(Re)packing Equal Disks into Rectangle
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| Publicat a: | Discrete & Computational Geometry vol. 72, no. 4 (Dec 2024), p. 1596 |
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| Autor principal: | |
| Altres autors: | , , , |
| Publicat: |
Springer Nature B.V.
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| Matèries: | |
| Accés en línia: | Citation/Abstract Full Text - PDF |
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| 001 | 3129051311 | ||
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| 022 | |a 0179-5376 | ||
| 022 | |a 1432-0444 | ||
| 024 | 7 | |a 10.1007/s00454-024-00633-1 |2 doi | |
| 035 | |a 3129051311 | ||
| 045 | 2 | |b d20241201 |b d20241231 | |
| 084 | |a 65756 |2 nlm | ||
| 100 | 1 | |a Fomin, Fedor V. |u University of Bergen, Bergen, Norway (GRID:grid.7914.b) (ISNI:0000 0004 1936 7443) | |
| 245 | 1 | |a (Re)packing Equal Disks into Rectangle | |
| 260 | |b Springer Nature B.V. |c Dec 2024 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a The problem of packing of equal disks (or circles) into a rectangle is a fundamental geometric problem. (By a packing here we mean an arrangement of disks in a rectangle without overlapping.) We consider the following algorithmic generalization of the equal disk packing problem. In this problem, for a given packing of equal disks into a rectangle, the question is whether by changing positions of a small number of disks, we can allocate space for packing more disks. More formally, in the repacking problem, for a given set of n equal disks packed into a rectangle and integers k and h, we ask whether it is possible by changing positions of at most h disks to pack n+k<inline-graphic xlink:href="454_2024_633_Article_IEq1.gif" /> disks. Thus the problem of packing equal disks is the special case of our problem with n=h=0<inline-graphic xlink:href="454_2024_633_Article_IEq2.gif" />. While the computational complexity of packing equal disks into a rectangle remains open, we prove that the repacking problem is NP-hard already for h=0<inline-graphic xlink:href="454_2024_633_Article_IEq3.gif" />. Our main algorithmic contribution is an algorithm that solves the repacking problem in time (h+k)O(h+k)·|I|O(1)<inline-graphic xlink:href="454_2024_633_Article_IEq4.gif" />, where |I| is the input size. That is, the problem is fixed-parameter tractable parameterized by k and h. | |
| 653 | |a Algorithms | ||
| 653 | |a Rectangles | ||
| 653 | |a Packaging | ||
| 653 | |a Disks | ||
| 700 | 1 | |a Golovach, Petr A. |u University of Bergen, Bergen, Norway (GRID:grid.7914.b) (ISNI:0000 0004 1936 7443) | |
| 700 | 1 | |a Inamdar, Tanmay |u Indian Institute of Technology, Jodhpur, Jodhpur, India (GRID:grid.467228.d) (ISNI:0000 0004 1806 4045) | |
| 700 | 1 | |a Saurabh, Saket |u University of Bergen, Bergen, Norway (GRID:grid.7914.b) (ISNI:0000 0004 1936 7443); Institute of Mathematical Sciences, Chennai, India (GRID:grid.462414.1) (ISNI:0000 0004 0504 909X) | |
| 700 | 1 | |a Zehavi, Meirav |u Ben-Guiron University, Beer-Sheva, Israel (GRID:grid.462414.1) | |
| 773 | 0 | |t Discrete & Computational Geometry |g vol. 72, no. 4 (Dec 2024), p. 1596 | |
| 786 | 0 | |d ProQuest |t Science Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3129051311/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3129051311/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |