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Time Optimal Self-assembly for 2D and 3D Shapes: The Case of Squares and Cubes

  • Florent Becker
  • Éric Rémila
  • Nicolas Schabanel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5347)

Abstract

Self-assembling tile systems are a model for assembling DNA-based nano artefacts. In the currently known constructions, most of the effort is put on garanteeing the size of the output object, whereas the geometrical efficiency of the assembling of the shape itself is left aside. We propose in this paper a framework to obtain provably time efficient self-assembling tile systems. Our approach consists in studying how the flow of information has to circulate within the desired shape to guarantee an optimal time construction. We show how this study can yield an adequate ordering of the tiling process from which one can deduced a provably time efficient tile systems for that shape. We apply our framework to squares and cubes for which we obtain time optimal self-assembling tile systems.

Keywords

Self-assembling Tilings Time Optimal Construction 2D and 3D Discrete Geometry 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Florent Becker
    • 1
  • Éric Rémila
    • 1
  • Nicolas Schabanel
    • 2
  1. 1.Université de Lyon – LIP, UMR 5668 ENS Lyon CNRS UCBLFrance
  2. 2.CNRS, Universidad de Chile — CMMChile

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