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A manually-checkable proof for the NP-hardness of 11-color pattern self-assembly tileset synthesis

Author

Listed:
  • Aleck Johnsen

    (Northwestern University)

  • Ming-Yang Kao

    (Northwestern University)

  • Shinnosuke Seki

    (Aalto University
    The University of Electro-Communications)

Abstract

Patterned self-assembly tile set synthesis (pats) aims at minimizing the number of distinct DNA tile types used to self-assemble a given rectangular color pattern. For an integer k, k-pats is the subproblem of pats that restricts input patterns to those with at most k colors. We give an efficient verifier, and based on that, we establish a manually-checkable proof for the NP-hardness of 11-pats; the best previous manually-checkable proof is for 29-pats.

Suggested Citation

  • Aleck Johnsen & Ming-Yang Kao & Shinnosuke Seki, 2017. "A manually-checkable proof for the NP-hardness of 11-color pattern self-assembly tileset synthesis," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 496-529, February.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:2:d:10.1007_s10878-015-9975-6
    DOI: 10.1007/s10878-015-9975-6
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    References listed on IDEAS

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    1. Paul W K Rothemund & Nick Papadakis & Erik Winfree, 2004. "Algorithmic Self-Assembly of DNA Sierpinski Triangles," PLOS Biology, Public Library of Science, vol. 2(12), pages 1-1, December.
    2. Erik Winfree & Furong Liu & Lisa A. Wenzler & Nadrian C. Seeman, 1998. "Design and self-assembly of two-dimensional DNA crystals," Nature, Nature, vol. 394(6693), pages 539-544, August.
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