### Abstract

Polygons are a paramount data structure in computational geometry. While the complexity of many algorithms on simple polygons or polygons with holes depends on the size of the input polygon, the intrinsic complexity of the problems these algorithms solve is often related to the reflex vertices of the polygon. In this paper, we give an easy-to-describe linear-time method to replace an input polygon P by a polygon P′ such that (1) P′, contains P, (2) P′, has its reflex vertices at the same positions as P, and (3) the number of vertices of P′ is linear in the number of reflex vertices. Since the solutions of numerous problems on polygons (including shortest paths, geodesic hulls, separating point sets, and Voronoi diagrams) are equivalent for both P and P′, our algorithm can be used as a preprocessing step for several algorithms and makes their running time dependent on the number of reflex vertices rather than on the size of P.

Original language | English |
---|---|

Title of host publication | Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings |

Pages | 11-21 |

Number of pages | 11 |

DOIs | |

Publication status | Published - 2013 Dec 1 |

Externally published | Yes |

Event | 24th International Symposium on Algorithms and Computation, ISAAC 2013 - Hong Kong, China Duration: 2013 Dec 16 → 2013 Dec 18 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 8283 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 24th International Symposium on Algorithms and Computation, ISAAC 2013 |
---|---|

Country | China |

City | Hong Kong |

Period | 13/12/16 → 13/12/18 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Geodesic-preserving polygon simplification'. Together they form a unique fingerprint.

## Cite this

*Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings*(pp. 11-21). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8283 LNCS). https://doi.org/10.1007/978-3-642-45030-3_2