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

Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Theoretical Computer Science |

Volume | 662 |

DOIs | |

State | Published - Feb 1 2017 |

### Fingerprint

### Keywords

- Distributed graph algorithms

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

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

**Improved distributed local approximation algorithm for minimum 2-dominating set in planar graphs.** / Czygrinow, Andrzej; Hanćkowiak, M.; Szymańska, E.; Wawrzyniak, W.; Witkowski, M.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 662, pp. 1-8. https://doi.org/10.1016/j.tcs.2016.12.001

}

TY - JOUR

T1 - Improved distributed local approximation algorithm for minimum 2-dominating set in planar graphs

AU - Czygrinow, Andrzej

AU - Hanćkowiak, M.

AU - Szymańska, E.

AU - Wawrzyniak, W.

AU - Witkowski, M.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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.

AB - 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.

KW - Distributed graph algorithms

UR - http://www.scopus.com/inward/record.url?scp=85009077500&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85009077500&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2016.12.001

DO - 10.1016/j.tcs.2016.12.001

M3 - Article

AN - SCOPUS:85009077500

VL - 662

SP - 1

EP - 8

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -