产品网络的二分（带宽）宽度及其在数据中心中的应用
Bisection (Band)Width of Product Networks with Application to Data Centers
摘要：
互连网络的二分宽度在并行计算中一直很重要，因为它限制了可以从网络的一侧移动到另一侧的信息量，即，二分带宽。事实证明，对于一些网络家庭来说，找到它的确切值是一个挑战。例如，寻找多维环面的精确平分宽度的问题是由莱顿提出的，并且已经开放了近20年。在本文中，我们提供了确切的值的二分法宽度的环面，以及几个d维经典的并行拓扑结构，可以通过应用笛卡尔积的图形。要做到这一点，我们首先提供了两个一般性的结果，允许获得上界和下界的二分法宽度的产品图作为其因子图的一些属性的函数。我们还应用这些结果获得的d维BCube网络，最近提出的数据中心拓扑结构的二分带宽的界限。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
