### Abstract

We give an algorithm to compute all the local peaks in the k-level of an arrangement of n lines in O(n log n) + Õ((kn)^{2/3}) time. We can also find τ largest peaks in O(n log^{2} n) + Õ((τn)^{2/3}) time. Moreover, we consider the longest edge in a parametric minimum spanning tree (in other words, a bottleneck edge for connectivity), and give an algorithm to compute the parameter value (within a given interval) maximizing/minimizing the length of the longest edge in MST. The time complexity is Õ(n^{8/7}k^{1/7} + nk^{1/3}).

Original language | English |
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Pages | 241-248 |

Number of pages | 8 |

Publication status | Published - 2001 Jan 1 |

Event | 17th Annual Symposium on Computational Geometry (SCG'01) - Medford, MA, United States Duration: 2001 Jun 3 → 2001 Jun 5 |

### Other

Other | 17th Annual Symposium on Computational Geometry (SCG'01) |
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Country | United States |

City | Medford, MA |

Period | 01/6/3 → 01/6/5 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

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## Cite this

Katoh, N., & Tokuyama, T. (2001).

*Notes on computing peaks in k-levels and parametric spanning trees*. 241-248. Paper presented at 17th Annual Symposium on Computational Geometry (SCG'01), Medford, MA, United States.