## Abstract

We describe a simple deterministic O(-1 log ") round distributed algorithm for (2α+ 1) (1 + ) approximation of minimum weighted dominating set on graphs with arboricity at most α. Here Δdenotes the maximum degree. We also show a lower bound proving that this round complexity is nearly optimal even for the unweighted case, via a reduction from the celebrated KMW lower bound on distributed vertex cover approximation [Kuhn, Moscibroda, and Wattenhofer JACM'16]. Our algorithm improves on all the previous results (that work only for unweighted graphs) including a randomized O(α2) approximation inO(logn) rounds [Lenzen andWattenhofer DISC'10], a deterministic O(α log ") approximation in O(log ") rounds [Lenzen and Wattenhofer DISC'10], a deterministic O(α) approximation in O(log2 ") rounds [implicit in Bansal and Umboh IPL'17 and Kuhn, Moscibroda, and Wattenhofer SODA'06], and a randomized O(α) approximation in O(α logn) rounds [Morgan, Solomon and Wein DISC'21]. We also provide a randomized O(α log ") round distributed algorithm that sharpens the approximation factor to α (1 + o (1)). If each node is restricted to do polynomial-time computations, our approximation factor is tight in the first order as it is NP-hard to achieve α - 1 - approximation [Bansal and Umboh IPL'17].

Original language | English |
---|---|

Title of host publication | PODC 2022 - Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery |

Pages | 292-300 |

Number of pages | 9 |

ISBN (Electronic) | 9781450392624 |

DOIs | |

State | Published - 20 Jul 2022 |

Externally published | Yes |

Event | 41st ACM Symposium on Principles of Distributed Computing, PODC 2022 - Salerno, Italy Duration: 25 Jul 2022 → 29 Jul 2022 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
---|

### Conference

Conference | 41st ACM Symposium on Principles of Distributed Computing, PODC 2022 |
---|---|

Country/Territory | Italy |

City | Salerno |

Period | 25/07/22 → 29/07/22 |

### Bibliographical note

Publisher Copyright:© 2022 ACM.

## Keywords

- approximation algorithms
- arboricity
- distributed computing
- dominating set

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications