平面图中的不经意批量购买
Oblivious Buy-at-Bulk in Planar Graphs
摘要：
在图中的不经意批量购买网络设计问题中，任务是为图中的每一对源-目的地计算一组固定的路径，使得任何一组需求都可以沿着这些路径路由。需求可以在中间边缘处聚合，其中融合成本由规范（非负凹）函数$f$指定。我们给出了一个新的算法，平面图是不经意的要求，也是不经意的融合函数$f$。该算法是确定性的，并在多项式时间内计算固定的路径集，并保证$O(\log n)$的近似比为任何一组的需求和任何规范的融合功能$f$，其中$n$是节点的数量。该算法是渐近最优的，因为它是已知的，这个问题不能近似比$Ω(\log n)$比率更好。据我们所知，这是第一个紧密的平面图分析，并提高了近似比的一个因素，$\log n$与以前已知的结果。
英文摘要：
In the oblivious buy-at-bulk network design problem in a graph, the task is to compute a fixed set of paths for every pair of source-destinations in the graph, such that any set of demands can be routed along these paths. The demands could be aggregated at intermediate edges where the fusion-cost is specified by a canonical (non-negative concave) function $f$. We give a novel algorithm for planar graphs which is oblivious with respect to the demands, and is also oblivious with respect to the fusion function $f$. The algorithm is deterministic and computes the fixed set of paths in polynomial time, and guarantees a $O(\log n)$ approximation ratio for any set of demands and any canonical fusion function $f$, where $n$ is the number of nodes. The algorithm is asymptotically optimal, since it is known that this problem cannot be approximated with better than $Ω(\log n)$ ratio. To our knowledge, this is the first tight analysis for planar graphs, and improves the approximation ratio by a factor of $\log n$ with respect to previously known results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
