花型装配中的组合优化
Combinatorial Optimization in Pattern Assembly
摘要：
图案自组装瓦片集综合（Pattern self-assembled tile set synthesis，PATS）是一个以最小化可唯一自组装给定矩形图案的直线瓦片组装系统为目标的组合优化问题，是NP难问题.当PATS由常数c参数化时，它变得实际上有意义，使得任何给定的图案都保证最多包含c种颜色（c-PATS）。我们首先研究简单的模式和性质的最小RTAS他们。在此基础上，设计了一个59色的图案，将3SAT约简为59色的图案，并证明了59-PATS是NP-难的。
英文摘要：
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 first investigate simple patterns and properties of minimum RTASs for them. Then based on them, we design a 59-colored pattern to which 3SAT is reduced, and prove that 59-PATS is NP-hard.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
