We study the maximum-flow/minimum-cut problem on scale-free networks, i.e., graphs whose degree distribution follows a power-law. We propose a simple algorithm that capitalizes on the fact that often only a small fraction of such a network is relevant for the flow. At its core, our algorithm augments Dinitz's algorithm with a balanced bidirectional search. Our experiments on a scale-free random network model indicate sublinear run time. On scale-free real-world networks, we outperform the commonly used highest-label Push-Relabel implementation by up to two orders of magnitude. Compared to Dinitz's original algorithm, our modifications reduce the search space, e.g., by a factor of 275 on an autonomous systems graph. Beyond these good run times, our algorithm has an additional advantage compared to Push-Relabel. The latter computes a preflow, which makes the extraction of a minimum cut potentially more difficult. This is relevant, for example, for the computation of Gomory-Hu trees. On a social network with 70000 nodes, our algorithm computes the Gomory-Hu tree in 3 seconds compared to 12 minutes when using Push-Relabel.

中文翻译：

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有效计算无标度网络中的最大流量

我们研究了无标度网络上的最大流/最小割问题，即度分布遵循幂律的图。我们提出了一个简单的算法，它利用了这样一个事实，即通常只有一小部分这样的网络与流相关。在其核心，我们的算法通过平衡的双向搜索增强了 Dinitz 的算法。我们在无标度随机网络模型上的实验表明亚线性运行时间。在无标度的现实世界网络上，我们的性能比常用的最高标签 Push-Relabel 实现高两个数量级。与 Dinitz 的原始算法相比，我们的修改减少了搜索空间，例如，在自治系统图上减少了 275 倍。除了这些良好的运行时间之外，与 Push-Relabel 相比，我们的算法还有一个额外的优势。后者计算预流，这使得提取最小切割可能更加困难。例如，这与 Gomory-Hu 树的计算有关。在具有 70000 个节点的社交网络上，我们的算法在 3 秒内计算出 Gomory-Hu 树，而使用 Push-Relabel 时需要 12 分钟。