On two dimensional Packing

Yossi Azar; Leah Epstein

doi:10.1007/3-540-61422-2_142

On two dimensional Packing

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

Abstract

The paper considers packing of rectangles into an infinite bin. Similar to the Tetris game, the rectangles arrive from the top and, once placed, cannot be moved again. The rectangles are moved inside the bin to reach their place. For the case in which rotations are allowed, we design an algorithm whose performance ratio is constant. In contrast, if rotations are not allowed, we show that no algorithm of constant ratio exists. For this case we design an algorithm with performance ratio of O(log [Formula presented]), where ϵ s the minimum width of any rectangle. We also show that no algorithm can achieve a better ratio than /2[Formula presented]) for this cane.

Original language	English
Title of host publication	Algorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings
Editors	Rolf Karlsson, Andrzej Lingas
Publisher	Springer Verlag
Pages	321-332
Number of pages	12
ISBN (Print)	3540614222, 9783540614227
DOIs	https://doi.org/10.1007/3-540-61422-2_142
State	Published - 1996
Externally published	Yes
Event	5th Scandinavian Workshop on Algorithm Theory, SWAT 1996 - Reykjavik, Iceland Duration: 3 Jul 1996 → 5 Jul 1996

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1097
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	5th Scandinavian Workshop on Algorithm Theory, SWAT 1996
Country/Territory	Iceland
City	Reykjavik
Period	3/07/96 → 5/07/96

Bibliographical note

Funding Information:
* This work was submitted as part of the M.Sc. thesis of the second author. An extended abstract of this paper appeared in ``Proc. of SWAT '96, 5th Scandinavian Workshop on Algorithm Theory. Reykjavik, Iceland, July 1996,'' pp. 321—332. ²E-mail: azar@math.tau.ac.il. Research supported in part by Allon Fellowship and by the Israel Science Foundation administered by the Israel Academy of Sciences. ³E-mail: lea@math.tau.ac.il.

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1996.

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science (all)

Access to Document

10.1007/3-540-61422-2_142

Cite this

Azar, Y., & Epstein, L. (1996). On two dimensional Packing. In R. Karlsson, & A. Lingas (Eds.), Algorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings (pp. 321-332). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1097). Springer Verlag. https://doi.org/10.1007/3-540-61422-2_142

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title = "On two dimensional Packing",

abstract = "The paper considers packing of rectangles into an infinite bin. Similar to the Tetris game, the rectangles arrive from the top and, once placed, cannot be moved again. The rectangles are moved inside the bin to reach their place. For the case in which rotations are allowed, we design an algorithm whose performance ratio is constant. In contrast, if rotations are not allowed, we show that no algorithm of constant ratio exists. For this case we design an algorithm with performance ratio of O(log [Formula presented]), where ϵ s the minimum width of any rectangle. We also show that no algorithm can achieve a better ratio than /2[Formula presented]) for this cane.",

author = "Yossi Azar and Leah Epstein",

note = "Funding Information: * This work was submitted as part of the M.Sc. thesis of the second author. An extended abstract of this paper appeared in ``Proc. of SWAT '96, 5th Scandinavian Workshop on Algorithm Theory. Reykjavik, Iceland, July 1996,'' pp. 321—332. ²E-mail: azar@math.tau.ac.il. Research supported in part by Allon Fellowship and by the Israel Science Foundation administered by the Israel Academy of Sciences. ³E-mail: lea@math.tau.ac.il. Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 1996.; 5th Scandinavian Workshop on Algorithm Theory, SWAT 1996 ; Conference date: 03-07-1996 Through 05-07-1996",

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doi = "10.1007/3-540-61422-2_142",

language = "English",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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booktitle = "Algorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings",

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Azar, Y & Epstein, L 1996, On two dimensional Packing. in R Karlsson & A Lingas (eds), Algorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1097, Springer Verlag, pp. 321-332, 5th Scandinavian Workshop on Algorithm Theory, SWAT 1996, Reykjavik, Iceland, 3/07/96. https://doi.org/10.1007/3-540-61422-2_142

On two dimensional Packing. / Azar, Yossi; Epstein, Leah.
Algorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings. ed. / Rolf Karlsson; Andrzej Lingas. Springer Verlag, 1996. p. 321-332 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1097).

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

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N1 - Funding Information: * This work was submitted as part of the M.Sc. thesis of the second author. An extended abstract of this paper appeared in ``Proc. of SWAT '96, 5th Scandinavian Workshop on Algorithm Theory. Reykjavik, Iceland, July 1996,'' pp. 321—332. ²E-mail: azar@math.tau.ac.il. Research supported in part by Allon Fellowship and by the Israel Science Foundation administered by the Israel Academy of Sciences. ³E-mail: lea@math.tau.ac.il. Publisher Copyright: © Springer-Verlag Berlin Heidelberg 1996.

PY - 1996

Y1 - 1996

N2 - The paper considers packing of rectangles into an infinite bin. Similar to the Tetris game, the rectangles arrive from the top and, once placed, cannot be moved again. The rectangles are moved inside the bin to reach their place. For the case in which rotations are allowed, we design an algorithm whose performance ratio is constant. In contrast, if rotations are not allowed, we show that no algorithm of constant ratio exists. For this case we design an algorithm with performance ratio of O(log [Formula presented]), where ϵ s the minimum width of any rectangle. We also show that no algorithm can achieve a better ratio than /2[Formula presented]) for this cane.

AB - The paper considers packing of rectangles into an infinite bin. Similar to the Tetris game, the rectangles arrive from the top and, once placed, cannot be moved again. The rectangles are moved inside the bin to reach their place. For the case in which rotations are allowed, we design an algorithm whose performance ratio is constant. In contrast, if rotations are not allowed, we show that no algorithm of constant ratio exists. For this case we design an algorithm with performance ratio of O(log [Formula presented]), where ϵ s the minimum width of any rectangle. We also show that no algorithm can achieve a better ratio than /2[Formula presented]) for this cane.

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

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Azar Y, Epstein L. On two dimensional Packing. In Karlsson R, Lingas A, editors, Algorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings. Springer Verlag. 1996. p. 321-332. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-61422-2_142

On two dimensional Packing

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Bibliographical note

ASJC Scopus subject areas

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