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
Combinatorial optimization problems in self-assembly
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Algorithmic self-assembly of dna
Algorithmic self-assembly of dna
Theory and experiments in algorithmic self-assembly
Theory and experiments in algorithmic self-assembly
Complexities for generalized models of self-assembly
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Invadable self-assembly: combining robustness with efficiency
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Toward minimum size self-assembled counters
DNA13'07 Proceedings of the 13th international conference on DNA computing
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DNA self-assembly is a promising paradigm for nanotechnology. In this paper we study the problem of finding tile systems of minimum size that assemble a given shape in the Tile Assembly Model, defined by Rothemund and Winfree (Proceedings of the thirty-second annual ACM symposium on theory of computing, 2000). We present a tile system that assembles an $$N\times\lceil\log_2 N\rceil$$ rectangle in asymptotically optimal $$\Uptheta(N)$$ time. This tile system has only 7 tiles. Earlier constructions need at least 8 tiles (Chen et al. Proceedings of symposium on discrete algorithms, 2004). We managed to reduce the number of tiles without increasing the assembly time. The new tile system works at temperature 3. The new construction was found by the combination of exhaustive computerized search of the design space and manual adjustment of the search output.