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Bounds for partitioning rectilinear polygons

Authors:

Teofilo Gonzalez,

Si-Qing ZhengAuthors Info & Claims

SCG '85: Proceedings of the first annual symposium on Computational geometry

Pages 281 - 287

https://doi.org/10.1145/323233.323269

Published: 01 June 1985 Publication History

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Abstract

We study the problem of partitioning a rectilinear polygon with interior points into rectangles by introducing a set of line segments. All points must be included in at least one of the line segments introduced and the objective function is to introduce a set of line segments such that the sum of their lengths is minimal. Since this problem is computationally intractable, we present efficient approximation algorithms for its solution. The solutions generated by our algorithms are guaranteed to be within a fixed constant of the optimal solution value. Even though the constant approximation bound is not so small, we conjecture that in general the solutions our algorithms generate are close to optimal.

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Kim HLee JAhn H(2023)Rectangular partitions of a rectilinear polygonComputational Geometry10.1016/j.comgeo.2022.101965110(101965)Online publication date: Mar-2023
https://doi.org/10.1016/j.comgeo.2022.101965
Du DPardalos PHu XWu WDu DPardalos PHu XWu W(2022)Restriction and Steiner TreeIntroduction to Combinatorial Optimization10.1007/978-3-031-10596-8_9(259-291)Online publication date: 6-Jul-2022
https://doi.org/10.1007/978-3-031-10596-8_9
Subercaze JGravier CRocher P(2016)A Merging Heuristic for the Rectangle Decomposition of Binary MatricesProceedings of the 15th International Symposium on Experimental Algorithms - Volume 968510.1007/978-3-319-38851-9_21(310-325)Online publication date: 5-Jun-2016
https://dl.acm.org/doi/10.1007/978-3-319-38851-9_21
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Bounds for partitioning rectilinear polygons

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Improved bounds for rectangular and guillotine partitions

We study the problem of partitioning a rectangle S with a set of interior points Q intorectangles by introducing a set of line segments of least total length. The set of partitioning line segments must include every point in Q. Since this problem is ...
Partitioning rectilinear polygons into simpler components
On partitioning rectilinear polygons into star-shaped polygons
Abstract
We present an algorithm for finding optimum partitions of simple monotone rectilinear polygons into star-shaped polygons. The algorithm may introduce Steiner points and its time complexity isO(n), wheren is the number of vertices in the polygon. ...

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SCG '85: Proceedings of the first annual symposium on Computational geometry

June 1985

322 pages

ISBN:0897911636

DOI:10.1145/323233

Chairman:
Joseph O'Rourke
Johns Hopkins Univ., Baltimore, MD

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Published: 01 June 1985

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SCG85: The 1st Annual ACM SIGACT/SIGGRAPH Symposium on Computational Geometry 1985

June 5 - 7, 1985

Maryland, Baltimore, USA

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Kim HLee JAhn H(2023)Rectangular partitions of a rectilinear polygonComputational Geometry10.1016/j.comgeo.2022.101965110(101965)Online publication date: Mar-2023
https://doi.org/10.1016/j.comgeo.2022.101965
Du DPardalos PHu XWu WDu DPardalos PHu XWu W(2022)Restriction and Steiner TreeIntroduction to Combinatorial Optimization10.1007/978-3-031-10596-8_9(259-291)Online publication date: 6-Jul-2022
https://doi.org/10.1007/978-3-031-10596-8_9
Subercaze JGravier CRocher P(2016)A Merging Heuristic for the Rectangle Decomposition of Binary MatricesProceedings of the 15th International Symposium on Experimental Algorithms - Volume 968510.1007/978-3-319-38851-9_21(310-325)Online publication date: 5-Jun-2016
https://dl.acm.org/doi/10.1007/978-3-319-38851-9_21
Deng PWu WShragowitz EDu D(2016)Adaptive PartitionsEncyclopedia of Algorithms10.1007/978-1-4939-2864-4_2(18-22)Online publication date: 22-Apr-2016
https://doi.org/10.1007/978-1-4939-2864-4_2
Deng PWu WShragowitz EDu D(2014)Adaptive PartitionsEncyclopedia of Algorithms10.1007/978-3-642-27848-8_2-2(1-6)Online publication date: 12-Nov-2014
https://doi.org/10.1007/978-3-642-27848-8_2-2
Deng PWu WShragowitz E(2008)Adaptive PartitionsEncyclopedia of Algorithms10.1007/978-0-387-30162-4_2(4-7)Online publication date: 2008
https://doi.org/10.1007/978-0-387-30162-4_2
Ackerman EBarequet GPinter R(2006)On the number of rectangulations of a planar point setJournal of Combinatorial Theory Series A10.1016/j.jcta.2005.10.003113:6(1072-1091)Online publication date: 1-Aug-2006
https://dl.acm.org/doi/10.1016/j.jcta.2005.10.003
Levcopoulos CÖstlin A(2005)Linear-time heuristics for minimum weight rectangulationAlgorithm Theory — SWAT'9610.1007/3-540-61422-2_138(271-283)Online publication date: 7-Jun-2005
https://doi.org/10.1007/3-540-61422-2_138
Cheng XDu DKim JRuan L(2005)Optimal Rectangular PartitionsHandbook of Combinatorial Optimization10.1007/0-387-23830-1_7(313-327)Online publication date: 2005
https://doi.org/10.1007/0-387-23830-1_7
Ackerman EBarequet GPinter RMunro I(2004)On the number of rectangular partitionsProceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms10.5555/982792.982904(736-745)Online publication date: 11-Jan-2004
https://dl.acm.org/doi/10.5555/982792.982904
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Improved bounds for rectangular and guillotine partitions

Partitioning rectilinear polygons into simpler components

On partitioning rectilinear polygons into star-shaped polygons

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Abstract

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Recommendations

Improved bounds for rectangular and guillotine partitions

Partitioning rectilinear polygons into simpler components

On partitioning rectilinear polygons into star-shaped polygons

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