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

机译：产品网络的二等分（带）宽度及其在数据中心的应用

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摘要

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.
机译：互连网络的二等分宽度在并行计算中一直很重要，因为它限制了信息可以从网络的一侧移动到另一侧的速度，即二等分带宽。对于某些网络家族来说，找到其确切价值已证明是具有挑战性的。例如，Leighton [1，问题1.281]提出了寻找多维圆环的精确等分宽度的问题，并且这个问题已经开放了将近20年。我们提供了两个一般结果，这些结果使我们能够根据其乘积图的某些属性来获得任何乘积图的等分宽度的上限和下限。通过推导圆环的等分宽度以及可以通过应用图的笛卡尔积获得的几种d维经典平行拓扑的精确值，可以显示这些结果的功效。我们还将这些结果应用于数据中心，方法是获取d维BCube网络（一种最近提出的数据中心拓扑）的二分带宽的界限。

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