This paper addresses point-to-point packet routing in undirected networks, which is the most important communication primitive in most networks. The main result proves the existence of routing tables that guarantee a polylog-competitive completion-time $\textbf{deterministically}$: in any undirected network, it is possible to give each node simple stateless deterministic local forwarding rules, such that, any adversarially chosen set of packets are delivered as fast as possible, up to polylog factors. All previous routing strategies crucially required randomization for both route selection and packet scheduling. The core technical contribution of this paper is a new local packet scheduling result of independent interest. This scheduling strategy integrates well with recent sparse semi-oblivious path selection strategies. Such strategies deterministically select not one but several candidate paths for each packet and require a global coordinator to select a single good path from those candidates for each packet. Another challenge is that, even if a single path is selected for each packet, no strategy for scheduling packets along low-congestion paths that is both local and deterministic is known. Our novel scheduling strategy utilizes the fact that every semi-oblivious routing strategy uses only a small (polynomial) subset of candidate routes. It overcomes the issue of global coordination by furthermore being provably robust to adversarial noise. This avoids the issue of having to choose a single path per packet because congestion caused by ineffective candidate paths can be treated as noise. Our results imply the first deterministic universally-optimal algorithms in the distributed supported-CONGEST model for many important global distributed tasks, including computing minimum spanning trees, approximate shortest paths, and part-wise aggregates.

翻译：本文研究无向网络中的点对点分组路由问题，这是大多数网络中最核心的通信原语。主要结果证明了存在能够保证polylog竞争性完成时间的**确定性**路由表：在任意无向网络中，可为每个节点赋予简单的无状态确定性本地转发规则，使得任意对抗性选择的分组集合都能以接近最优的速度（仅相差polylog因子）完成投递。此前所有路由策略在路由选择与分组调度中均必须依赖随机化。本文的核心技术贡献在于提出一种具有独立价值的新型本地分组调度结果。该调度策略能与近期提出的稀疏半 oblivious 路径选择策略良好集成。此类策略为每个分组确定性地选取不止一条而是多条候选路径，但需要全局协调器为每个分组从候选路径中选取单一最优路径。另一挑战在于：即便为每个分组选定单一路径，目前尚无既满足本地性又具备确定性的低拥塞路径分组调度策略。本文提出的新型调度策略利用半 oblivious 路由策略仅使用少量（多项式规模）候选路由子集这一特性，通过证明其对对抗性噪声具有鲁棒性来规避全局协调问题。这避免了为每个分组选择单一路径的难题，因为低效候选路径造成的拥塞可视为噪声处理。我们的结果在分布式supported-CONGEST模型下，为最小生成树计算、近似最短路径求解、部分区域聚合等多项重要全局分布式任务首次提供了确定性通用最优算法。