3-color Bounded Patterned Self-assembly
Computational Complexity
2013-06-17 v1
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.
Keywords
Cite
@article{arxiv.1306.3257,
title = {3-color Bounded Patterned Self-assembly},
author = {Lila Kari and Steffen Kopecki and Shinnosuke Seki},
journal= {arXiv preprint arXiv:1306.3257},
year = {2013}
}