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Staged Assembly

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 122 Accesses

Years and Authors of Summarized Original Work

  • 2008; Demaine, Demaine, Fekete, Ishaque, Rafalin, Schweller, Souvaine

  • 2013; Demaine, Eisenstat, Ishaque, Winslow

  • 2013; Winslow

Problem Definition

Algorithmic self-assembly is concerned with hands-off assembly of complex structures by mixing collections of simple particles that aggregate according to local rules. Staged self-assembly utilizes sequences of mixings to reduce the number of particle types used. The standard model of staged self-assembly builds on the abstract Tile Assembly Model (aTAM) of Winfree [7], where each particle is a non-rotatable unit square tile with a labeled glue on each side. Tiles attach to other tiles edgewise via glues of the same label, forming polyomino-shaped aggregates called assemblies.

In the simplest model, a pair of assemblies (of which single tiles are a special case) can attach via a single matching glue. In a more general model, a pair of assemblies can attach if they share a total of τ ∈ ℕglues....

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Recommended Reading

  1. 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): self-assembly in the 2HAM vs. aTAM. In: STACS 2013, Kiel, LIPIcs, vol 20. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, pp 172–184

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  2. Chen H, Doty D (2012) Parallelism and time in hierarchical self-assembly. In: Proceedings of the 23rd annual ACM-SIAM symposium on discrete algorithms (SODA), Kyoto, pp 1163–1182

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  3. Demaine ED, Demaine ML, Fekete SP, Ishaque M, Rafalin E, Schweller RT, Souvaine DL (2008) Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues. Nat Comput 7(3):347–370

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  4. Demaine ED, Eisenstat S, Ishaque M, Winslow A (2013) One-dimensional staged self-assembly. Nat Comput 12(2):247–258

    Article  MathSciNet  MATH  Google Scholar 

  5. Luhrs C (2010) Polyomino-safe DNA self-assembly via block replacement. Nat Comput 9(1):97–109

    Article  MathSciNet  MATH  Google Scholar 

  6. Soloveichik D, Winfree E (2007) Complexity of self-assembled shapes. SIAM J Comput 36(6):1544–1569

    Article  MathSciNet  MATH  Google Scholar 

  7. Winfree E (1998) Algorithmic self-assembly of DNA. PhD thesis, Caltech

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  8. Winslow A (2013a) Staged self-assembly and polyomino context-free grammars. In: Soloveichik D, Yurke B (eds) DNA 19, Tempe

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  9. Winslow A (2013b) Staged self-assembly and polyomino context-free grammars. PhD thesis, Tufts University

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Author information

Authors and Affiliations

  1. Department of Computer Science, Tufts University, Medford, MA, USA

    Andrew Winslow

Authors
  1. Andrew Winslow
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Corresponding author

Correspondence to Andrew Winslow .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Winslow, A. (2016). Staged Assembly. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_668

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