Approximating k-connected m-dominating sets

Zeev Nutov

doi:10.4230/LIPIcs.ESA.2020.73

Approximating k-connected m-dominating sets

Zeev Nutov

Computer Science discipline

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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 { _m^m₋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 {_m^m₋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.

Original language	English
Title of host publication	28th Annual European Symposium on Algorithms, ESA 2020
Editors	Fabrizio Grandoni, Grzegorz Herman, Peter Sanders
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959771627
DOIs	https://doi.org/10.4230/LIPIcs.ESA.2020.73
State	Published - 1 Aug 2020
Event	28th Annual European Symposium on Algorithms, ESA 2020 - Virtual, Pisa, Italy Duration: 7 Sep 2020 → 9 Sep 2020

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	173
ISSN (Print)	1868-8969

Conference

Conference	28th Annual European Symposium on Algorithms, ESA 2020
Country/Territory	Italy
City	Virtual, Pisa
Period	7/09/20 → 9/09/20

Bibliographical note

Publisher Copyright:
© Zeev Nutov.

Keywords

Approximation algorithm
M-dominating set
Rooted subset k-connectivity
Subset k-connectivity
k-connected graph

Access to Document

10.4230/LIPIcs.ESA.2020.73

Cite this

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title = "Approximating k-connected m-dominating sets",

abstract = "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.",

keywords = "Approximation algorithm, M-dominating set, Rooted subset k-connectivity, Subset k-connectivity, k-connected graph",

author = "Zeev Nutov",

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Nutov, Z 2020, Approximating k-connected m-dominating sets. in F Grandoni, G Herman & P Sanders (eds), 28th Annual European Symposium on Algorithms, ESA 2020., 73, Leibniz International Proceedings in Informatics, LIPIcs, vol. 173, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 28th Annual European Symposium on Algorithms, ESA 2020, Virtual, Pisa, Italy, 7/09/20. https://doi.org/10.4230/LIPIcs.ESA.2020.73

Approximating k-connected m-dominating sets. / Nutov, Zeev.
28th Annual European Symposium on Algorithms, ESA 2020. ed. / Fabrizio Grandoni; Grzegorz Herman; Peter Sanders. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2020. 73 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 173).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Approximating k-connected m-dominating sets

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

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