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Computing Minimum Tile Sets to Self-Assemble Color Patterns

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Algorithms and Computation (ISAAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8283))

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Abstract

Patterned self-assembly tile set synthesis (PATS) aims at finding a minimum tile set to uniquely self-assemble a given rectangular pattern. For k ≥ 1, k-PATS is a variant of PATS that restricts input patterns to those with at most k colors. We prove the \(\mathcal{NP}\)-hardness of 29-PATS, where the best known is that of 60-PATS.

This work is supported in part by NSF Grants CCF-1049899 and CCF-1217770 to A. J. and M-Y. K.; and HIIT Pump Priming Grants No. 902184/T30606 and Academy of Finland, Postdoctoral Researcher Grants 13266670/T30606 to S. S.

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Author information

Authors and Affiliations

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

    Aleck C. Johnsen & Ming-Yang Kao

  2. Department of Information and Computer Science, Aalto University, P.O. Box 15400, FI-00076, Aalto, Finland

    Shinnosuke Seki

Authors
  1. Aleck C. Johnsen
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  2. Ming-Yang Kao
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  3. Shinnosuke Seki
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Chinese University of Hong Kong, Shatin, 100084, Hong Kong, China

    Leizhen Cai

  2. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Clear Water Bay, 100044, Hong Kong, China

    Siu-Wing Cheng

  3. Department of Computer Science, University of Hong Kong, Porfkulam, 100084, Hong Kong, China

    Tak-Wah Lam

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© 2013 Springer-Verlag Berlin Heidelberg

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Johnsen, A.C., Kao, MY., Seki, S. (2013). Computing Minimum Tile Sets to Self-Assemble Color Patterns. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_65

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  • DOI: https://doi.org/10.1007/978-3-642-45030-3_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45029-7

  • Online ISBN: 978-3-642-45030-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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