research-article

Better bounds on the union complexity of locally fat objects

Author:

Mark de BergAuthors Info & Claims

SoCG '10: Proceedings of the twenty-sixth annual symposium on Computational geometry

Pages 39 - 47

https://doi.org/10.1145/1810959.1810968

Published: 13 June 2010 Publication History

Abstract

We prove that the union complexity of a set of n constant-complexity locally fat objects (which can be curved and/or non-convex) in the plane is O(λ_t+2(n) log n), where t is the maximum number of times the boundaries of any two objects intersect. This improves the previously best known bound by a logarithmic factor.

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Cited By

Ezra E(2019)On the Union of Cylinders in Three DimensionsDiscrete & Computational Geometry10.5555/3116270.311649345:1(45-64)Online publication date: 1-Jan-2019
https://dl.acm.org/doi/10.5555/3116270.3116493
Pettie S(2015)Sharp Bounds on Davenport-Schinzel Sequences of Every OrderJournal of the ACM10.1145/279407562:5(1-40)Online publication date: 2-Nov-2015
https://dl.acm.org/doi/10.1145/2794075
Ezra EAronov BSharir MRandall D(2011)Improved bound for the union of fat trianglesProceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithms10.5555/2133036.2133172(1778-1785)Online publication date: 23-Jan-2011
https://dl.acm.org/doi/10.5555/2133036.2133172
Show More Cited By

Index Terms

Better bounds on the union complexity of locally fat objects
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

SoCG '10: Proceedings of the twenty-sixth annual symposium on Computational geometry

June 2010

452 pages

ISBN:9781450300162

DOI:10.1145/1810959

Program Chairs:
David Kirkpatrick
University of British Columbia, Canada
,
Joseph Mitchell
SUNY Stony Brook, USA

Copyright © 2010 ACM.

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Publication History

Published: 13 June 2010

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SoCG '10: Symposium on Computational Geometry

June 13 - 16, 2010

Utah, Snowbird, USA

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Cited By

Ezra E(2019)On the Union of Cylinders in Three DimensionsDiscrete & Computational Geometry10.5555/3116270.311649345:1(45-64)Online publication date: 1-Jan-2019
https://dl.acm.org/doi/10.5555/3116270.3116493
Pettie S(2015)Sharp Bounds on Davenport-Schinzel Sequences of Every OrderJournal of the ACM10.1145/279407562:5(1-40)Online publication date: 2-Nov-2015
https://dl.acm.org/doi/10.1145/2794075
Ezra EAronov BSharir MRandall D(2011)Improved bound for the union of fat trianglesProceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithms10.5555/2133036.2133172(1778-1785)Online publication date: 23-Jan-2011
https://dl.acm.org/doi/10.5555/2133036.2133172
Ezra E(2010)On the Union of Cylinders in Three DimensionsDiscrete & Computational Geometry10.1007/s00454-010-9312-x45:1(45-64)Online publication date: 21-Dec-2010
https://doi.org/10.1007/s00454-010-9312-x

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