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

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Authors

EUGEN Czeizler POPA Alexandru

Year of publication 2013
Type Article in Periodical
Magazine / Source Theoretical Computer Science
MU Faculty or unit

Faculty of Informatics

Citation
Web http://www.sciencedirect.com/science/article/pii/S0304397513003605
Doi http://dx.doi.org/10.1016/j.tcs.2013.05.009
Field Informatics
Keywords DNA self-assembly; Tile assembly model; Pattern assembly; Minimal tile sets; NP-hardness
Description 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.
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