New geometric algorithms for fully connected staged self-assembly
Name
1505.07862.pdf
Description
Accepted version
Size
857.07 KB
Format
Adobe PDF
Checksum (MD5)
62e27a9762c6e7318adc1378b7e74c53
Author(s)
Demaine, Erik D
Fekete, Sándor P
Scheffer, Christian
Schmidt, Arne
Date Issued
2017
Journal
Theoretical Computer Science
Publisher
Elsevier BV
Version
Author's final manuscript
Abstract
© 2016 Elsevier B.V. We consider staged self-assembly systems, in which square-shaped tiles can be added to bins in several stages. Within these bins, the tiles may connect to each other, depending on the glue types of their edges. Previous work by Demaine et al. showed that a relatively small number of tile types suffices to produce arbitrary shapes in this model. However, these constructions were only based on a spanning tree of the geometric shape, so they did not produce full connectivity of the underlying grid graph in the case of shapes with holes; self-assembly of fully connected assemblies with a polylogarithmic number of stages was left as a major open problem. We resolve this challenge by presenting new systems for staged assembly that produce fully connected polyominoes in O(log2n) stages, for various scale factors and temperature τ=2 as well as τ=1. Our constructions work even for shapes with holes and use only a constant number of glues and tiles. Moreover, the underlying approach is more geometric in nature, implying that it promises to be more feasible for shapes with compact geometric description.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/J.TCS.2016.11.020
