Encyclopedia of Algorithms

Editors: Ming-Yang Kao

Hierarchical Self-Assembly

DOI: https://doi.org/10.1007/978-1-4939-2864-4_667


Years and Authors of Summarized Original Work

  • 2005; Aggarwal, Cheng, Goldwasser, Kao, Espanes, Schweller

  • 2012; Chen, Doty

  • 2013; Cannon, Demaine, Demaine, Eisenstat, Patitz, Schweller, Summers, Winslow

Problem Definition

The general idea of hierarchical self-assembly (a.k.a., multiple tile [2], polyomino [8, 10], two-handed [3, 5, 6]) is to model self-assembly of tiles in which attachment of two multi-tile assemblies is allowed, as opposed to all attachments being that of a single tile onto a larger assembly. Several problems concern comparing hierarchical self-assembly to its single-tile-attachment variant (called the “seeded” model of self-assembly), so we define both models here. The model of hierarchical self-assembly was first defined (in a slightly different form that restricted the size of assemblies that could attach) by Aggarwal, Cheng, Goldwasser, Kao, Moisset de Espanes, and Schweller [2]. Several generalizations of the model exist that incorporated staged mixing of test...

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Hierarchical assembly Intrinsic universality Running time Self-assembly Verification 

Recommended Reading

  1. 1.
    Adleman LM, Cheng Q, Goel A, Huang M-D (2001) Running time and program size for self-assembled squares. In: STOC 2001: proceedings of the thirty-third annual ACM symposium on theory of computing, Hersonissos. ACM, pp 740–748CrossRefGoogle Scholar
  2. 2.
    Aggarwal G, Cheng Q, Goldwasser MH, Kao M-Y, Moisset de Espanés P, Schweller RT (2005) Complexities for generalized models of self-assembly. SIAM J Comput 34:1493–1515. Preliminary version appeared in SODA 2004Google Scholar
  3. 3.
    Cannon S, Demaine ED, Demaine ML, Eisenstat S, Patitz MJ, Schweller RT, Summers SM, Winslow A (2013) Two hands are better than one (up to constant factors). In: STACS 2013: proceedings of the thirtieth international symposium on theoretical aspects of computer science, Kiel, pp 172–184Google Scholar
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    Chen H-L, Doty D (2012) Parallelism and time in hierarchical self-assembly. In: SODA 2012: proceedings of the 23rd annual ACM-SIAM symposium on discrete algorithms, Kyoto, pp 1163–1182Google Scholar
  5. 5.
    Demaine ED, Patitz MJ, Rogers T, Schweller RT, Summers SM, Woods D (2013) The two-handed tile assembly model is not intrinsically universal. In: ICALP 2013: proceedings of the 40th international colloquium on automata, languages and programming, Riga, July 2013Google Scholar
  6. 6.
    Doty D, Patitz MJ, Reishus D, Schweller RT, Summers SM (2010) Strong fault-tolerance for self-assembly with fuzzy temperature. In: FOCS 2010: proceedings of the 51st annual IEEE symposium on foundations of computer science, Las Vegas, pp 417–426Google Scholar
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    Epstein IR, Pojman JA (1998) An introduction to nonlinear chemical dynamics: oscillations, waves, patterns, and chaos. Oxford University Press, OxfordGoogle Scholar
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    Luhrs C (2010) Polyomino-safe DNA self-assembly via block replacement. Nat Comput 9(1):97–109. Preliminary version appeared in DNA 2008Google Scholar
  9. 9.
    Winfree E (1998) Algorithmic self-assembly of DNA. PhD thesis, California Institute of Technology, June 1998Google Scholar
  10. 10.
    Winfree E (2006) Self-healing tile sets. In: Chen J, Jonoska N, Rozenberg G (eds) Nanotechnology: science and computation. Natural computing series. Springer, Berlin/New York, pp 55–78CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Computing and Mathematical SciencesCalifornia Institute of TechnologyPasadenaUSA