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

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

Research output: Contribution to journalArticlepeer-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 languageEnglish
JournalDiscrete and Computational Geometry
DOIs
StateAccepted/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

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