Distributed approximation algorithms for the minimum dominating set in KH-minor-free graphs

Andrzej Czygrinow; Michał Hanćkowiak; Wojciech Wawrzyniak; Marcin Witkowski

doi:10.4230/LIPIcs.ISAAC.2018.22

Distributed approximation algorithms for the minimum dominating set in K_H-minor-free graphs

Andrzej Czygrinow, Michał Hanćkowiak, Wojciech Wawrzyniak, Marcin Witkowski

CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)

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

1 Scopus citations

Abstract

In this paper we will give two distributed approximation algorithms (in the Local model) for the minimum dominating set problem. First we will give a distributed algorithm which finds a dominating set D of size O(γ(G)) in a graph G which has no topological copy of K_h. The algorithm runs L_h rounds where L_h is a constant which depends on h only. This procedure can be used to obtain a distributed algorithm which given > 0 finds in a graph G with no K_h-minor a dominating set D of size at most (1 + )γ(G). The second algorithm runs in O(log^∗ |V (G)|) rounds.

Original language	English (US)
Title of host publication	29th International Symposium on Algorithms and Computation, ISAAC 2018
Editors	Wen-Lian Hsu, Der-Tsai Lee, Chung-Shou Liao
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages	22:1–22:12
ISBN (Electronic)	9783959770941
DOIs	https://doi.org/10.4230/LIPIcs.ISAAC.2018.22
State	Published - Dec 1 2018
Event	29th International Symposium on Algorithms and Computation, ISAAC 2018 - Jiaoxi, Yilan, Taiwan, Province of China Duration: Dec 16 2018 → Dec 19 2018

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	123
ISSN (Print)	1868-8969

Conference

Conference	29th International Symposium on Algorithms and Computation, ISAAC 2018
Country/Territory	Taiwan, Province of China
City	Jiaoxi, Yilan
Period	12/16/18 → 12/19/18

Keywords

Distributed algorithms
MDS
Minor-closed family of graphs

ASJC Scopus subject areas

Software

Access to Document

10.4230/LIPIcs.ISAAC.2018.22

Cite this

Czygrinow, A., Hanćkowiak, M., Wawrzyniak, W., & Witkowski, M. (2018). Distributed approximation algorithms for the minimum dominating set in K_H-minor-free graphs. In W-L. Hsu, D-T. Lee, & C-S. Liao (Eds.), 29th International Symposium on Algorithms and Computation, ISAAC 2018 (pp. 22:1–22:12). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 123). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2018.22

Distributed approximation algorithms for the minimum dominating set in K_H-minor-free graphs. / Czygrinow, Andrzej; Hanćkowiak, Michał; Wawrzyniak, Wojciech; Witkowski, Marcin.

29th International Symposium on Algorithms and Computation, ISAAC 2018. ed. / Wen-Lian Hsu; Der-Tsai Lee; Chung-Shou Liao. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. p. 22:1–22:12 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 123).

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

Czygrinow, A, Hanćkowiak, M, Wawrzyniak, W & Witkowski, M 2018, Distributed approximation algorithms for the minimum dominating set in K_H-minor-free graphs. in W-L Hsu, D-T Lee & C-S Liao (eds), 29th International Symposium on Algorithms and Computation, ISAAC 2018. Leibniz International Proceedings in Informatics, LIPIcs, vol. 123, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, pp. 22:1–22:12, 29th International Symposium on Algorithms and Computation, ISAAC 2018, Jiaoxi, Yilan, Taiwan, Province of China, 12/16/18. https://doi.org/10.4230/LIPIcs.ISAAC.2018.22

Czygrinow A, Hanćkowiak M, Wawrzyniak W, Witkowski M. Distributed approximation algorithms for the minimum dominating set in K_H-minor-free graphs. In Hsu W-L, Lee D-T, Liao C-S, editors, 29th International Symposium on Algorithms and Computation, ISAAC 2018. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018. p. 22:1–22:12. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.ISAAC.2018.22

Czygrinow, Andrzej ; Hanćkowiak, Michał ; Wawrzyniak, Wojciech ; Witkowski, Marcin. / Distributed approximation algorithms for the minimum dominating set in K_H-minor-free graphs. 29th International Symposium on Algorithms and Computation, ISAAC 2018. editor / Wen-Lian Hsu ; Der-Tsai Lee ; Chung-Shou Liao. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. pp. 22:1–22:12 (Leibniz International Proceedings in Informatics, LIPIcs).

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