One-dimensional staged self-assembly
Author(s)Demaine, Erik D.; Eisenstat, Sarah Charmian; Ishaque, Mashhood; Winslow, Andrew
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We introduce the problem of staged self-assembly of one-dimensional nanostructures, which becomes interesting when the elements are labeled (e.g., representing functional units that must be placed at specific locations). In a restricted model in which each operation has a single terminal assembly, we prove that assembling a given string of labels with the fewest stages is equivalent, up to constant factors, to compressing the string to be uniquely derived from the smallest possible context-free grammar (a well-studied O(logn)-approximable problem). Without this restriction, we show that the optimal assembly can be substantially smaller than the optimal context-free grammar, by a factor of Ω √n/log n even for binary strings of length n. Fortunately, we can bound this separation in model power by a quadratic function in the number of distinct glues or tiles allowed in the assembly, which is typically small in practice.
17th International Conference, DNA 17, Pasadena, CA, USA, September 19-23, 2011. Proceedings
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
DNA Computing and Molecular Programming
Springer Berlin / Heidelberg
Demaine, Erik D. et al. “One-Dimensional Staged Self-assembly.” DNA Computing and Molecular Programming. Ed. Luca Cardelli & William Shih. LNCS Vol. 6937. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. 100–114.
Author's final manuscript