### Abstract

We consider the problem of computing the centroid of all the vertices in a non-degenerate arrangement of n lines. The trivial approach requires the enumeration of all (n/2) vertices. We present an O(n log^{2} n) algorithm for computing this centroid. For arrangements of n segments we give an O(n^{4/3+ε}) algorithm for computing the centroid of its vertices. For the special case that all the segments of the arrangement are chords of a simply connected planar region we achieve an O(n log^{5} n) time bound. Our bounds also generalize to certain natural weighted versions of those problems.

Original language | English (US) |
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Title of host publication | Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings |

Pages | 519-528 |

Number of pages | 10 |

State | Published - Dec 1 2007 |

Event | 10th International Workshop on Algorithms and Data Structures, WADS 2007 - Halifax, Canada Duration: Aug 15 2007 → Aug 17 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4619 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 10th International Workshop on Algorithms and Data Structures, WADS 2007 |
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Country | Canada |

City | Halifax |

Period | 8/15/07 → 8/17/07 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings*(pp. 519-528). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4619 LNCS).

**On computing the centroid of the vertices of an arrangement and related problems.** / Ajwani, Deepak; Ray, Saurabh; Seidel, Raimund; Tiwary, Hans Raj.

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

*Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4619 LNCS, pp. 519-528, 10th International Workshop on Algorithms and Data Structures, WADS 2007, Halifax, Canada, 8/15/07.

}

TY - GEN

T1 - On computing the centroid of the vertices of an arrangement and related problems

AU - Ajwani, Deepak

AU - Ray, Saurabh

AU - Seidel, Raimund

AU - Tiwary, Hans Raj

PY - 2007/12/1

Y1 - 2007/12/1

N2 - We consider the problem of computing the centroid of all the vertices in a non-degenerate arrangement of n lines. The trivial approach requires the enumeration of all (n/2) vertices. We present an O(n log2 n) algorithm for computing this centroid. For arrangements of n segments we give an O(n4/3+ε) algorithm for computing the centroid of its vertices. For the special case that all the segments of the arrangement are chords of a simply connected planar region we achieve an O(n log5 n) time bound. Our bounds also generalize to certain natural weighted versions of those problems.

AB - We consider the problem of computing the centroid of all the vertices in a non-degenerate arrangement of n lines. The trivial approach requires the enumeration of all (n/2) vertices. We present an O(n log2 n) algorithm for computing this centroid. For arrangements of n segments we give an O(n4/3+ε) algorithm for computing the centroid of its vertices. For the special case that all the segments of the arrangement are chords of a simply connected planar region we achieve an O(n log5 n) time bound. Our bounds also generalize to certain natural weighted versions of those problems.

UR - http://www.scopus.com/inward/record.url?scp=38149055778&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38149055778&partnerID=8YFLogxK

M3 - Conference contribution

SN - 3540739483

SN - 9783540739487

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 519

EP - 528

BT - Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings

ER -