article

An approximation algorithm for dissecting a rectangle into rectangles with specified areas

Authors:

Hiroshi Nagamochi,

Yuusuke AbeAuthors Info & Claims

Discrete Applied Mathematics, Volume 155, Issue 4

Pages 523 - 537

https://doi.org/10.1016/j.dam.2006.08.005

Published: 20 February 2007 Publication History

Abstract

Given a rectangle R with area @a and a set of n positive reals A={a"1,a"2,...,a"n} with @?"a"""i"@?"Aa"i=@a, we consider the problem of dissecting R into n rectangles r"i with area a"i(i=1,2,...,n) so that the set R of resulting rectangles minimizes an objective function such as the sum of the perimeters of the rectangles in R, the maximum perimeter of the rectangles in R, and the maximum aspect ratio of the rectangles in R, where we call the problems with these objective functions PERI-SUM, PERI-MAX and ASPECT-RATIO, respectively. We propose an O(nlogn) time algorithm that finds a dissection R of R that is a 1.25-approximate solution to PERI-SUM, a 23-approximate solution to PERI-MAX, and has an aspect ratio at most max{@r(R),3,1+max"i"="1","...","n"-"1a"i"+"1a"i}, where @r(R) denotes the aspect ratio of R.

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Cited By

Quoc Trung BThi-Mai-Anh BViet Chinh NQuang Dung PManh Cuong N(2023)Metaheuristic for a soft-rectangle packing problem with guillotine constraintsProceedings of the 12th International Symposium on Information and Communication Technology10.1145/3628797.3628918(715-722)Online publication date: 7-Dec-2023
https://dl.acm.org/doi/10.1145/3628797.3628918
Limberger DScheibel WDöllner JTrapp M(2022)Visual variables and configuration of software mapsJournal of Visualization10.1007/s12650-022-00868-126:1(249-274)Online publication date: 16-Sep-2022
https://dl.acm.org/doi/10.1007/s12650-022-00868-1
Tang YGao W(2021)Processor-Aware Cache-Oblivious Algorithms✱Proceedings of the 50th International Conference on Parallel Processing10.1145/3472456.3472506(1-10)Online publication date: 9-Aug-2021
https://dl.acm.org/doi/10.1145/3472456.3472506
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Index Terms

An approximation algorithm for dissecting a rectangle into rectangles with specified areas
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis
      1. Approximation
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
  2. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image Discrete Applied Mathematics

Discrete Applied Mathematics Volume 155, Issue 4

February, 2007

159 pages

ISSN:0166-218X

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Copyright © Elsevier B.V. © 2006.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 20 February 2007

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Cited By

Quoc Trung BThi-Mai-Anh BViet Chinh NQuang Dung PManh Cuong N(2023)Metaheuristic for a soft-rectangle packing problem with guillotine constraintsProceedings of the 12th International Symposium on Information and Communication Technology10.1145/3628797.3628918(715-722)Online publication date: 7-Dec-2023
https://dl.acm.org/doi/10.1145/3628797.3628918
Limberger DScheibel WDöllner JTrapp M(2022)Visual variables and configuration of software mapsJournal of Visualization10.1007/s12650-022-00868-126:1(249-274)Online publication date: 16-Sep-2022
https://dl.acm.org/doi/10.1007/s12650-022-00868-1
Tang YGao W(2021)Processor-Aware Cache-Oblivious Algorithms✱Proceedings of the 50th International Conference on Parallel Processing10.1145/3472456.3472506(1-10)Online publication date: 9-Aug-2021
https://dl.acm.org/doi/10.1145/3472456.3472506
Scheibel WLimberger DDöllner JBurch MWestenberg MNguyen QZhao Y(2020)Survey of treemap layout algorithmsProceedings of the 13th International Symposium on Visual Information Communication and Interaction10.1145/3430036.3430041(1-9)Online publication date: 8-Dec-2020
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Liu YShi LZhang JRobertazzi T(2019)Layer based partition for matrix multiplication on heterogeneous mesh networksProceedings of the High Performance Computing Symposium10.5555/3338075.3338079(1-12)Online publication date: 29-Apr-2019
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Beaumont OBecker BDeFlumere AEyraud-Dubois LLambert TLastovetsky A(2019)Recent Advances in Matrix Partitioning for Parallel Computing on Heterogeneous PlatformsIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2018.285315130:1(218-229)Online publication date: 1-Jan-2019
https://dl.acm.org/doi/10.1109/TPDS.2018.2853151
Bui QVidal THà M(2019)On three soft rectangle packing problems with guillotine constraintsJournal of Global Optimization10.1007/s10898-019-00741-w74:1(45-62)Online publication date: 1-May-2019
https://dl.acm.org/doi/10.1007/s10898-019-00741-w
Eyraud-Dubois LLambert T(2018)Using Static Allocation Algorithms for Matrix Matrix Multiplication on Multicores and GPUsProceedings of the 47th International Conference on Parallel Processing10.1145/3225058.3225066(1-10)Online publication date: 13-Aug-2018
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Beaumont OEyraud-Dubois LLambert T(2016)Cuboid Partitioning for Parallel Matrix Multiplication on Heterogeneous PlatformsProceedings of the 22nd International Conference on Euro-Par 2016: Parallel Processing - Volume 983310.1007/978-3-319-43659-3_13(171-182)Online publication date: 24-Aug-2016
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De Oliveira J(2009)Two algorithms for automatic page layout and possible applicationsMultimedia Tools and Applications10.1007/s11042-009-0267-y43:3(275-301)Online publication date: 1-Jul-2009
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