DR

This paper determines the exact bisection width of multidimensional torus networks and other product topologies, providing bounds for data center network designs, which is crucial for understanding their communication capacity.

Contribution

It presents the first exact calculation of the bisection width for multidimensional tori and offers general bounds for product graphs, including applications to data center topologies.

Findings

Exact bisection width of multidimensional torus obtained

Bounds for bisection bandwidth of BCube networks established

General results for product graph bisection width derived

Abstract

The bisection width of interconnection networks has always been important in parallel computing, since it bounds the amount of information that 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 and has remained open for almost 20 years. In this paper we provide 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. To do so, we first provide two general results that allow to obtain upper and lower bounds on the bisection width of a product graph as a function of some properties of its factor graphs. We also apply these results to obtain bounds for the bisection bandwidth of a d-dimensional BCube network, a recently proposed topology for data centers.