Staged Self-assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues

  • Erik D. Demaine
  • Martin L. Demaine
  • Sándor P. Fekete
  • Mashhood Ishaque
  • Eynat Rafalin
  • Robert T. Schweller
  • Diane L. Souvaine
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4848)


We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are motivated by a practical nanofabrication scenario through protein-based bioengineering. Staging allows us to break through the traditional lower bounds in tile self-assembly by encoding the shape in the staging algorithm instead of the tiles. All of our results are based on the practical assumption that only a constant number of glues, and thus only a constant number of tiles, can be engineered, as each new glue type requires significant biochemical research and experiments. Under this assumption, traditional tile self-assembly cannot even manufacture an n ×n square; in contrast, we show how staged assembly enables manufacture of arbitrary orthogonal shapes in a variety of precise formulations of the model.


Tile System Decomposition Tree Kolmogorov Complexity Full Connectivity Stage Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • Martin L. Demaine
    • 1
  • Sándor P. Fekete
    • 2
  • Mashhood Ishaque
    • 3
  • Eynat Rafalin
    • 4
  • Robert T. Schweller
    • 5
  • Diane L. Souvaine
    • 3
  1. 1.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA
  2. 2.Institut für Mathematische OptimierungTechnische Universität BraunschweigBraunschweigGermany
  3. 3.Department of Computer ScienceTufts UniversityMedfordUSA
  4. 4.Google Inc. 
  5. 5.Department of Computer ScienceUniversity of Texas Pan AmericanEdinburgUSA

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