# Approximating k-connected m-dominating sets

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## ملخص

A subset S of nodes in a graph G is a k-connected m-dominating set ((k, m)-cds) if the subgraph G[S] induced by S is k-connected and every v ∈ V \ S has at least m neighbors in S. 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. For m ≥ k we obtain the following approximation ratios. For general graphs our ratio O(k ln n) improves the previous best ratio O(k2 ln n) of [26] and matches the best known ratio for unit weights of [34]. For unit disk graphs we improve the ratio O(k ln k) of [26] to min { mmk, k2/3 · O(ln2 k) – this is the first sublinear ratio for the problem, and the first polylogarithmic ratio O(ln2 k)/ when m ≥ (1 + )k; furthermore, we obtain ratio min {mmk, k · O(ln2 k) for uniform weights. These results are obtained by showing the same ratios for the Subset k-Connectivity problem when the set of terminals is an m-dominating set.

اللغة الأصلية الإنجليزيّة 28th Annual European Symposium on Algorithms, ESA 2020 Fabrizio Grandoni, Grzegorz Herman, Peter Sanders Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing 9783959771627 https://doi.org/10.4230/LIPIcs.ESA.2020.73 نُشِر - 1 أغسطس 2020 28th Annual European Symposium on Algorithms, ESA 2020 - Virtual, Pisa, إيطالياالمدة: ٧ سبتمبر ٢٠٢٠ → ٩ سبتمبر ٢٠٢٠

### سلسلة المنشورات

الاسم Leibniz International Proceedings in Informatics, LIPIcs 173 1868-8969

### !!Conference

!!Conference 28th Annual European Symposium on Algorithms, ESA 2020 إيطاليا Virtual, Pisa ٧/٠٩/٢٠ → ٩/٠٩/٢٠