## Abstract

The problem of distributively constructing a minimum spanning tree has been thoroughly studied. The root of this spanning tree is often elected as a leader, and then centralized algorithms are run in the distributed system. If, however, we have fault tolerance in mind, selecting a random spanning tree and a random leader are more desirable. If we manage to select a random tree, the probability that a bad channel will disconnect some nodes from the random tree is relatively small. Otherwise, a small number of predetermined edges will greatly effect the system's behavior. In this paper we present an algorithm for choosing a random leader (RL), and distributed random spanning tree algorithms (RST), where random means, that each spanning tree in the underlying graph has the same probability of being selected. We give optimal algorithms for the complete graph and the ring. We also describe an RST algorithm for the general graph, and discuss the relation between RST and RL algorithms.

Original language | English |
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Title of host publication | Distributed Algorithms - 3rd International Workshop, Proceedings |

Editors | Jean-Claude Bermond, Michel Raynal |

Publisher | Springer Verlag |

Pages | 1-12 |

Number of pages | 12 |

ISBN (Print) | 9783540516873 |

DOIs | |

State | Published - 1989 |

Externally published | Yes |

Event | 3rd International Workshop on Distributed Algorithms, WDAG 1989 - Nice, France Duration: 26 Sep 1989 → 28 Sep 1989 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 392 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 3rd International Workshop on Distributed Algorithms, WDAG 1989 |
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Country/Territory | France |

City | Nice |

Period | 26/09/89 → 28/09/89 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 1989.