## Abstract

We present deterministic distributed algorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is at least (1 - ε) times the optimal in Δ^{O(1/ε)} + O (1/ε^{2})·log∗(n) rounds where n is the number of vertices in the graph and Δ is the maximum degree. Our algorithm for the edge-weighted case computes a matching whose weight is at least (1 - ε) times the optimal in log(min{1/w_{min}, n/ε})^{O(1/ε)}·(Δ^{O(1/ε)} + log∗(n)) rounds for edge-weights in [w_{min}, 1]. The best previous algorithms for both the unweighted case and the weighted case are by Lotker, Patt-Shamir, and Pettie (SPAA 2008). For the unweighted case they give a randomized (1 - ε)-approximation algorithm that runs in O((log(n))/ε^{3}) rounds. For the weighted case they give a randomized (1/2 - ε)-approximation algorithm that runs in O(log(ε^{-1})·log(n)) rounds. Hence, our results improve on the previous ones when the parameters Δ, ε and w_{min} are constants (where we reduce the number of runs from O(log(n)) to O(log∗(n))), and more generally when Δ, 1/ε and 1/w_{min} are sufficiently slowly increasing functions of n. Moreover, our algorithms are deterministic rather than randomized.

Original language | English |
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Title of host publication | ICDCN 2015 - Proceedings of the 16th International Conference on Distributed Computing and Networking |

Publisher | Association for Computing Machinery |

ISBN (Electronic) | 9781450329286 |

DOIs | |

State | Published - 4 Jan 2015 |

Externally published | Yes |

Event | 16th International Conference on Distributed Computing and Networking, ICDCN 2015 - Goa, India Duration: 4 Jan 2015 → 7 Jan 2015 |

### Publication series

Name | ACM International Conference Proceeding Series |
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Volume | 04-07-January-2015 |

### Conference

Conference | 16th International Conference on Distributed Computing and Networking, ICDCN 2015 |
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Country/Territory | India |

City | Goa |

Period | 4/01/15 → 7/01/15 |

### Bibliographical note

Publisher Copyright:Copyright 2015 ACM.

### Funding

M.M was partially funded by the Israeli Ministry of Science and Technology. Research supported by the Israel Science Foundation grant number 671/13.

Funders | Funder number |
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Israel Science Foundation | 671/13 |

Ministry of science and technology, Israel |

## Keywords

- Centralized local algorithms
- Distributed local algorithms
- Graph algorithms
- Maximum matching
- Maximum weighted matching