## Abstract

We consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed by P if P stabs every element of S. Given a segment set S, we study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or perimeter) is optimized. We show that if the elements of S are pairwise disjoint, the problem can be solved in polynomial time. In particular, this solves an open problem posed by Löffler and van Kreveld [Algorithmica 56(2), 236-269 (2010)] [16] about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments. Our algorithm can also be extended to work for a more general problem, in which instead of segments, the set S consists of a collection of point sets with pairwise disjoint convex hulls. We also prove that for general segments our stabbing problem is NP-hard.

Original language | English |
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Pages (from-to) | 14-29 |

Number of pages | 16 |

Journal | Computational Geometry: Theory and Applications |

Volume | 48 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 Jan |

## Keywords

- Imprecise points
- Segments
- Stabber
- Transversal

## ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics