Paper by Martin L. Demaine

Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Mashhood Ishaque, Eynat Rafalin, Robert T. Schweller, and Diane L. Souvaine, “Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues”, Natural Computing, volume 7, number 3, September 2008, pages 347–370. Special issue of selected papers from the 13th International Meeting on DNA Computing, 2007.

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. Under this assumption, traditional tile self-assembly cannot even manufacture an n × n square; in contrast, we show how staged assembly in theory enables manufacture of arbitrary shapes in a variety of precise formulations of the model.

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The tile bound of 16 in Table 1 row 5 (arbitrary shape) and in Theorem 5 is incorrect; the correct bound (for the same algorithm) is 52.

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Related papers:
StagedAssembly_DNA2007 (Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues)

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