One-dimensional staged self-assembly
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paper(1).pdf
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Accepted version
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232.38 KB
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Author(s)
Demaine, Erik D
Eisenstat, Sarah
Ishaque, Mashhood
Winslow, Andrew
Date Issued
2013
Journal
Natural Computing
Publisher
Springer Nature America, Inc
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 steps 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(log n)-approximable problem) and that the problem is NP-hard. 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. © 2012 Springer Science+Business Media Dordrecht.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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DOI of Published Version
https://doi.org/10.1007/S11047-012-9359-0
