### Abstract

In this paper we consider the 2-dominating set problem (2MDS). We look for a smallest subset of vertices D⊆V with the property that every vertex in V∖D is adjacent to at least 2 vertices of D. We are interested in the distributed complexity of this problem in the local model, where the nodes have no identifiers but there is a port ordering available. We propose a distributed local (constant time) algorithm yielding a 6-approximation in the class of planar graphs. Earlier result shows that in this case, for any ϵ>0, there is no deterministic distributed local/constant-round algorithm providing a (5−ϵ)-approximation of the 2MDS.

Original language | English (US) |
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Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Theoretical Computer Science |

Volume | 662 |

DOIs | |

State | Published - Feb 1 2017 |

### Keywords

- Distributed graph algorithms

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Theoretical Computer Science*,

*662*, 1-8. https://doi.org/10.1016/j.tcs.2016.12.001