## Abstract

We consider the problem of finding the weight of a Euclidean minimum spanning tree for a set of n points in ℝ^{d}. We focus on the situation when the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a structured way. We present an algorithm that estimates with high probability the weight of a Euclidean minimum spanning tree of a set of points to within 1 + ε using only Õ(√n poly(1/ε)) queries for constant d. The algorithm assumes that the input is supported by a minimal bounding cube enclosing it, by orthogonal range queries, and by cone approximate nearest neighbors queries.

Original language | English |
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Pages | 813-822 |

Number of pages | 10 |

State | Published - 2003 |

Event | Configuralble Computing: Technology and Applications - Boston, MA, United States Duration: 2 Nov 1998 → 3 Nov 1998 |

### Conference

Conference | Configuralble Computing: Technology and Applications |
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Country/Territory | United States |

City | Boston, MA |

Period | 2/11/98 → 3/11/98 |

## ASJC Scopus subject areas

- Software
- General Mathematics