We propose a framework for speeding up maximum flow computation by using predictions. A prediction is a flow, i.e., an assignment of non-negative flow values to edges, which satisfies the flow conservation property, but does not necessarily respect the edge capacities of the actual instance (since these were unknown at the time of learning). We present an algorithm that, given an -edge flow network and a predicted flow, computes a maximum flow in time, where is the error of the prediction, i.e., the sum over the edges of the absolute difference between the predicted and optimal flow values. Moreover, we prove that, given an oracle access to a distribution over flow networks, it is possible to efficiently PAC-learn a prediction minimizing the expected error over that distribution. Our results fit into the recent line of research on learning-augmented algorithms, which aims to improve over worst-case bounds of classical algorithms by using predictions, e.g., machine-learned from previous similar instances. So far, the main focus in this area was on improving competitive ratios for online problems. Following Dinitz et al. (2021) , our results are among the firsts to improve the running time of an offline problem.

中文翻译：

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学习增强最大流量

我们提出了一个通过使用预测来加速最大流计算的框架。预测是一个流，即将非负流值分配给边缘，它满足流守恒性质，但不一定尊重实际实例的边缘容量（因为这些在学习时是未知的）。我们提出了一种算法，给定一个边流网络和一个预测流，计算时间上的最大流，其中 是预测误差，即预测流值和最佳流值之间的绝对差的边缘总和。此外，我们证明，如果预言机可以访问流网络上的分布，则可以有效地进行 PAC 学习，从而最小化该分布上的预期误差。我们的结果符合最近关于学习增强算法的研究，该算法旨在通过使用预测（例如从以前的类似实例进行机器学习）来改进经典算法的最坏情况界限。到目前为止，该领域的主要重点是提高在线问题的竞争率。继迪尼茨等人之后。(2021)，我们的结果是第一个改善离线问题的运行时间的结果。