## Abstract

This article presents a fast distributed algorithm to compute a small k-dominating set D (for any fixed k) and to compute its induced graph partition (breaking the graph into radius k clusters centered around the vertices of D). The time complexity of the algorithm is O(k log*n). Small k-dominating sets have applications in a number of areas, including routing with sparse routing tables, the design of distributed data structures, and center selection in a distributed network. The main application described in this article concerns a fast distributed algorithm for constructing a minimum-weight spanning tree (MST). On an n-vertex network of diameter d, the new algorithm constructs an MST in time O(√n log* n +d), improving on previous results.

Original language | English |
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Pages (from-to) | 40-66 |

Number of pages | 27 |

Journal | Journal of Algorithms |

Volume | 28 |

Issue number | 1 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

### Bibliographical note

Funding Information:This article presents a fast distributed algorithm to compute a small k-dominating set D for any fixed k) and to compute its induced graph partition breaking the graph into radius k clusters centered around the vertices of D). The time complexity of the algorithm is O k log* n). Small k-dominating sets have applications in a number of areas, including routing with sparse routing tables, the design of distributed data structures, and center selection in a distributed network. The main application described in this article concerns a fast distributed algorithm for constructing a minimum-weight spanning tree MST). On an n-vertex network of diameter d, the new algorithm constructs an MST in time O ’n log* n q d), improving on previous results. Q 1998 Academic Press * E-mail address: [email protected]. ²E-mail address: [email protected]. ³ Supported in part by a Walter and Elise Haas Career Development Award and by a grant from the Basic Research Foundation. Part of the work was done while visiting IBM T. J. Watson Research Center. 1A preliminary version of this article has appeared as an extended abstract in Proceedings of the Fourteenth ACM Symposium on Principles of Distributed Computing, Ottawa, Canada, August 1995.

### Funding

This article presents a fast distributed algorithm to compute a small k-dominating set D for any fixed k) and to compute its induced graph partition breaking the graph into radius k clusters centered around the vertices of D). The time complexity of the algorithm is O k log* n). Small k-dominating sets have applications in a number of areas, including routing with sparse routing tables, the design of distributed data structures, and center selection in a distributed network. The main application described in this article concerns a fast distributed algorithm for constructing a minimum-weight spanning tree MST). On an n-vertex network of diameter d, the new algorithm constructs an MST in time O ’n log* n q d), improving on previous results. Q 1998 Academic Press * E-mail address: [email protected]. ²E-mail address: [email protected]. ³ Supported in part by a Walter and Elise Haas Career Development Award and by a grant from the Basic Research Foundation. Part of the work was done while visiting IBM T. J. Watson Research Center. 1A preliminary version of this article has appeared as an extended abstract in Proceedings of the Fourteenth ACM Symposium on Principles of Distributed Computing, Ottawa, Canada, August 1995.

Funders | Funder number |
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Basic Research Foundation |