Synthesizing Minimal Tile Sets for Complex Patterns in the Framework of Patterned DNA Self-Assembly

  • Eugen Czeizler
  • Alexandru Popa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7433)


Ma and Lombardi (2009) introduce and study the Pattern self-Assembly Tile set Synthesis (PATS) problem. In particular they show that the optimization version of the PATS problem is NP-hard. However, their NP-hardness proof turns out to be incorrect. Our main result is to give a correct NP-hardness proof via a reduction from the 3SAT. By definition, the PATS problem assumes that the assembly of a pattern starts always from an “L”-shaped seed structure, fixing the borders of the pattern. In this context, we study the assembly complexity of various pattern families and we show how to construct families of patterns which require a non-constant number of tiles to be assembled.


Assembly Complexity Truth Assignment Tile Type Tile Assembly Model Tile Assembly System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Eugen Czeizler
    • 1
  • Alexandru Popa
    • 2
  1. 1.Department of Information and Computer Science, School of ScienceAalto UniversityAaltoFinland
  2. 2.Department of Communications and Networking, School of Electrical EngineeringAalto UniversityAaltoFinland

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