## Abstract

Given a set P of points in the plane, a geometric minimum-diameter spanning tree (GMDST) of P is a spanning tree of P such that the longest path through the tree is minimized. For several years, the best upper bound on the time to compute a GMDST was cubic with respect to the number of points in the input set. Recently, Timothy Chan introduced a subcubic time algorithm. In this paper we present an algorithm that generates a tree whose diameter is no more than (1 + ε) times that of a GMDST, for any ε > 0. Our algorithm reduces the problem to several grid-aligned versions of the problem and runs within time O(ε^{-3}+ n) and space O(n).

Original language | English |
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Pages (from-to) | 577-589 |

Number of pages | 13 |

Journal | Algorithmica |

Volume | 38 |

Issue number | 4 |

DOIs | |

State | Published - 1 Jan 2004 |

## Keywords

- Approximation algorithm
- Geometric graph
- Minimum diameter spanning tree

## ASJC Scopus subject areas

- General Computer Science
- Computer Science Applications
- Applied Mathematics