In a landmark 1981 paper, Valiant and Brebner gave birth to the study of oblivious routing and, simultaneously, introduced its most powerful and ubiquitous method: Valiant load balancing (VLB). By routing messages through a randomly sampled intermediate node, VLB lengthens routing paths by a factor of two but gains the crucial property of obliviousness. Forty years later, with datacenters handling workloads whose communication pattern varies too rapidly to allow centralized coordination, VLB continues to take center stage as a widely used - and in some cases provably optimal - way to balance load in the network obliviously to the traffic demands. However, the ability of the network to rapidly reconfigure its interconnection topology gives rise to new possibilities. In this work we revisit the question of whether VLB remains optimal in the novel setting of reconfigurable networks. Prior work showed that VLB achieves the optimal tradeoff between latency and guaranteed throughput. In this work we show that a strictly superior latency-throughput tradeoff is achievable when the throughput bound is relaxed to hold with high probability. The same improved tradeoff is also achievable with guaranteed throughput under time-stationary demands, provided the latency bound is relaxed to hold with high probability and that the network is allowed to be semi-oblivious, using an oblivious (randomized) connection schedule but demand-aware routing. We prove that the latter result is not achievable by any fully-oblivious reconfigurable network design, marking a rare case in which semi-oblivious routing has a provable asymptotic advantage over oblivious routing. To analyze our routing scheme we prove an exponential tail bound which may be of independent interest, concerning the distribution of values of a bilinear form on an orbit of a permutation group action.

翻译：在1981年的一篇里程碑式论文中，Valiant和Brebner开创了隐匿路由的研究，并同时引入了其最强大且普遍的方法：Valiant负载均衡（VLB）。通过经由随机采样的中间节点路由消息，VLB将路由路径长度增加一倍，但获得了隐匿性这一关键特性。四十年后，面对通信模式变化过快而无法集中协调的数据中心工作负载，VLB仍占据核心地位，成为一种广泛使用——在某些情况下被证明是最优的——在网络中隐匿平衡负载的方法。然而，网络快速重构其互连拓扑的能力带来了新的可能性。本文重新审视了在可重构网络这一新场景中VLB是否仍保持最优的问题。先前研究表明，VLB在延迟与保证吞吐量之间实现了最优权衡。本文证明，当吞吐量界限放宽为以高概率成立时，可实现严格更优的延迟-吞吐量权衡。若延迟界限以高概率成立，且网络允许采用半隐匿设计（使用隐匿（随机化）连接调度但需求感知路由），则在时间平稳需求下，相同改进的权衡也可通过保证吞吐量实现。我们证明后一结论无法被任何全隐匿可重构网络设计所达到，这标志着半隐匿路由在隐匿路由上具有可证明渐进优势的罕见案例。为分析我们的路由方案，我们证明了一个指数尾界（可能具有独立兴趣），该尾界涉及置换群作用轨道的双线性型值分布。