Abstract
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.
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Acknowledgements
This work was supported by the NSF of China (Nos. 11471097 and 11971146), the NSF of Hebei Province (Nos. A2017403010, A2019205089 and A2019205092).
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Wang, X., Li, X., Hou, B. et al. A greedy algorithm for the fault-tolerant outer-connected dominating set problem. J Comb Optim 41, 118–127 (2021). https://doi.org/10.1007/s10878-020-00668-z
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DOI: https://doi.org/10.1007/s10878-020-00668-z