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Efficient Algorithms for Self Assembling Triangular and Other Nano Structures

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Book cover Bioinformatics Research and Applications (ISBRA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 5542))

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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. Winfree [1] formalized a two dimensional (2D) tile assembly model based on Wang’s tiling technique. Algorithms with an optimal tile complexity of (\(\Theta(\frac{\log(N)}{\log(\log(N))})\)) 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 Θ(log(N)). We also describe how this framework can be used to construct other shapes.

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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

Authors
  1. Vamsi Kundeti
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  2. Sanguthevar Rajasekaran
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Editor information

Editors and Affiliations

  1. Computer Science & Engineering Department, University of Connecticut, 371 Fairfield Way, Unit 2155, CT 06269, Storrs, USA

    Ion Măndoiu

  2. Bioinformatics Research Group (BioRG), School of Computing and Information Sciences, Florida International University, 11200 SW 8th Street, Room ECS254, University Park, FL 33199, Miami, USA

    Giri Narasimhan

  3. Department of Computer Science, Georgia State University, P.O. Box 3994, GA 30302-3994, Atlanta, USA

    Yanqing Zhang

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© 2009 Springer-Verlag Berlin Heidelberg

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Kundeti, V., Rajasekaran, S. (2009). Efficient Algorithms for Self Assembling Triangular and Other Nano Structures. In: Măndoiu, I., Narasimhan, G., Zhang, Y. (eds) Bioinformatics Research and Applications. ISBRA 2009. Lecture Notes in Computer Science(), vol 5542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01551-9_15

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  • DOI: https://doi.org/10.1007/978-3-642-01551-9_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01550-2

  • Online ISBN: 978-3-642-01551-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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