TY - GEN

T1 - Approximating k-connected m-dominating sets

AU - Nutov, Zeev

N1 - Publisher Copyright: © Zeev Nutov.

PY - 2020/8/1

Y1 - 2020/8/1

N2 - 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 { mm−k, 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 {mm−k, √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.

AB - 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 { mm−k, 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 {mm−k, √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.

KW - Approximation algorithm

KW - M-dominating set

KW - Rooted subset k-connectivity

KW - Subset k-connectivity

KW - k-connected graph

UR - http://www.scopus.com/inward/record.url?scp=85092519922&partnerID=8YFLogxK

U2 - https://doi.org/10.4230/LIPIcs.ESA.2020.73

DO - https://doi.org/10.4230/LIPIcs.ESA.2020.73

M3 - منشور من مؤتمر

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 28th Annual European Symposium on Algorithms, ESA 2020

A2 - Grandoni, Fabrizio

A2 - Herman, Grzegorz

A2 - Sanders, Peter

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 28th Annual European Symposium on Algorithms, ESA 2020

Y2 - 7 September 2020 through 9 September 2020

ER -