The packet routing problem asks to select routing paths that minimize the maximum edge congestion for a set of packets specified by source-destination vertex pairs. We revisit a semi-oblivious approach to this problem: each source-destination pair is assigned a small set of predefined paths before the demand is revealed, while the sending rates along the paths can be optimally adapted to the demand. This approach has been considered in practice in network traffic engineering due to its superior robustness and performance as compared to both oblivious routing and traditional traffic engineering approaches. We show the existence of sparse semi-oblivious routings: only $O(\log n)$ paths are selected between each pair of vertices. The routing is $(poly \log n)$-competitive for all demands against the offline-optimal congestion objective. Even for the well-studied case of hypercubes, no such result was known: our deterministic and oblivious selection of $O(\log n)$ paths is the first simple construction of a deterministic oblivious structure that near-optimally assigns source-destination pairs to few routes. Our results contrast the current solely-negative landscape of results for semi-oblivious routing. We give the sparsity-competitiveness trade-off for lower sparsities and nearly match it with a lower bound. Our construction is extremely simple: Sample the few paths from any competitive oblivious routing. Indeed, this natural construction was used in traffic engineering as an unproven heuristic. We give a satisfactory theoretical justification for their empirical effectiveness: the competitiveness of the construction improves exponentially with the number of paths. Finally, when combined with the recent hop-constrained oblivious routing, we also obtain sparse and competitive structures for the completion-time objective.

翻译：数据包路由问题需为指定源-目标顶点对的集合选择路由路径，以最小化最大边拥塞。我们重新审视该问题的半遗忘方法：在需求揭示前为每个源-目标对分配少量预定义路径，路径上的发送速率可根据需求最优调整。该方法因相比遗忘路由和传统流量工程方法具有更优鲁棒性和性能，已在网络流量工程实践中得到应用。我们证明了稀疏半遗忘路由的存在性：每对顶点间仅选择$O(\log n)$条路径。该路由对所有需求具有$(\mathrm{poly} \log n)$竞争比，优于离线最优拥塞目标。即便对于超立方体这一经典案例，此前也无类似结果：我们确定性且遗忘地选择$O(\log n)$条路径，是首个能近最优地将源-目标对分配至少量路径的确定性遗忘结构简单构造。我们的结果与当前半遗忘路由仅存在负面结论的现状形成鲜明对比。我们给出了更低稀疏度下的稀疏性-竞争比权衡，并通过下界几乎匹配该权衡。构造极其简单：从任意竞争性遗忘路由中采样少量路径。事实上，该自然构造已在流量工程中作为未经验证的启发式方法使用，我们为其经验有效性提供了令人满意的理论依据：构造的竞争性随路径数量呈指数级提升。最后，当结合近期提出的跳数约束遗忘路由时，我们还可获得面向完成时间目标的稀疏且竞争性结构。