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DOI: 10.4230/LIPIcs.DNA.2020.8
Design Automation of Polyomino Set That Self-Assembles into a Desired Shape

Authors: Yuta Matsumura, Ibuki Kawamata, and Satoshi Murata

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract
The problem of finding the smallest DNA tile set that self-assembles into a desired pattern or shape is a research focus that has been investigated by many researchers. In this paper, we take a polyomino, which is a non-square element composed of several connected square units, as an element of assembly and consider the design problem of the minimal set of polyominoes that self-assembles into a desired shape. We developed a self-assembly simulator of polyominoes based on the agent-based Monte Carlo method, in which the potential energy among the polyominoes is evaluated and the simulation state is updated toward the direction to decrease the total potential. Aggregated polyominoes are represented as an agent, which can move, merge, and split during the simulation. In order to search the minimal set of polyominoes, two-step evaluation strategy is adopted, because of enormous search space including many parameters such as the shape, the size, and the glue types attached to the polyominoes. The feasibility of the proposed method is shown through three examples with different size and complexity.
Cite as

Yuta Matsumura, Ibuki Kawamata, and Satoshi Murata. Design Automation of Polyomino Set That Self-Assembles into a Desired Shape. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{matsumura_et_al:LIPIcs.DNA.2020.8,
  author =	{Matsumura, Yuta and Kawamata, Ibuki and Murata, Satoshi},
  title =	{{Design Automation of Polyomino Set That Self-Assembles into a Desired Shape}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{8:1--8:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.8},
  URN =		{urn:nbn:de:0030-drops-129614},
  doi =		{10.4230/LIPIcs.DNA.2020.8},
  annote =	{Keywords: DNA polyomino, DNA nanostructure, DNA tile, Agent based simulation, Self-assembly, Combinatorial optimization, Simulated annealing}
}
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