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Computing a face in an arrangement of line segments

Authors:

Bernard Chazelle,

Herbert Edelsbrunner,

Leonidas Guibas,

Micha Sharir,

Jack SnoeyinkAuthors Info & Claims

SODA '91: Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms

Pages 441 - 448

Published: 01 March 1991 Publication History

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References

[1]

P. Alevizos, J.D. Boissonnat and F. Preparata, An optimal algorithm for the boundary of ~ cell in a union of rays, in Geometry and Robotics (J.D. Boissonnat and J.P. Laumond, eds.), Lectur Notes in Computer Science 391, Springer Verlag, 1989, pp, 247-274.

Digital Library

Google Scholar

[2]

J.D. Boissonnat, O. Devillers, R. Schott, M. Telllaud and M. Yvinec, On-line geometric algorithms with good expected behaviours, Proc. Journdes G~ometriques Algorithmiques~ Sophia-Antipolis, June 1990, pp. 7-13.

Google Scholar

[3]

K. Clarkson and P. Shot, Applications of random sampling in computational geometry II, Discrete Comput. Geom. 4 (1989), pp. 387-421.

Google Scholar

[4]

H. Edelsbrunner, L. Guibas and M. Sharir, The complexity and construction of many faces in arrangements of lines and of segments, Discrete Comput. Geom. 5 (1990), pp. 161-1~6.

Google Scholar

[5]

H. Edelsbrunner and E. Mficke, Simulation of simplicity- A technique to cope with degenerate cases in geometric algorithms, ACM Trans. Graphics9(1)(1990) pp. 66-104.

Digital Library

Google Scholar

[6]

L. Guibas, D. Knuth and M. Sharir, Randomized incremental construction of Voronoi and Delaunay diagrams, Proc. 17th Int. Colloq. on Automata, Languages and Programming, 1990, pp. 414-431.

Digital Library

Google Scholar

[7]

L. Guibas, M. Sharir and S. Sifrony, On the general motion planning problem with two degrees of freedom, Discrete Comput. Geom. 4 (1989), pp. 491-521.

Google Scholar

[8]

J. Hershberger, Finding the upper envelope of n line segments in O(nlogn) time, Infor. Proc. Letters 33 (1989), pp. 169-174.

Digital Library

Google Scholar

[9]

K. Mulmuley, A fast planar partition algorithm I, Proc. ~9th IEEE Syrup. on Foundations of Computer Science, 1989, pp. 580-589.

Google Scholar

[10]

R. Pollack, M. Sharir and S. Sifrony, Separating two simple polygons by a sequence of translations, Discrete Comput. Geom. 3 (1988), pp. 123-136.

Google Scholar

[11]

R. Seidel, private communication.

Google Scholar

[12]

A. Wiernik and M. Sharir, Planar realization of nonlinear Davenport Schinzel sequences by segments, Discrete Comput. Geom. 3 (1988), pp. 15-47.

Digital Library

Google Scholar

Cited By

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Berg MMatoušek JSchwarzkopf O(1995)Piecewise linear paths among convex obstaclesDiscrete & Computational Geometry10.1007/BF0257069414:1(9-29)Online publication date: 1-Dec-1995
https://dl.acm.org/doi/10.1007/BF02570694
de Berg MDobrindt KSchwarzkopf OLeighton FGoodrich M(1994)On lazy randomized incremental constructionProceedings of the twenty-sixth annual ACM symposium on Theory of Computing10.1145/195058.195113(105-114)Online publication date: 23-May-1994
https://dl.acm.org/doi/10.1145/195058.195113
de Berg MMatoušek JSchwarzkopf OKosaraju RJohnson DAggarwal A(1993)Piecewise linear paths among convex obstaclesProceedings of the twenty-fifth annual ACM symposium on Theory of Computing10.1145/167088.167224(505-514)Online publication date: 1-Jun-1993
https://dl.acm.org/doi/10.1145/167088.167224
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Index Terms

Computing a face in an arrangement of line segments
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
2. Theory of computation
  1. Design and analysis of algorithms
  2. Randomness, geometry and discrete structures
    1. Computational geometry

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In COCOA 2015, Korman et al. studied the following geometric covering problem: given a set S of n line segments in the plane, find a minimum number of line segments such that every cell in the arrangement of the line segments is covered. Here, a ...
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It is shown that given a set of n line segments, their connected components can be computed in time O(n4/3log3n). A bound of o(n4/3) for this problem would imply a similar bound for detecting, for a given set of n points and n lines, whether some point ...

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SODA '91: Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms

March 1991

482 pages

ISBN:0897913760

Chairman:
Alok Aggarwal

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 March 1991

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SODA91

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SIGACT
SIAM

SODA91: Conference on Discrete Algorithms

January 28 - 30, 1991

California, San Francisco, USA

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Overall Acceptance Rate 411 of 1,322 submissions, 31%

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Berg MMatoušek JSchwarzkopf O(1995)Piecewise linear paths among convex obstaclesDiscrete & Computational Geometry10.1007/BF0257069414:1(9-29)Online publication date: 1-Dec-1995
https://dl.acm.org/doi/10.1007/BF02570694
de Berg MDobrindt KSchwarzkopf OLeighton FGoodrich M(1994)On lazy randomized incremental constructionProceedings of the twenty-sixth annual ACM symposium on Theory of Computing10.1145/195058.195113(105-114)Online publication date: 23-May-1994
https://dl.acm.org/doi/10.1145/195058.195113
de Berg MMatoušek JSchwarzkopf OKosaraju RJohnson DAggarwal A(1993)Piecewise linear paths among convex obstaclesProceedings of the twenty-fifth annual ACM symposium on Theory of Computing10.1145/167088.167224(505-514)Online publication date: 1-Jun-1993
https://dl.acm.org/doi/10.1145/167088.167224
Mehlhorn KSharir MWelzl EFrederickson G(1992)Tail estimates for the space complexity of randomized incremental algorithmsProceedings of the third annual ACM-SIAM symposium on Discrete algorithms10.5555/139404.139423(89-93)Online publication date: 1-Sep-1992
https://dl.acm.org/doi/10.5555/139404.139423
Arkin EHalperin DKedem KMitchell JNaor NDrysdale R(1991)Arrangements of segments that share endpointsProceedings of the seventh annual symposium on Computational geometry10.1145/109648.109684(324-333)Online publication date: 1-Jun-1991
https://dl.acm.org/doi/10.1145/109648.109684
Halperin DDrysdale R(1991)On the complexity of a single cell in certain arrangements of surfaces in 3-space (extended abstract)Proceedings of the seventh annual symposium on Computational geometry10.1145/109648.109683(314-323)Online publication date: 1-Jun-1991
https://dl.acm.org/doi/10.1145/109648.109683
Aurenhammer FSchwarzkopf ODrysdale R(1991)A simple on-line randomized incremental algorithm for computing higher order Voronoi diagramsProceedings of the seventh annual symposium on Computational geometry10.1145/109648.109664(142-151)Online publication date: 1-Jun-1991
https://dl.acm.org/doi/10.1145/109648.109664

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Approximability of Covering Cells with Line Segments

Approximability of covering cells with line segments

On Computing Connected Components of Line Segments

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Approximability of Covering Cells with Line Segments

Approximability of covering cells with line segments

On Computing Connected Components of Line Segments

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