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Discrete ℓ1 Double Bubble Solution is at Most Ceiling Plus Two of the Continuous Solution.

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Title: Discrete ℓ1 Double Bubble Solution is at Most Ceiling Plus Two of the Continuous Solution.
Authors: Duncan, Parker1,2 (AUTHOR), O'Dwyer, Rory3 (AUTHOR) rodwyer@stanford.edu, Procaccia, Eviatar B.1 (AUTHOR)
Source: Discrete & Computational Geometry. Mar2024, Vol. 71 Issue 2, p688-707. 20p.
Subjects: Ceilings
Abstract: In this paper we show that the solution of the discrete Double Bubble problem over Z 2 is at most the ceiling function plus two of the continuous solution to the Double Bubble problem, with respect to the ℓ 1 norm, found in Morgan et al. (J. Geom. Anal. 8(1), 97–115 (1998)) and Duncan et al. (J. Geom. Anal. 33(1), # 31 (2023)). [ABSTRACT FROM AUTHOR]
Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: In this paper we show that the solution of the discrete Double Bubble problem over Z 2 is at most the ceiling function plus two of the continuous solution to the Double Bubble problem, with respect to the ℓ 1 norm, found in Morgan et al. (J. Geom. Anal. 8(1), 97–115 (1998)) and Duncan et al. (J. Geom. Anal. 33(1), # 31 (2023)). [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00454-023-00501-4
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              Text: Mar2024
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