## Abstract

A bottleneck plane perfect matching of a set of n points in ℝ^{2} is defined to be a perfect non-crossing matching that minimizes the length of the longest edge; the length of this longest edge is known as bottleneck. The problem of computing a bottleneck plane perfect matching has been proved to be NP-hard. We present an algorithm that computes a bottleneck plane matching of size at least (formula presented.) in O(n log^{2} n)-time. Then we extend our idea toward an O(n log n)-time approximation algorithm which computes a plane matching of size at least (formula presented.) whose edges have length at most (formula presented.) the bottleneck.

Original language | English |
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Article number | 1394 |

Pages (from-to) | 718-731 |

Number of pages | 14 |

Journal | Computational Geometry: Theory and Applications |

Volume | 48 |

Issue number | 9 |

DOIs | |

State | Published - 1 Oct 2015 |

## Keywords

- Approximation algorithm
- Bottleneck matching
- Geometric graph
- Plane matching
- Unit disk graph

## ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics