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

Parker Duncan; Rory O’Dwyer; Eviatar B. Procaccia

doi:10.1007/s00454-023-00501-4

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

Parker Duncan, Rory O’Dwyer, Eviatar B. Procaccia

Data and Decision Sciences

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we show that the solution of the discrete Double Bubble problem over Z² is at most the ceiling function plus two of the continuous solution to the Double Bubble problem, with respect to the ℓ¹ 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)).

Original language	English
Journal	Discrete and Computational Geometry
DOIs	https://doi.org/10.1007/s00454-023-00501-4
State	Accepted/In press - 2023

Keywords

Discrete isoperimetry
Double Bubble problem
Square lattice
Wulff shape

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Access to Document

10.1007/s00454-023-00501-4

Cite this

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title = "Discrete ℓ1 Double Bubble Solution is at Most Ceiling Plus Two of the Continuous Solution",

abstract = "In this paper we show that the solution of the discrete Double Bubble problem over Z2 is at most the ceiling function plus two of the continuous solution to the Double Bubble problem, with respect to the ℓ1 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)).",

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KW - Discrete isoperimetry

KW - Double Bubble problem

KW - Square lattice

KW - Wulff shape

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