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Efficient Packings of Unit Squares in a Large Square

  • Fan Chung
  • Ron GrahamEmail author
Ricky Pollack Memorial Issue
  • 9 Downloads

Abstract

How efficiently can a large square of side length x be packed with non-overlapping unit squares? In this note, we show that the uncovered area W(x) can be made as small as \(O(x^{3/5})\). This improves an earlier estimate which showed that \(W(x) = O\bigl (x^{({3+\sqrt{2}})/{7} }\log x\bigr )\).

Keywords

Square packing Optimization Tiling 

Mathematics Subject Classification

52C15 

Notes

Acknowledgements

We would like to express our appreciation for the energetic enthusiasm we found at the 33rd Bellairs Winter Workshop on Computational Geometry in Barbados where some of this research was carried out.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSan DiegoUSA
  2. 2.Department of Computer Science and EngineeringUniversity of CaliforniaSan DiegoUSA

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