Abstract
The Pattern self-Assembly Tile set Synthesis (PATS) problem is to determine a set of coloured tiles that self-assemble to implement a given rectangular colour pattern. We give an exhaustive branch-and-bound algorithm to find tile sets of minimum cardinality for the PATS problem. Our algorithm makes use of a search tree in the lattice of partitions of the ambient rectangular grid, and an efficient bounding function to prune this search tree. Empirical data on the performance of the algorithm shows that it compares favourably to previously presented heuristic solutions to the problem.
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References
Adleman, L., Cheng, Q., Goel, A., Huang, M.-D., Kempe, D., de Espanés, P.M., Rothemund, P.W.K.: Combinatorial optimization problems in self-assembly. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC 2002), pp. 23–32. ACM, New York (2002)
Göös, M., Orponen, P.: Synthesizing minimal tile sets for patterned DNA self-assembly. A detailed version, arXiv:0911.2924
Lathrop, J.I., Lutz, J.H., Summers, S.M.: Strict self-assembly of discrete Sierpinski triangles. Theoretical Computer Science 410(4-5), 384–405 (2009)
Lin, C., Liu, Y., Rinker, S., Yan, H.: DNA tile based self-assembly: building complex nanoarchitectures. Chem. Phys. Chem. 7(8), 1641–1647 (2006)
Ma, X., Lombardi, F.: Synthesis of tile sets for DNA self-assembly. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 27(5), 963–967 (2008)
Ma, X., Lombardi, F.: On the computational complexity of tile set synthesis for DNA self-assembly. IEEE Transactions on Circuits and Systems II: Express Briefs 56(1), 31–35 (2009)
Park, S.H., Pistol, C., Ahn, S.J., Reif, J.H., Lebeck, A.R., Dwyer, C., LaBean, T.H.: Finite-size, fully addressable DNA tile lattices formed by hierarchical assembly procedures. Angewandte Chemie International Edition 45(5), 735–739 (2006)
Park, S.H., Yan, H., Reif, J.H., LaBean, T.H., Finkelstein, G.: Electronic nanostructures templated on self-assembled DNA scaffolds. Nanotechnology 15, S525–S527 (2004)
Rothemund, P.W.K.: Theory and Experiments in Algorithmic Self-assembly. PhD thesis, University of Southern California (2001)
Rothemund, P.W.K.: Folding DNA to create nanoscale shapes and patterns. Nature 440, 297–302 (2006)
Rothemund, P.W.K., Winfree, E.: The program-size complexity of self-assembled squares (extended abstract). In: Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (STOC 2000), pp. 459–468. ACM, New York (2000)
Winfree, E.: Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology (1998)
Yan, H., Park, S.H., Finkelstein, G., Reif, J.H., LaBean, T.H.: DNA-templated self-assembly of protein arrays and highly conducive nanowires. Science 301, 1882–1884 (2003)
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Göös, M., Orponen, P. (2011). Synthesizing Minimal Tile Sets for Patterned DNA Self-assembly. In: Sakakibara, Y., Mi, Y. (eds) DNA Computing and Molecular Programming. DNA 2010. Lecture Notes in Computer Science, vol 6518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18305-8_7
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DOI: https://doi.org/10.1007/978-3-642-18305-8_7
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