更快地检测2-joins
Detecting 2-joins faster
摘要：
2-连接是边割集，其自然地出现在几类图的分解中，所述几类图在取导出子图的情况下闭合，例如平衡二部图、偶无洞图、完美图和无爪图。它们的检测需要在几个算法中进行，并且对于其中一些算法来说是最慢的步骤。检测2-连接的经典方法需要花费$O(n^3m)$时间，其中$n$是输入图的顶点数，$m$是其边数。为了检测\emph{non-path} 2-join（在使用2-join的所有已知算法中需要的特殊类型的2-join），已知最快的方法需要时间$O(n^4m)$。在这里，我们给出了这两个问题的$O(n^2m)$时间算法。结果是几种已知算法的加速。
英文摘要：
2-joins are edge cutsets that naturally appear in the decomposition of several classes of graphs closed under taking induced subgraphs, such as balanced bipartite graphs, even-hole-free graphs, perfect graphs and claw-free graphs. Their detection is needed in several algorithms, and is the slowest step for some of them. The classical method to detect a 2-join takes $O(n^3m)$ time where $n$ is the number of vertices of the input graph and $m$ the number of its edges. To detect \emph{non-path} 2-joins (special kinds of 2-joins that are needed in all of the known algorithms that use 2-joins), the fastest known method takes time $O(n^4m)$. Here, we give an $O(n^2m)$-time algorithm for both of these problems. A consequence is a speed up of several known 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。
