### 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 | Der-Tsai Lee, Chung-Shou Liao, Wen-Lian Hsu |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770941 |

DOIs | |

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 | Taiwan, Province of China |

City | Jiaoxi, Yilan |

Period | 12/16/18 → 12/19/18 |

### Fingerprint

### Keywords

- Distributed algorithms
- MDS
- Minor-closed family of graphs

### ASJC Scopus subject areas

- Software

### Cite this

_{H}-minor-free graphs In D-T. Lee, C-S. Liao, & W-L. Hsu (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. 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.

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

_{H}-minor-free graphs in D-T Lee, C-S Liao & W-L Hsu (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, 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

_{H}-minor-free graphs In Lee D-T, Liao C-S, Hsu W-L, editors, 29th International Symposium on Algorithms and Computation, ISAAC 2018. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.ISAAC.2018.22

}

TY - GEN

T1 - Distributed approximation algorithms for the minimum dominating set in K H -minor-free graphs

AU - Czygrinow, Andrzej

AU - Hanćkowiak, Michał

AU - Wawrzyniak, Wojciech

AU - Witkowski, Marcin

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - Distributed algorithms

KW - MDS

KW - Minor-closed family of graphs

UR - http://www.scopus.com/inward/record.url?scp=85063663800&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063663800&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ISAAC.2018.22

DO - 10.4230/LIPIcs.ISAAC.2018.22

M3 - Conference contribution

AN - SCOPUS:85063663800

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 29th International Symposium on Algorithms and Computation, ISAAC 2018

A2 - Lee, Der-Tsai

A2 - Liao, Chung-Shou

A2 - Hsu, Wen-Lian

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

ER -