## Abstract

We consider the problem of computing the weight of a Euclidean minimum spanning tree for a set of n points in ℝ ^{d}. We focus on the setting where 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 neighbor queries.

Original language | English |
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Pages (from-to) | 91-109 |

Number of pages | 19 |

Journal | SIAM Journal on Computing |

Volume | 35 |

Issue number | 1 |

DOIs | |

State | Published - 2006 |

## Keywords

- Minimum spanning tree
- Sublinear algorithms

## ASJC Scopus subject areas

- Computer Science (all)
- Mathematics (all)