English

Improved Online Square-into-Square Packing

Computational Geometry 2014-01-23 v1

Abstract

In this paper, we show an improved bound and new algorithm for the online square-into-square packing problem. This two-dimensional packing problem involves packing an online sequence of squares into a unit square container without any two squares overlapping. The goal is to find the largest area α\alpha such that any set of squares with total area α\alpha can be packed. We show an algorithm that can pack any set of squares with total area α3/8\alpha \leq 3/8 into a unit square in an online setting, improving the previous bound of 11/3211/32.

Keywords

Cite

@article{arxiv.1401.5583,
  title  = {Improved Online Square-into-Square Packing},
  author = {Brian Brubach},
  journal= {arXiv preprint arXiv:1401.5583},
  year   = {2014}
}

Comments

15 pages, 3 figures

R2 v1 2026-06-22T02:52:00.447Z