## Abstract

This article presents a randomized (Las Vegas) distributed algorithm that constructs a minimum spanning tree (MST) in weighted networks with optimal (up to polylogarithmic factors) time and message complexity. This algorithm runs in O (D + √ n) time and exchanges O (m) messages (both with high probability), where n is the number of nodes of the network, D is the hop-diameter, and m is the number of edges. This is the first distributed MST algorithm that matches simultaneously the time lower bound of Ω (D + √ n) [10] and the message lower bound of Ω(m) [31], which both apply to randomized Monte Carlo algorithms. The prior time and message lower bounds are derived using two completely different graph constructions; the existing lower-bound construction that shows one lower bound does not work for the other. To complement our algorithm, we present a new lower-bound graph construction for which any distributed MST algorithm requires both Ω (D + √ n) rounds and Ω(m) messages.

Original language | English (US) |
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Article number | 13 |

Journal | ACM Transactions on Algorithms |

Volume | 16 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2020 |

Externally published | Yes |

## Keywords

- Distributed algorithms
- Minimum spanning trees

## ASJC Scopus subject areas

- Mathematics (miscellaneous)