One-dimensional staged self-assembly
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Demaine-One-dimensional.pdf
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Author(s)
Demaine, Erik D.
Eisenstat, Sarah Charmian
Ishaque, Mashhood
Winslow, Andrew
Date Issued
September 2011
Journal
DNA Computing and Molecular Programming
Publisher
Springer Berlin / Heidelberg
Citation
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.
Version
Author's final manuscript
Abstract
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.
Description
17th International Conference, DNA 17, Pasadena, CA, USA, September 19-23, 2011. Proceedings
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/978-3-642-23638-9_10
