快速且紧凑的图割用于Boykov-Kolmogorov算法
Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm
AI总结：
本文改进了Boykov-Kolmogorov算法的时间复杂度，并提出了一种新的快速紧凑算法，实现了高效的图割计算，同时展示了内存高效的实现方法。
摘要：
计算图中的最小s-t割是解决多种计算机视觉问题的解决方案，通常使用Boykov-Kolmogorov（BK）算法。本文从理论和实践角度重新审视BK算法，将时间复杂度分析改进为O(mn|C|)，并提出新的快速且紧凑的BK（fcBK）算法，时间复杂度为O(m|C|)，其中m、n和|C|分别表示边数、顶点数和割的容量。我们还提出了一种紧凑的图表示，使我们的实现能够在128GB内存的机器上处理多达10^9个顶点和10^10条边的图。我们发现我们的BK算法实现是评估全面的基准数据集上最快的可用实现，突显了内存高效实现的重要性。我们公开了我们的实现，供进一步研究和实现开发。
英文摘要：
Computing a minimum $s$-$t$ cut in a graph is a solution to a wide range of computer vision problems and is often done using the Boykov-Kolmogorov (BK) algorithm. In this paper, we revisit the BK algorithm from both a theoretical and practical point of view. We improve the analysis of the time complexity of the BK algorithm to $O(mn|C|)$ and propose a new algorithm, the fast BK (fBK) algorithm, with a time complexity of $O(m|C|)$, where $m$, $n$, and $|C|$ are the number of edges, the number of vertices, and the capacity of the cut, respectively. We additionally propose a compact graph representation that allows our implementations of the BK and fBK algorithms to find a minimum $s$-$t$ cut in a graph with up to $10^9$ vertices and $10^{10}$ edges on a machine with 128 GB of memory. We denote these as $\texttt{cBK}$ and $\texttt{fcBK}$, respectively. Despite $\texttt{fcBK}$ having the better worst-case guarantee, we find $\texttt{cBK}$ to be the fastest available implementation within the family of BK algorithms when evaluating on a comprehensive set of benchmark datasets, highlighting the importance of memory-efficient implementations. We make our implementations publicly available for further research and implementation development within minimum $s$-$t$ cut algorithms.
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。
