Combinatorial Optimization in Pattern Assembly
Computational Complexity
2013-01-17 v1 Data Structures and Algorithms
Abstract
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.
Keywords
Cite
@article{arxiv.1301.3771,
title = {Combinatorial Optimization in Pattern Assembly},
author = {Shinnosuke Seki},
journal= {arXiv preprint arXiv:1301.3771},
year = {2013}
}