Finding 2-Edge and 2-Vertex Strongly Connected Components in Quadratic Time
Finding 2-Edge and 2-Vertex Strongly Connected Components in Quadratic Time
复制标题
在二次时间内查找 2 边和 2 顶点强连通分量
DOI：
10.1007/978-3-662-47672-7_58
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Veronika Loitzenbauer
中科院分区：
文献类型：
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作者：
Monika Henzinger;Sebastian Krinninger;Veronika Loitzenbauer
我们提出了计算有向图的2边和2顶点强连通分量的更快算法。虽然在线性时间内可以找到2边和2顶点连接分量的无向图，但已知的具有边界和顶点的间接图只有相当简单的o （mn）时间算法。我们使用分层稀疏化技术来获得实时运行的算法。对于2边强连接组件，该算法实现了20年来首次运行时间的改进。此外，我们还提出了两边强连接组件的一次算法，从而提高了运行时间超过theO（mn）。我们的方法扩展了任何常数的k-边和k-顶点强连接分量，并具有叉边连接和叉顶点连接的运行时间。
We present faster algorithms for computing the 2-edge and 2-vertex strongly connected components of a directed graph. While inundirectedgraphs the 2-edge and 2-vertex connected components can be found in linear time, indirectedgraphs withmedges andnvertices only rather simpleO(mn)-time algorithms were known. We use a hierarchical sparsification technique to obtain algorithms that run in time. For 2-edge strongly connected components our algorithm gives the first running time improvement in 20 years. Additionally we present an-time algorithm for 2-edge strongly connected components, and thus improve over theO(mn) running time also when. Our approach extends tok-edge andk-vertex strongly connected components for any constantkwith a running time offork-edge-connectivity andfork-vertex-connectivity.