## Abstract

This paper considers the problem of distributively constructing a minimum-weight spanning tree (MST) for graphs of constant diameter in the bounded-messages model, where each message can contain at most B bits for some parameter B. It is shown that the time required to compute an MST for graphs of diameter 4 or 3 can be as high as Ω(3√n/B) and Ω(4√n/2√B), respectively. The lower bound holds even if the algorithm is allowed to be randomized. On the other hand, it is shown that O(log n) time units suffice to compute an MST deterministically for graphs with diameter 2, when B = O(log n). These results complement a previously known lower bound of Ω(2√n/B) for graphs of diameter Ω(log n).

Original language | English |
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Pages | 63-71 |

Number of pages | 9 |

DOIs | |

State | Published - 1 Jan 2001 |

Externally published | Yes |

Event | 20th Annual ACM Symposium on Principles of Distributed Computing - Newport, Rhode Island, United States Duration: 26 Aug 2001 → 29 Aug 2001 |

### Conference

Conference | 20th Annual ACM Symposium on Principles of Distributed Computing |
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Country/Territory | United States |

City | Newport, Rhode Island |

Period | 26/08/01 → 29/08/01 |