Synthesizing minimal tile sets for complex patterns in the framework of patterned DNA self-assembly

Eugen Czeizler, Alexandru Popa

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


The Pattern self-Assembly Tile set Synthesis (PATS) problem asks to determine a set of coloured tiles which, left alone in the solution, would self-assemble to implement a given rectangular colour pattern. Ma and Lombardi (2009) introduce and study the PATS problem from a combinatorial optimization point of view, trying to find algorithms which would minimize the required number of distinct tile types. In particular, they claimed that the above optimization 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.

Original languageEnglish
Pages (from-to)23-37
Number of pages15
JournalTheoretical Computer Science
Publication statusPublished - Aug 12 2013


  • DNA self-assembly
  • Minimal tile sets
  • NP-hardness
  • Pattern assembly
  • Tile assembly model

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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