Paper by Erik D. Demaine

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.

BibTeX

@Article{Staged1D_NACO,
  AUTHOR        = {Erik D. Demaine and Sarah Eisenstat and Mashhood Ishaque and Andrew Winslow},
  TITLE         = {One-Dimensional Staged Self-Assembly},
  JOURNAL       = {Natural Computing},
  journalurl    = {https://link.springer.com/journal/11047},
  VOLUME        = 12,
  NUMBER        = 2,
  YEAR          = 2013,
  PAGES         = {247--258},

  length        = {20 pages},
  withstudent   = 1,
  doi           = {https://dx.doi.org/10.1007/s11047-012-9359-0},
  dblp          = {https://dblp.org/rec/journals/nc/DemaineEIW13},
  comments      = {This paper is also available from <A HREF="http://dx.doi.org/10.1007/s11047-012-9359-0">SpringerLink</A>.},
  replaces      = {Staged1D_DNA2011},
  papers        = {Staged1D_DNA2011},
}

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:

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Related papers:

Staged1D_DNA2011 (One-Dimensional Staged Self-Assembly)