Fast algorithms for k-shredders and k-node connectivity augmentation (extended abstract)
Fast algorithms for k-shredders and k-node connectivity augmentation (extended abstract)
复制标题
k-shredders 和 k-node 连接增强的快速算法（扩展摘要）
DOI：
10.1145/237814.237826
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
R. Thurimella
中科院分区：
文献类型：
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作者：
J. Cheriyan;R. Thurimella
一个无向图的k个分离器k个分解器是一个k个节点的集合，它的去除导致两个或更多个三个或更多个连通分支设给定的无向图是k个节点连通的，设n表示节点的数目解决一个公开问题，我们证明了计算k个分离器的数目是P完全的，但是我们提出了一个O k n k n时间确定性算法来确定所有k个分解器。解决了一个悬而未决的问题，有效地和k分离器，其去除最大化连接组件的数量对于k，我们的运行时间是在已知的用于测试k节点连通性的最快算法的k倍之内。切碎器的一个应用是通过有效地添加近似最小数量的新边来将节点连通性从k增加到k。JCT B给出了O n时间增强算法，使得新边的数目在从下界到k的加法项内我们将运行时间改进为O min k p n k n logn kn，同时实现相同的性能保证对于k，运行时间与测试k节点连通性的运行时间相比是有利的
A k separator k shredder of an undirected graph is a set of k nodes whose removal results in two or more three or more connected components Let the given undirected graph be k node connected and let n denote the number of nodes Solving an open question we show that the problem of counting the number of k separators is P complete However we present an O k n k n time deterministic algorithm for nding all the k shredders This solves an open question e ciently nd a k separator whose removal maximizes the number of connected components For k our running time is within a factor of k of the fastest algorithm known for testing k node connectivity One application of shredders is in increasing the node connectivity from k to k by e ciently adding an approximately minimum number of new edges Jord an JCT B gave an O n time augmentation algorithm such that the number of new edges is within an additive term of k from a lower bound We improve the running time to O min k p n k n logn kn while achieving the same performance guarantee For k the running time compares favorably with the running time for testing k node connectivity
H.NAGAMOCHI、T.LBARAKI：“一种用于查找 k 连接图的稀疏 k 连接生成子图的线性时间算法”Algorithmica。
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