# A Faster Algorithm for Computing Straight Skeletons

- Handle URI:
- http://hdl.handle.net/10754/316713
- Title:
- A Faster Algorithm for Computing Straight Skeletons
- Authors:
- Abstract:
- We present a new algorithm for computing the straight skeleton of a polygon. For a polygon with n vertices, among which r are reflex vertices, we give a deterministic algorithm that reduces the straight skeleton computation to a motorcycle graph computation in O(n (log n) log r) time. It improves on the previously best known algorithm for this reduction, which is randomised, and runs in expected O(n √(h+1) log² n) time for a polygon with h holes. Using known motorcycle graph algorithms, our result yields improved time bounds for computing straight skeletons. In particular, we can compute the straight skeleton of a non-degenerate polygon in O(n (log n) log r + r^(4/3 + ε)) time for any ε > 0. On degenerate input, our time bound increases to O(n (log n) log r + r^(17/11 + ε))
- Advisors:
- Committee Member:
- KAUST Department:
- Program:
- Issue Date:
- 6-May-2014
- Type:
- Thesis

- Appears in Collections:
- Theses; Computer Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

# Full metadata record

DC Field | Value | Language |
---|---|---|

dc.contributor.advisor | Vigneron, Antoine E. | en |

dc.contributor.author | Mencel, Liam A. | en |

dc.date.accessioned | 2014-05-11T07:02:12Z | - |

dc.date.available | 2014-05-11T07:02:12Z | - |

dc.date.issued | 2014-05-06 | en |

dc.identifier.uri | http://hdl.handle.net/10754/316713 | en |

dc.description.abstract | We present a new algorithm for computing the straight skeleton of a polygon. For a polygon with n vertices, among which r are reflex vertices, we give a deterministic algorithm that reduces the straight skeleton computation to a motorcycle graph computation in O(n (log n) log r) time. It improves on the previously best known algorithm for this reduction, which is randomised, and runs in expected O(n √(h+1) log² n) time for a polygon with h holes. Using known motorcycle graph algorithms, our result yields improved time bounds for computing straight skeletons. In particular, we can compute the straight skeleton of a non-degenerate polygon in O(n (log n) log r + r^(4/3 + ε)) time for any ε > 0. On degenerate input, our time bound increases to O(n (log n) log r + r^(17/11 + ε)) | en |

dc.language.iso | en | en |

dc.subject | straight skeleton | en |

dc.subject | algorithm | en |

dc.subject | computional geometry | en |

dc.subject | theory | en |

dc.title | A Faster Algorithm for Computing Straight Skeletons | en |

dc.type | Thesis | en |

dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | en |

thesis.degree.grantor | King Abdullah University of Science and Technology | en_GB |

dc.contributor.committeemember | Hadwiger, Markus | en |

dc.contributor.committeemember | Moshkov, Mikhail | en |

thesis.degree.discipline | Computer Science | en |

thesis.degree.name | Master of Science | en |

dc.person.id | 124179 | en |

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