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Efficient Algorithms for Self Assembling Triangular and Other Nano Structures

  • Vamsi Kundeti
  • Sanguthevar Rajasekaran
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5542)

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.

Keywords

Bond Strength Assembly Process Binary Counter Tile Assembly Model Tile 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 2009

Authors and Affiliations

  • Vamsi Kundeti
    • 1
  • Sanguthevar Rajasekaran
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of ConnecticutStorrsUSA

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