## Abstract

We present the first polynomial self-stabilizing algorithm for finding a 1-maximal matching in a general graph. The previous best known algorithm has been presented by Manne et al. [20]and we show in this paper it has a sub-exponential time complexity under the distributed adversarial daemon. Our new algorithm is an adaptation of the Manne et al. algorithm and works under the same daemon, but with a complexity in O(m×n^{2}) moves, with n is the number of nodes and m is the number of edges. This is the first self-stabilizing algorithm that solve this problem with a polynomial complexity. Moreover, our algorithm only needs one more boolean variable than the previous one.

Original language | English |
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Pages (from-to) | 54-78 |

Number of pages | 25 |

Journal | Theoretical Computer Science |

Volume | 782 |

DOIs | |

State | Published - 23 Aug 2019 |

Externally published | Yes |

## Keywords

- 1-maximal matching
- Self-stabilization
- [Formula presented]-approximation

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science