Paper Info
Title
Synthesizing minimal tile sets for complex patterns in the framework of patterned DNA self-assembly
Abstract
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.
Year
DOI
Venue
2013
10.1016/j.tcs.2013.05.009
DNA
Keywords
DocType
Volume
correct NP-hardness proof,required number,rectangular colour pattern,DNA self-assembly,PATS problem,non-constant number,NP-hardness proof,optimization problem,combinatorial optimization point,complex pattern,minimal tile set,various pattern family,assembly complexity
Journal
499,
ISSN
Citations 
PageRank 
0304-3975
5
0.50
References 
Authors
8
2
Name
Order
Citations
PageRank
Eugen Czeizler110716.76
Alexandru Popa27013.34