Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Self-Assembly at Temperature 1

  • Pierre-Étienne Meunier
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_663

Years and Authors of Summarized Original Work

  • 2000; Rothemund, Winfree

  • 2009; Doty, Patitz, Summers

  • 2011; Cook, Fu, Schweller

  • 2014; Meunier, Patitz, Summers, Theyssier, Winslow, Woods

Problem Definition

Temperature 1 (also called noncooperative) self-assembly is a model of the formation of structures by growing and branching tips. Despite its ubiquity in nature (in systems such as plants and mycelium or percolation processes) and apparent dynamic simplicity, it is one of the least understood models of self-assembly.

This model was introduced in a broader framework called the abstract Tile Assembly Model (aTAM) [10]. In the aTAM, we consider tile assembly systems, which are defined by a finite set T of square or cubic tile types, an initial seed assembly\(\sigma\)

Keywords

Computational geometry Concurrency Self-assembly 
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Recommended Reading

  1. 1.
    Adleman LM, Cheng Q, Goel A, Huang MDA, Kempe D, de Espanés PM, Rothemund PWK (2002) Combinatorial optimization problems in self-assembly. In: Proceedings of the thirty-fourth annual ACM symposium on theory of computing (STOC), Montréal, pp 23–32Google Scholar
  2. 2.
    Cook M, Fu Y, Schweller RT (2011) Temperature 1 self-assembly: deterministic assembly in 3D and probabilistic assembly in 2D. In: Proceedings of the 22nd annual ACM-SIAM symposium on discrete algorithms (SODA), San Francisco, pp 570–589, arxiv preprint: arXiv:0912.0027Google Scholar
  3. 3.
    Doty D, Lutz JH, Patitz MJ, Summers SM, Woods D (2009) Intrinsic universality in self-assembly. In: Proceedings of the 27th international symposium on theoretical aspects of computer science (STACS), Nancy, pp 275–286. arxiv preprint: arXiv:1001.0208Google Scholar
  4. 4.
    Doty D, Lutz JH, Patitz MJ, Schweller RT, Summers SM, Woods D (2012) The tile assembly model is intrinsically universal. In: Proceedings of the 53rd annual IEEE symposium on foundations of computer science (FOCS), New Brunswick, pp 439–446. arxiv preprint: arXiv:1111.3097Google Scholar
  5. 5.
    Doty D, Patitz MJ, Summers SM (2009) Limitations of self-assembly at temperature 1. In: Proceedings of the fifteenth international meeting on DNA computing and molecular programming, Fayetteville, 8–11 June 2009, pp 283–294. arxiv preprint: arXiv:0906.3251Google Scholar
  6. 6.
    Maňuch J, Stacho L, Stoll C (2010) Two lower bounds for self-assemblies at temperature 1. J Comput Biol 17(6):841–852MathSciNetCrossRefGoogle Scholar
  7. 7.
    Meunier PE, Patitz MJ, Summers SM, Theyssier G, Winslow A, Woods D (2014) Intrinsic universality in tile self-assembly requires cooperation. In: Proceedings of the 25th annual ACM-SIAM symposium on discrete algorithms (SODA), Portland, pp 752–771. arxiv preprint: arXiv:1304.1679Google Scholar
  8. 8.
    Reif JH, Song T (2013) Complexity and computability of temperature-1 tilings. In: FNANO 2013, poster abstractGoogle Scholar
  9. 9.
    Rothemund PWK, Winfree E (2000) The program-size complexity of self-assembled squares (extended abstract). In: Proceedings of the thirty-second annual ACM symposium on theory of computing (STOC), Portland. ACM, pp 459–468. doi:http://doi.acm.org/10.1145/335305.335358
  10. 10.
    Winfree E (1998) Algorithmic self-assembly of DNA. PhD thesis, California Institute of TechnologyGoogle Scholar
  11. 11.
    Woods D (2013) Intrinsic universality and the computational power of self-assembly. In: Neary T, Cook M (eds) MCU, Zürich. EPTCS, vol 128, pp 16–22Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Le Laboratoire d’Informatique Fondamentale de Marseille (LIF)Aix-Marseille UniversitéMarseilleFrance