稀疏半 oblivious 路由：少量随机路径即足够
Sparse Semi-Oblivious Routing: Few Random Paths Suffice
AI总结：
本文证明稀疏半 oblivious 路由的存在性：每对顶点仅需 $O(\log n)$ 条随机采样路径即可对所有需求达到 $poly \log n$ 竞争比，并给出稀疏度-竞争比权衡及下界，为流量工程中的启发式方法提供了理论依据。
摘要：
数据包路由问题要求为给定源-目的顶点对的集合选择路由路径，以最小化最大边拥塞。我们重新审视一种半 oblivious 方法：在需求揭示之前，每个源-目的对分配一组预定义的路径，而沿路径的发送速率可以最优地适应需求。由于该方法相比 oblivious 路由和传统流量工程方法具有优越的鲁棒性和性能，已在网络流量工程实践中得到考虑。\n我们证明了稀疏半 oblivious 路由的存在性：每对顶点之间仅选择 $O(\log n)$ 条路径。该路由对所有需求相对于离线最优拥塞目标具有 $(poly \log n)$ 竞争比。即使在研究充分的超立方体情形下，此前也未知此类结果：我们确定性的且 oblivious 的 $O(\log n)$ 条路径选择是第一个简单构造的确定性 oblivious 结构，该结构将源-目的对近乎最优地分配到少量路径上。我们的结果与当前半 oblivious 路由领域仅有的负面结果形成对比。我们给出了较低稀疏度下的稀疏性-竞争比权衡，并用下界近乎匹配该权衡。\n我们的构造极其简单：从任意竞争性 oblivious 路由中采样少量路径。事实上，这种自然构造在流量工程中曾被用作未经证明的启发式方法。我们为其实验有效性提供了令人满意的理论证明：构造的竞争比随路径数量呈指数级提升。最后，当与最近的跳数受限 oblivious 路由结合时，我们还获得了针对完成时间目标的稀疏且具有竞争性的结构。
英文摘要：
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.
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