## Abstract

Let P be a set of 2n points in the plane, and let ^{MC} (resp., ^{MNC}) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of P. We study the problem of computing ^{MNC}. We first prove that the problem is NP-hard and does not admit a PTAS. Then, we present an O(^{n1.5log0.5}n)-time algorithm that computes a non-crossing matching M of P, such that bn(M)≤210×bn(^{MNC}), where bn(M) is the length of a longest edge in M. An interesting implication of our construction is that bn(^{MNC})/bn(^{MC})≤210. Finally, we show that when the points of P are in convex position, one can compute ^{MNC} in O(^{n3}) time, improving a result in [7].

Original language | English |
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Pages (from-to) | 447-457 |

Number of pages | 11 |

Journal | Computational Geometry: Theory and Applications |

Volume | 47 |

Issue number | 3 PART A |

DOIs | |

State | Published - 2014 |

Externally published | Yes |

## Keywords

- Approximation algorithms
- Bottleneck matching
- NP-hardness
- Non-crossing configuration