Computing Minimum Tile Sets to Self-Assemble Color Patterns

Patterned self-assembly tile set synthesis (PATS) aims at finding a minimum tile set to uniquely self-assemble a given rectangular pattern. For k ≥ 1, k-PATS is a variant of PATS that restricts input patterns to those with at most k colors. We prove the \(\mathcal{NP}\)-hardness of 29-PATS, where the best known is that of 60-PATS.

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