### Abstract

A k-dominating set in a graph G = (V,E) is a set U ¢ V such that ever 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 local model for the minimum k-dominating set problem for k ≥ 2 in graphs with no K_{3},_{h-}minor 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 + €)-Approximation for an arbitrary fixed € > 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) | 75-86 |

Number of pages | 12 |

Journal | CEUR Workshop Proceedings |

Volume | 1949 |

State | Published - 2017 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*CEUR Workshop Proceedings*,

*1949*, 75-86.