Note on “Efficient Packings of Unit Squares in a Large Square”
Arslanov M.Z. Bui H.D.
2025Springer
Discrete and Computational Geometry
2025
Given a large (generally non-integer) length x, the well-studied square packing problem asks how efficiently one can pack a square of side length x by non-overlapping unit squares. Let be the minimum area “wasted” in such a packing. Chung and Graham (Discrete Comput Geom 64(3):690–699, 2019. https://doi.org/10.1007/s00454-019-00088-9) claimed a proof that. This note identifies a calculation error in that paper that invalidates the claimed result. We illustrate the error in two ways: by directly analyzing where the mistake arose in an angle computation, and by checking against a simple geometric argument using the triangle inequality.
Optimization , Square packing , Tiling
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Institute of Information and Computational Technologies, Almaty, Kazakhstan
Singapore, Singapore
Institute of Information and Computational Technologies
Singapore
10 лет помогаем публиковать статьи Международный издатель
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