We present a new strongly polynomial algorithm for generalized flow maximization that is significantly simpler and faster than the previous strongly polynomial algorithm [34]. For the uncapacitated problem formulation, the complexity bound O ( mn ( m + n log n )log ( n 2 / m )) improves on the previous estimate by almost a factor O ( n 2 ). Even for small numerical parameter values, our running time bound is comparable to the best weakly polynomial algorithms. The key new technical idea is relaxing the primal feasibility conditions. This allows us to work almost exclusively with integral flows, in contrast to all previous algorithms for the problem.

中文翻译：

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一种更简单、更快速的广义流最大化强多项式算法

我们提出了一种新的用于广义流最大化的强多项式算法，它比以前的强多项式算法 [34] 更简单、更快。对于无能力的问题公式，复杂性界限○(锰(米+n日志n）日志 （n 2/米)) 将先前的估计提高了几乎一个因素○(n 2）。即使对于小的数值参数值，我们的运行时间限制也可以与最好的弱多项式算法相媲美。关键的新技术思想是放宽原始可行性条件。这使我们几乎可以完全使用积分流，这与之前所有针对该问题的算法不同。