重新探讨强多项式并行最大流
Strongly Polynomial Parallel Maximum Flow Revisited
中文总结 AI 辅助
该研究针对并行环境下带实数容量的有向网络最大流问题，提出一种强多项式最大流算法变体的随机并行实现，优化了工作量与深度的权衡，优于此前同类算法。
中文摘要 AI 辅助
我们研究并行环境下具有实数容量的有向网络中的最大流问题。对于含$n$个顶点和$m$条弧的网络，我们证明了Dadush、Orlin、Sidford和Végh在[SODA 2026]中提出的强多项式最大流算法变体的随机并行实现，其运行时间为$\tilde{O}(mn)$工作量和$\tilde{O}(m)$深度。这改进了此前强多项式并行最大流算法中工作量与深度的权衡关系：早期$\tilde{O}(n^3)$工作量算法的深度为$\tilde{O}(n^2)$[Shiloach和Vishkin，J. Algorithms 1982；Goldberg和Tarjan，J. ACM 1988]，而已知的$\tilde{O}(m)$深度方法则需要$\tilde{O}(mn^3)$工作量[Orlin，Oper. Res. 1993]。
英文摘要
We study the maximum flow problem in directed networks with real capacities in the parallel setting. For a network with $n$ vertices and $m$ arcs, we show that a randomized parallel implementation of a variant of the strongly polynomial max-flow algorithm of Dadush, Orlin, Sidford, and Végh [SODA 2026] runs in $\tilde{O}(mn)$ work and $\tilde{O}(m)$ depth. This improves upon the previously described tradeoffs between work and depth for strongly polynomial parallel maximum flow algorithms: earlier $\tilde{O}(n^3)$-work algorithms have $\tilde{O}(n^2)$ depth [Shiloach and Vishkin, J. Algorithms 1982; Goldberg and Tarjan, J. ACM 1988], while the known $\tilde{O}(m)$-depth approach uses $\tilde{O}(mn^3)$ work [Orlin, Oper. Res. 1993].
