### Abstract

A k-dominating set in a graph G=(V,E) is a set U⊆V such that every vertex of G is either in U or has at least k neighbors in U. In this paper we give simple distributed approximation algorithms in the standard Local model of computations for the minimum k-dominating set problem for k≥2 in graphs with no K_{3,h}-minor for some h∈Z^{+} and graphs with no K_{4,4}-minor. In particular, this gives fast distributed approximations for graphs of bounded genus and linklessly embeddable graphs. The algorithms give a constant approximation ratio and run in a constant number of rounds. In addition, we will give a (1+ϵ)-approximation for an arbitrary fixed ϵ>0 which runs in O(log^{⁎}n) rounds where n is the order of a graph.

Original language | English (US) |
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Pages (from-to) | 327-338 |

Number of pages | 12 |

Journal | Theoretical Computer Science |

Volume | 809 |

DOIs | |

State | Published - Feb 24 2020 |

Externally published | Yes |

### Keywords

- Bounded genus graphs
- Distributed algorithms
- Dominating set

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Theoretical Computer Science*,

*809*, 327-338. https://doi.org/10.1016/j.tcs.2019.12.027