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

Deepak Ajwani; Saurabh Ray; Raimund Seidel; Hans Raj Tiwary

doi:10.1007/978-3-540-73951-7_45

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

Deepak Ajwani
, Saurabh Ray
, Raimund Seidel
, Hans Raj Tiwary

Department of Mathematics

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

8 Scopus citations

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 log² 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 log⁵ n) time bound. Our bounds also generalize to certain natural weighted versions of those problems.

Original language	English
Title of host publication	Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings
Publisher	Springer Verlag
Pages	519-528
Number of pages	10
ISBN (Print)	3540739483, 9783540739487
DOIs	https://doi.org/10.1007/978-3-540-73951-7_45
State	Published - 1 Jan 2007
Event	10th International Workshop on Algorithms and Data Structures, WADS 2007 - Halifax, Canada Duration: 15 Aug 2007 → 17 Aug 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4619 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Workshop on Algorithms and Data Structures, WADS 2007
Country/Territory	Canada
City	Halifax
Period	15/08/07 → 17/08/07

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-540-73951-7_45

Cite this

Ajwani, D., Ray, S., Seidel, R., & Tiwary, H. R. (2007). On computing the centroid of the vertices of an arrangement and related problems. In 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). Springer Verlag. https://doi.org/10.1007/978-3-540-73951-7_45

Ajwani, Deepak ; Ray, Saurabh ; Seidel, Raimund et al. / On computing the centroid of the vertices of an arrangement and related problems. Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings. Springer Verlag, 2007. pp. 519-528 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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 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.",

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Ajwani, D, Ray, S, Seidel, R & Tiwary, HR 2007, On computing the centroid of the vertices of an arrangement and related problems. in 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, Springer Verlag, pp. 519-528, 10th International Workshop on Algorithms and Data Structures, WADS 2007, Halifax, Canada, 15/08/07. https://doi.org/10.1007/978-3-540-73951-7_45

On computing the centroid of the vertices of an arrangement and related problems. / Ajwani, Deepak; Ray, Saurabh; Seidel, Raimund et al.
Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings. Springer Verlag, 2007. p. 519-528 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4619 LNCS).

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

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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.

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M3 - Conference contribution

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SN - 9783540739487

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

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Ajwani D, Ray S, Seidel R, Tiwary HR. On computing the centroid of the vertices of an arrangement and related problems. In Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings. Springer Verlag. 2007. p. 519-528. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-73951-7_45

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

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