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：随着光路交换等新型网络技术的引入，数据中心网络正变得越来越灵活。这些技术支持可编程网络拓扑，能够根据网络流量模式进行重新配置，从而在重构收益（即更短路由）与成本（即开销）之间实现权衡。自调整网络旨在通过利用流量模式来解决这一权衡问题，无论该模式是逐步显现的（在线动态拓扑）还是预先已知的（离线静态拓扑）。本文首次探索自调整k叉树网络的研究方向。作为现有二叉搜索树网络（如SplayNet）的更强大泛化形式，这类网络构成了自调整网络设计的核心。k叉搜索树网络作为自然泛化，提供了更高节点度、固定节点数下更短的路由长度，以及拓扑重构下的本地路由能力。我们首先通过动态规划在$O(n^3 \cdot k)$时间内计算任意流量模式下的离线（最优）静态网络，并针对均匀分布流量的特殊情况将复杂度改进至$O(n^2 \cdot k)$。随后提出一种基于质心的网络拓扑结构，可同时适用于离线静态与在线动态场景。在离线均匀负载情况下，我们以线性时间$O(n)$构建该准最优网络，最终提出SplayNet的在线自调整k叉搜索树版本。我们在真实与合成网络轨迹上对$k=2$的新结构进行实验评估（以便与现有SplayNet比较）。结果表明：在多数真实网络轨迹及中低局部性合成轨迹中，该方法优于SplayNet；在所有剩余轨迹中仅略逊于SplayNet。