**Reference**:- Erik D. Demaine, Sarah Eisenstat, Mashhood Ishaque, and Andrew Winslow, “One-Dimensional Staged Self-Assembly”,
*Natural Computing*, volume 12, number 2, 2013, pages 247–258. **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. **Comments**:- This paper is also available from SpringerLink.
**Length**:- The paper is 20 pages.
**Availability**:- The paper is available in PostScript (6743k), gzipped PostScript (640k), and PDF (591k).
- See information on file formats.
- [Google Scholar search]
**Related papers**:- Staged1D_DNA2011 (One-Dimensional Staged Self-Assembly)

See also other papers by Erik Demaine.

Last updated September 20, 2023 by Erik Demaine.