Online square and cube packing

Leah Epstein, Rob Van Stee

Research output: Contribution to journalArticlepeer-review


In online square packing, squares of different sizes arrive online and need to be packed into unit squares which are called bins. The goal is to minimize the number of bins used. Online cube packing is defined analogously. We show an upper bound of 2.2697 and a lower bound of 1.6406 for online square packing, and an upper bound of 2.9421 and a lower bound of 1.6680 for online cube packing. The upper bound for squares can be further reduced to 2.24437 using a computer proof. These results improve on the previously known results for the two problems. We also show improved lower bounds for higher dimensions.

Original languageEnglish
Pages (from-to)595-606
Number of pages12
JournalActa Informatica
Issue number9
StatePublished - Oct 2005

ASJC Scopus subject areas

  • Software
  • Information Systems
  • Computer Networks and Communications


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