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。主要成果证明了存在确保多对数竞争完成时间的路由表：在任何无向网络中，可为每个节点赋予简单的无状态确定性本地转发规则，使得任意对抗选择的分组集合都能在接近最优的多对数因子范围内尽快投递。此前所有路由策略均需依赖随机化进行路径选择与分组调度。本文的核心技术贡献在于提出了一种具有独立价值的新型本地分组调度策略。该调度策略能与近期提出的稀疏半遗忘路径选择策略良好结合。这类策略为每个分组确定性选择多条候选路径而非单一路径，并需要全局协调者为每个分组从候选中筛选唯一最优路径。另一个挑战在于，即使为每个分组选定唯一路径，目前仍缺乏既能实现本地化调度又能保持确定性的低拥塞路径调度策略。本调度策略的创新之处在于：利用每个半遗忘路由策略仅使用小规模（多项式级）候选路径子集的特性，通过证明其对对抗性噪声具有稳健性，从而规避全局协调问题。由于无效候选路径造成的拥塞可视为噪声处理，因此无需为每个分组选择唯一路径。该成果在分布式支持拥塞模型下，为最小生成树计算、近似最短路计算和部分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。