The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Running time and program size for self-assembled squares
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Combinatorial optimization problems in self-assembly
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the computational complexity of tile set synthesis for DNA self-assembly
IEEE Transactions on Circuits and Systems II: Express Briefs
Synthesizing minimal tile sets for patterned DNA self-assembly
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
One-dimensional staged self-assembly
DNA'11 Proceedings of the 17th international conference on DNA computing and molecular programming
Synthesizing small and reliable tile sets for patterned DNA self-assembly
DNA'11 Proceedings of the 17th international conference on DNA computing and molecular programming
Synthesis of Tile Sets for DNA Self-Assembly
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Hi-index | 5.23 |
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.