### 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) |
---|---|

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.

**Distributed approximation algorithms for k-dominating set in graphs of bounded genus and linklessly embeddable graphs Regular Submission.** / Czygrinow, Andrzej; Hańckowiak, Michał; Wawrzyniak, Wojciech; Witkowski, Marcin.

Research output: Contribution to journal › Article

*CEUR Workshop Proceedings*, vol. 1949, pp. 75-86.

}

TY - JOUR

T1 - Distributed approximation algorithms for k-dominating set in graphs of bounded genus and linklessly embeddable graphs Regular Submission

AU - Czygrinow, Andrzej

AU - Hańckowiak, Michał

AU - Wawrzyniak, Wojciech

AU - Witkowski, Marcin

PY - 2017

Y1 - 2017

N2 - 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 K3,h-minor and graphs with no K4,4-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.

AB - 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 K3,h-minor and graphs with no K4,4-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.

UR - http://www.scopus.com/inward/record.url?scp=85031940846&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85031940846&partnerID=8YFLogxK

M3 - Article

VL - 1949

SP - 75

EP - 86

JO - CEUR Workshop Proceedings

JF - CEUR Workshop Proceedings

SN - 1613-0073

ER -