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One-dimensional staged self-assembly.
One-dimensional staged self-assembly.
- Source :
-
Natural Computing . Jun2013, Vol. 12 Issue 2, p247-258. 12p. - Publication Year :
- 2013
-
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 $$\Omega(\sqrt{n/\log n})$$ 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15677818
- Volume :
- 12
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Natural Computing
- Publication Type :
- Academic Journal
- Accession number :
- 87785424
- Full Text :
- https://doi.org/10.1007/s11047-012-9359-0