A manually-checkable proof for the NP-hardness of 11-color pattern self-assembly tile set synthesis
نویسندگان
چکیده
Patterned self-assembly tile set synthesis (Pats) aims at finding a minimum tile set to uniquely self-assemble a given rectangular (color) pattern. For k ≥ 1, k-Pats is a variant of Pats that restricts input patterns to those with at most k colors. A computer-assisted proof has been recently proposed for 2-Pats by Kari et al. [arXiv:1404.0967 (2014)]. In contrast, the best known manually-checkable proof is for the NP-hardness of 29Pats by Johnsen, Kao, and Seki [ISAAC 2013, LNCS 8283, pp. 699-710]. We propose a manually-checkable proof for the NP-hardness of 11-Pats.
منابع مشابه
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 color 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 NP-hardness of 29-PATS, where the best known is that of 60-PATS.
متن کامل3-Color Bounded Patterned Self-assembly - (Extended 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 ...
متن کاملSearch Methods for Tile Sets in Patterned DNA Self-Assembly
The Pattern self-Assembly Tile set Synthesis (PATS) problem, which arises in the theory of structured DNA self-assembly, is to determine a set of coloured tiles that, starting from a bordering seed structure, self-assembles to a given rectangular colour pattern. The task of finding minimum-size tile sets is known to be NP-hard. We explore several complete and incomplete search techniques for fi...
متن کاملCombinatorial Optimization in Pattern Assembly
Pattern self-assembly tile set synthesis (Pats) is a combinatorial optimization problem which aim at minimizing a rectilinear tile assembly system (RTAS) that uniquely self-assembles a given rectangular pattern, and is known to be NP-hard. Pats gets practically meaningful when it is parameterized by a constant c such that any given pattern is guaranteed to contain at most c colors (c-Pats). We ...
متن کامل$2^{(\log N)^{1/4-o(1)}}$ Hardness for Hypergraph Coloring
We show that it is quasi-NP-hard to color 2-colorable 8-uniform hypergraphs with 2 1/8−o(1) colors, where N is the number of vertices. There has been much focus on hardness of hypergraph coloring recently. In [17], Guruswami, H̊astad, Harsha, Srinivasan and Varma showed that it is quasi-NP-hard to color 2-colorable 8-uniform hypergraphs with 2 Ω( √ log log N) colors. Their result is obtained by ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comb. Optim.
دوره 33 شماره
صفحات -
تاریخ انتشار 2017