### 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 |

### Keywords

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

### ASJC Scopus subject areas

- Software

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## 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