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- W2949827110 abstract "A graph is $k$-connected if it has $k$ internally-disjoint paths between every pair of nodes. A subset $S$ of nodes in a graph $G$ is a $k$-connected set if the subgraph $G[S]$ induced by $S$ is $k$-connected; $S$ is an $m$-dominating set if every $v in V setminus S$ has at least $m$ neighbors in $S$. If $S$ is both $k$-connected and $m$-dominating then $S$ is a $k$-connected $m$-dominating set, or $(k,m)$-cds for short. In the $k$-Connected $m$-Dominating Set ($(k,m)$-CDS) problem the goal is to find a minimum weight $(k,m)$-cds in a node-weighted graph. We consider the case $m geq k$ and obtain the following approximation ratios. For unit disc-graphs we obtain ratio $O(kln k)$, improving the previous ratio $O(k^2 ln k)$. For general graphs we obtain the first non-trivial approximation ratio $O(k^2 ln n)$." @default.
- W2949827110 created "2019-06-27" @default.
- W2949827110 creator A5003622145 @default.
- W2949827110 date "2017-03-13" @default.
- W2949827110 modified "2023-09-27" @default.
- W2949827110 title "Improved approximation algorithms for $k$-connected $m$-dominating set problems" @default.
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