For a graph \(G=(V,E)\), a vertex set \(C\subseteq V\) is an m-fold outer-connected dominating set (m-fold OCDS) of G if every vertex in \(V\backslash C\) has at least m neighbors in C and the subgraph of G induced by \(V\backslash C\) is connected. In this paper, we present a greedy algorithm to compute an m-fold OCDS in general graphs, which returns a solution of size at most \(\alpha +1+\ln (\Delta +m+1)\) times that of a minimum m-fold OCDS, where \(\Delta \) is the maximum degree of the graph and \(\alpha \) is a positive number at most \(\Delta \)+m+1.

中文翻译：

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容错外联支配集问题的贪心算法

对于图\（G =（V，E）\） ，顶点组\（C \ subseteq V \）是米-倍 外-连接 支配 组（米-倍 OCDS）的ģ如果在每个顶点\（ V \反斜杠C \）在C中至少有m个邻居，并且\（V \反斜杠C \）引起的G的子图已连接。在本文中，我们提出了一种贪心算法来计算一般图中的m倍OCDS，该算法最多返回大小的解\（\ alpha +1+ \ ln（\ Delta + m + 1）\）乘以最小m倍OCDS的乘积，其中\（\ Delta \）是图的最大程度，而\（\ alpha \）最多为\（\ Delta \） + m +1的正数。