### Abstract

We consider a natural variation of the concept of stabbing a segment by a simple polygon: a segment is stabbed by a simple polygon P if at least one of its two endpoints is contained in P. A segment set S is stabbed by P if every segment of S is stabbed by P. We show that if S is a set of pairwise disjoint segments, the problem of computing the minimum perimeter polygon stabbing S can be solved in polynomial time. We also prove that for general segments the problem is NP-hard. Further, an adaptation of our polynomial-time algorithm solves an open problem posed by Löffler and van Kreveld [Algorithmica 56(2), 236-269 (2010)] about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments.

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

Title of host publication | Algorithms and Complexity - 8th International Conference, CIAC 2013, Proceedings |

Pages | 146-157 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 2013 |

Event | 8th International Conference on Algorithms and Complexity, CIAC 2013 - Barcelona, Spain Duration: 2013 May 22 → 2013 May 24 |

### Publication series

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

Volume | 7878 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 8th International Conference on Algorithms and Complexity, CIAC 2013 |
---|---|

Country | Spain |

City | Barcelona |

Period | 13/5/22 → 13/5/24 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'New results on stabbing segments with a polygon'. Together they form a unique fingerprint.

## Cite this

*Algorithms and Complexity - 8th International Conference, CIAC 2013, Proceedings*(pp. 146-157). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7878 LNCS). https://doi.org/10.1007/978-3-642-38233-8_13