Encyclopedia of Algorithms

Editors: Ming-Yang Kao

Randomized Self-Assembly

DOI: https://doi.org/10.1007/978-1-4939-2864-4_669


Years and Authors of Summarized Original Work

  • 2006; Becker, Rapaport, Rémila

  • 2008; Kao, Schweller

  • 2009; Chandran, Gopalkrishnan, Reif

  • 2010; Doty

Problem Definition

We use the abstract tile assembly model of Winfree [6], which models the aggregation of monomers called tiles that attach one at a time to a growing structure, starting from a single seed tile, in which bonds (“glues”) on the tile are specific (glues only stick to glues of the same type on other tiles) and cooperative (so that multiple weak glues are necessary to attach a tile). The general idea of randomizedself-assembly is to use the inherent randomness of self-assembly to help the assembly process. If multiple types of tiles are able to bind to a single binding site, then we assume that their relative concentrations determine the probability that each succeeds. With careful design, we can use the same tile set to create different structures, by changing the concentrations to affect what is likely to assemble. Another...

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Linear assembly Randomized Tile complexity 

Recommended Reading

  1. 1.
    Becker F, Rapaport I, Rémila E (2006) Self-assembling classes of shapes with a minimum number of tiles, and in optimal time. In: FSTTCS 2006: foundations of software technology and theoretical computer science, Kolkata, pp 45–56Google Scholar
  2. 2.
    Chandran H, Gopalkrishnan N, Reif JH (2012) Tile complexity of linear assemblies. SIAM J Comput 41(4):1051–1073. Preliminary version appeared in ICALP 2009Google Scholar
  3. 3.
    Doty D (2010) Randomized self-assembly for exact shapes. SIAM J Comput 39(8):3521–3552. Preliminary version appeared in FOCS 2009Google Scholar
  4. 4.
    Kao M-Y, Schweller RT (2008) Randomized self-assembly for approximate shapes. In: ICALP 2008: international colloqium on automata, languages, and programming, Reykjavik. Volume 5125 of Lecture notes in computer science. Springer, pp 370–384Google Scholar
  5. 5.
    Soloveichik D, Winfree E (2007) Complexity of self-assembled shapes. SIAM J Comput 36(6):1544–1569. Preliminary version appeared in DNA 2004Google Scholar
  6. 6.
    Winfree E (1998) Algorithmic self-assembly of DNA. PhD thesis, California Institute of Technology, June 1998Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Computing and Mathematical SciencesCalifornia Institute of TechnologyPasadenaUSA