arXiv 2111.087802021-11-16cs.DScs.NI

最优不经意可重构网络

Optimal Oblivious Reconfigurable Networks

Daniel Amir, Tegan Wilson, Vishal Shrivastav, Hakim Weatherspoon, Robert Kleinberg, Rachit Agarwal

备注：: 33 pages, 3 figures

摘要：

不经意路由在网络的理论和实践中都有着悠久的历史。在这项工作中，我们发起了正式的研究不经意路由的可重构网络，一个新的架构，最近在数据中心网络中脱颖而出的背景下。这些网络允许节点之间快速变化的有界度互连模式，但网络拓扑和路由路径的选择都必须不受流量需求矩阵的影响。我们的重点是在这些网络中最大化吞吐量和最小化延迟之间的权衡。对于每一个恒定的吞吐率，我们的特点（一个恒定的因素）的最小延迟可实现的一个不经意的可重构网络设计，满足给定的吞吐量保证。这两个目标之间的权衡结果令人惊讶地微妙：描绘它的曲线具有意想不到的扇形形状，反映了当路由路径的平均长度不是整数时负载平衡变得更加困难的事实，因为均衡所有路径长度是不可能的。我们的下界的证明使用LP对偶验证，Valiant负载均衡是最有效的不经意路由方案时，结合使用优化设计的可重构网络拓扑结构。我们的上界的证明使用代数结构，其中网络节点被确定为向量在有限域上，网络拓扑结构被描述的基本基础或一系列的Vandermonde矩阵，和路由路径被构造通过选择这些矩阵的列，以产生适当的混合路径长度在最短的时间间隔。

英文摘要：

Oblivious routing has a long history in both the theory and practice of networking. In this work we initiate the formal study of oblivious routing in the context of reconfigurable networks, a new architecture that has recently come to the fore in datacenter networking. These networks allow a rapidly changing bounded-degree pattern of interconnections between nodes, but the network topology and the selection of routing paths must both be oblivious to the traffic demand matrix. Our focus is on the trade-off between maximizing throughput and minimizing latency in these networks. For every constant throughput rate, we characterize (up to a constant factor) the minimum latency achievable by an oblivious reconfigurable network design that satisfies the given throughput guarantee. The trade-off between these two objectives turns out to be surprisingly subtle: the curve depicting it has an unexpected scalloped shape reflecting the fact that load-balancing becomes more difficult when the average length of routing paths is not an integer because equalizing all the path lengths is not possible. The proof of our lower bound uses LP duality to verify that Valiant load balancing is the most efficient oblivious routing scheme when used in combination with an optimally-designed reconfigurable network topology. The proof of our upper bound uses an algebraic construction in which the network nodes are identified with vectors over a finite field, the network topology is described by either the elementary basis or a sequence of Vandermonde matrices, and routing paths are constructed by selecting columns of these matrices to yield the appropriate mixture of path lengths within the shortest possible time interval.

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。

摘要：

英文摘要：

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