Datacenter networks are becoming increasingly flexible with the incorporation of new networking technologies, such as optical circuit switches. These technologies allow for programmable network topologies that can be reconfigured to better serve network traffic, thus enabling a trade-off between the benefits (i.e., shorter routes) and costs of reconfigurations (i.e., overhead). Self-Adjusting Networks (SANs) aim at addressing this trade-off by exploiting patterns in network traffic, both when it is revealed piecewise (online dynamic topologies) or known in advance (offline static topologies). In this paper, we take the first steps toward Self-Adjusting k-ary tree networks. These are more powerful generalizations of existing binary search tree networks (like SplayNets), which have been at the core of SAN designs. k-ary search tree networks are a natural generalization offering nodes of higher degrees, reduced route lengths for a fixed number of nodes, and local routing in spite of reconfigurations. We first compute an offline (optimal) static network for arbitrary traffic patterns in $O(n^3 \cdot k)$ time via dynamic programming, and also improve the bound to $O(n^2 \cdot k)$ for the special case of uniformly distributed traffic. Then, we present a centroid-based topology of the network that can be used both in the offline static and the online setting. In the offline uniform-workload case, we construct this quasi-optimal network in linear time $O(n)$ and, finally, we present online self-adjusting k-ary search tree versions of SplayNet. We evaluate experimentally our new structure for $k=2$ (allowing for a comparison with existing SplayNets) on real and synthetic network traces. Our results show that this approach works better than SplayNet in most of the real network traces and in average to low locality synthetic traces, and is only little inferior to SplayNet in all remaining traces.

翻译：数据中心网络随着新型网络技术（如光电路交换）的融入正变得日益灵活。这些技术允许可编程网络拓扑根据网络流量进行动态重构，从而在重构收益（更短路由）与成本（开销）之间实现权衡。自调节网络旨在通过挖掘网络流量模式（无论是分段呈现的在线动态拓扑还是预知的离线静态拓扑）来解决这一权衡问题。本文率先探索了自调节k叉树网络——这种架构是对现有二叉搜索树网络（如SplayNet）的强力泛化，后者一直是自调节网络设计的核心。k叉搜索树网络作为自然泛化方案，具有更高节点度数、固定节点数下更短路由长度以及重构过程中的本地路由特性。我们首先通过动态规划算法，在$O(n^3 \cdot k)$时间内为任意流量模式计算出离线（最优）静态网络，并在均匀分布流量的特例中将复杂度优化至$O(n^2 \cdot k)$。随后提出基于质心的网络拓扑结构，该结构可同时适用于离线静态与在线场景。针对离线均匀负载情况，我们能在线性时间$O(n)$内构建该准最优网络。最后，我们给出了SplayNet的在线自调节k叉搜索树版本。通过实际与合成网络流量数据，针对$k=2$的情况（便于与现有SplayNet对比）进行实验评估。结果表明，本文方法在大多数真实网络流量以及中低局部性合成的流量中优于SplayNet，仅在其余流量场景中略逊于SplayNet。