In the Connected Dominating Set (CDS) problem we are given a graph G and seek a min-size dominating set S such that the subgraph $G[S]$ of G induced by S is connected. In the 2-Edge-Connected Dominating Set problem $G[S]$ should be 2-edge-connected. We give the first non-trivial approximation algorithm for this problem, with expected approximation ratio $O({\log }^{2}n\cdot \log \log n\cdot {(\log \log \log n)}^3)$. We also show that the Subset Steiner CDS problem is approximation equivalent to the Group Steiner Tree problem.

中文翻译：

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一种2边连通支配集的多对数逼近算法

在连通支配集( CDS ) 问题中，我们给定了一个图G并寻找一个最小大小的支配集S，使得子图$G[秒]$由S引起的G是连通的。在 2 -Edge-Connected Domination Set问题中$G[秒]$应该是 2-edge-connected。我们给出了这个问题的第一个非平凡逼近算法，具有预期的逼近比$哦({\mathrm{日志}}^{2}n\cdot \mathrm{日志}\mathrm{日志}n\cdot {(\mathrm{日志}\mathrm{日志}\mathrm{日志}n)}^3)$. 我们还表明Subset Steiner CDS问题近似等效于Group Steiner Tree问题。