Abstract
Patterned self-assembly tile set synthesis (Pats) is the problem of finding a minimal tile set which uniquely self-assembles into a given pattern. Czeizler and Popa proved the NP-completeness of Pats and Seki showed that the Pats problem is already NP-complete for patterns with 60 colors. In search for the minimal number of colors such that Pats remains 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 NP-complete for patterns with just three colors and, as a byproduct of this result, we also obtain a novel proof for the NP-completeness of pats which is more concise than the previous proofs.
The research of L. K. and S. K. was supported by the NSERC Discovery Grant R2824A01 and UWO Faculty of Science grant to L. K. The research of S. S. was supported by the HIIT Pump Priming Project Grant 902184/T30606.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-319-01928-4_15
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Kari, L., Kopecki, S., Seki, S. (2013). 3-Color Bounded Patterned Self-assembly. In: Soloveichik, D., Yurke, B. (eds) DNA Computing and Molecular Programming. DNA 2013. Lecture Notes in Computer Science, vol 8141. Springer, Cham. https://doi.org/10.1007/978-3-319-01928-4_8
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DOI: https://doi.org/10.1007/978-3-319-01928-4_8
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