On Two Dimensional Packing

Yossi Azar, Leah Epstein

Research output: Contribution to journalArticlepeer-review


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(1/ε)), where ε is the minimum width of any rectangle. We also show that no algorithm can achieve a better ratio than Ω(√log(1/ε) ) for this case.

Original languageEnglish
Pages (from-to)290-310
Number of pages21
JournalJournal of Algorithms
Issue number2
StatePublished - Nov 1997
Externally publishedYes

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: [email protected]. Research supported in part by Allon Fellowship and by the Israel Science Foundation administered by the Israel Academy of Sciences. ³E-mail: [email protected].

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Computational Theory and Mathematics


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