The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Running time and program size for self-assembled squares
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Complexities for Generalized Models of Self-Assembly
SIAM Journal on Computing
Reducing tile complexity for self-assembly through temperature programming
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Complexity of Self-Assembled Shapes
SIAM Journal on Computing
Randomized Self-assembly for Approximate Shapes
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
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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 脳 N square (with a temperature of 驴 = 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 驴 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.