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Efficient algorithms for self assembling non-rectangular nano structures

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Abstract

Nano fabrication with biomolecular/DNA self assembly is a promising area of research. Building nano structures with self assembly is both efficient and inexpensive. Soloveichik and Winfree (SIAM J Comput 36(6):1544–1569, 2007) formalized a two dimensional (2D) tile assembly model based on Wang’s tiling technique. Algorithms with an optimal tile complexity of \(\left(\Uptheta\left(\frac{\log(N)}{\log(\log(N))}\right)\right)\) were proposed earlier to uniquely self assemble an N × N square (with a temperature of α = 2) on this model. However efficient constructions to assemble arbitrary shapes are not known and have remained open. In this paper we present self assembling algorithms to assemble a triangle of base 2N − 1 (units) and height N with a tile complexity of \(\Uptheta(\log(N)).\) We also describe how this framework can be used to construct other shapes such as rhombus, hexagon etc.

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Acknowledgements

This work has been supported in part by the following grants: NSF 0326155, NSF 0829916 and NIH 1R01GM079689-01A1.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Connecticut, Storrs, CT, 06269, USA

    Vamsi Kundeti & Sanguthevar Rajasekaran

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  1. Vamsi Kundeti
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  2. Sanguthevar Rajasekaran
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Correspondence to Vamsi Kundeti.

Additional information

Preliminary version of the paper appeared in ISBRA 2009.

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Kundeti, V., Rajasekaran, S. Efficient algorithms for self assembling non-rectangular nano structures. Nat Comput 10, 583–594 (2011). https://doi.org/10.1007/s11047-010-9210-4

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