### Abstract

Let P be a rectilinear simple polygon. The stabbing number of a partition of P into rectangles is the maximum number of rectangles stabbed by any axis-parallel line segment inside P. We present a 3-approximation algorithm for the problem of finding a partition with minimum stabbing number. It is based on an algorithm that finds an optimal partition for histograms. We also study Steiner triangulations of a simple (nonrectilinear) polygon P. Here the stabbing number is defined as the maximum number of triangles that can be stabbed by any line segment inside P. We give an O(1)-approximation algorithm for the problem of computing a Steiner triangulation with minimum stabbing number.

Original language | English (US) |
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Title of host publication | Proceedings of the 27th Annual Symposium on Computational Geometry, SCG'11 |

Pages | 407-416 |

Number of pages | 10 |

DOIs | |

State | Published - 2011 |

Event | 27th Annual ACM Symposium on Computational Geometry, SCG'11 - Paris, France Duration: Jun 13 2011 → Jun 15 2011 |

### Other

Other | 27th Annual ACM Symposium on Computational Geometry, SCG'11 |
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Country | France |

City | Paris |

Period | 6/13/11 → 6/15/11 |

### Fingerprint

### Keywords

- Approximation algorithms
- Computational geometry
- Polygons
- Rectangular decompositions
- Stabbing number
- Steiner triangulations

### ASJC Scopus subject areas

- Computational Mathematics
- Geometry and Topology
- Theoretical Computer Science

### Cite this

*Proceedings of the 27th Annual Symposium on Computational Geometry, SCG'11*(pp. 407-416) https://doi.org/10.1145/1998196.1998263

**Approximation algorithms for computing partitions with minimum stabbing number of rectilinear and simple polygons.** / Abam, Mohammad Ali; Aronov, Boris; De Berg, Mark; Khosravi, Amirali.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 27th Annual Symposium on Computational Geometry, SCG'11.*pp. 407-416, 27th Annual ACM Symposium on Computational Geometry, SCG'11, Paris, France, 6/13/11. https://doi.org/10.1145/1998196.1998263

}

TY - GEN

T1 - Approximation algorithms for computing partitions with minimum stabbing number of rectilinear and simple polygons

AU - Abam, Mohammad Ali

AU - Aronov, Boris

AU - De Berg, Mark

AU - Khosravi, Amirali

PY - 2011

Y1 - 2011

N2 - Let P be a rectilinear simple polygon. The stabbing number of a partition of P into rectangles is the maximum number of rectangles stabbed by any axis-parallel line segment inside P. We present a 3-approximation algorithm for the problem of finding a partition with minimum stabbing number. It is based on an algorithm that finds an optimal partition for histograms. We also study Steiner triangulations of a simple (nonrectilinear) polygon P. Here the stabbing number is defined as the maximum number of triangles that can be stabbed by any line segment inside P. We give an O(1)-approximation algorithm for the problem of computing a Steiner triangulation with minimum stabbing number.

AB - Let P be a rectilinear simple polygon. The stabbing number of a partition of P into rectangles is the maximum number of rectangles stabbed by any axis-parallel line segment inside P. We present a 3-approximation algorithm for the problem of finding a partition with minimum stabbing number. It is based on an algorithm that finds an optimal partition for histograms. We also study Steiner triangulations of a simple (nonrectilinear) polygon P. Here the stabbing number is defined as the maximum number of triangles that can be stabbed by any line segment inside P. We give an O(1)-approximation algorithm for the problem of computing a Steiner triangulation with minimum stabbing number.

KW - Approximation algorithms

KW - Computational geometry

KW - Polygons

KW - Rectangular decompositions

KW - Stabbing number

KW - Steiner triangulations

UR - http://www.scopus.com/inward/record.url?scp=79960191977&partnerID=8YFLogxK

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U2 - 10.1145/1998196.1998263

DO - 10.1145/1998196.1998263

M3 - Conference contribution

AN - SCOPUS:79960191977

SN - 9781450306829

SP - 407

EP - 416

BT - Proceedings of the 27th Annual Symposium on Computational Geometry, SCG'11

ER -