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- Title
3-color bounded patterned self-assembly.
- Authors
Kari, Lila; Kopecki, Steffen; Seki, Shinnosuke
- Abstract
The problem of patterned self-assembly tile set synthesis ( Pats) is to find a minimal tile set which uniquely self-assembles into a given pattern. Czeizler and Popa proved the $$\mathrm {NP}$$ -completeness of Pats and Seki showed that the Pats problem is already $$\mathrm {NP}$$ -complete for patterns with 60 colors. In search for the minimal number of colors such that Pats remains $$\mathrm {NP}$$ -complete, we introduce multiple bound Pats ( mbPats) where we allow bounds for the numbers of tile types of each color. We show that mbPats is $$\mathrm {NP}$$ -complete for patterns with just three colors and, as a byproduct of this result, we also obtain a novel proof for the $$\mathrm {NP}$$ -completeness of Pats which is more concise than the previous proofs.
- Subjects
CHEMICAL synthesis; VISUAL environment; DIMENSIONAL preference; PSYCHOLOGY of color; ELECTRONIC color sensors
- Publication
Natural Computing, 2015, Vol 14, Issue 2, p279
- ISSN
1567-7818
- Publication type
Article
- DOI
10.1007/s11047-014-9434-9