Combinatorial Optimization Problem in Designing DNA Self-Assembly Tile Sets

DNA self-assembly has been advocated as a bottom-up manufacturing technology (as applicable in the nano scales) and for algorithmic computation. However, previous research did not address the issue of designing a tile set for an arbitrary target pattern (as to ensure periodic repetition in its assembly) of finite size. This paper considers the synthesis of tile sets for DNA self-assembly and analyzes it as a combinatorial optimization problem. This problem is referred to as PATS (pattern assembling tile-set synthesis). A brief proof is provided for the NP-completeness of PATS.