Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut networks into smaller, more readily comprehensible blocks. In this work, we aim to partition the vertices of a graph into multiple blocks while minimizing the number of edges that connect different blocks. There is a multitude of cut or partitioning problems that have been the focus of research for multiple decades. This work develops highly-efficient algorithms for the (global) minimum cut problem, the balanced graph partitioning problem and the multiterminal cut problem. All of these algorithms are efficient in practice and freely available for use.
翻译:图表是来自不同背景的数据的自然代表, 如社会连接、 网络、 道路网络等等。 在过去的几十年中, 许多这些网络已经变得巨大, 需要高效的算法将网络分割成更小、 更便于理解的区块。 在这项工作中, 我们的目标是将图表的顶点分割成多个区块, 同时将连接不同区块的边缘数量最小化 。 数十年来, 有许多切割或分割问题一直是研究的焦点 。 这项工作为( 全球) 最小切开区块的问题、 平衡的图形分割问题和多端截断问题开发了高效的算法 。 所有这些算法在实践上是有效的,可以自由使用。