## Abstract

We present a silent self-stabilizing distributed algorithm computing a maximal $ p$-star decomposition of the underlying communication network. Under the unfair distributed scheduler, the most general scheduler model, the algorithm converges in at most $12Delta m + mathcalO(m+n)$ moves, where $m$ is the number of edges, $n$ is the number of nodes and $Delta $ is the maximum node degree. Regarding the time complexity, we obtain the following results: our algorithm outperforms the previously known best algorithm by a factor of $Delta $ with respect to the move complexity. While the round complexity for the previous algorithm was unknown, we show a $5big lfloor fracnp+1 big rfloor +5$ bound for our algorithm.

Original language | English |
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Pages (from-to) | 254-266 |

Number of pages | 13 |

Journal | Computer Journal |

Volume | 63 |

Issue number | 2 |

DOIs | |

State | Published - 19 Feb 2020 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2019 The British Computer Society 2019. All rights reserved. For permissions, please email: journals.permissions@oup.com.

## Keywords

- distributed algorithm
- graph decomposition
- move complexity
- p-star decomposition
- round complexity
- self-stabilization