Particle-Based Assembly Using Precise Global Control

Abstract In micro- and nano-scale systems, particles can be moved by using an external force like gravity or a magnetic field. the presence of adhesive that attach to each other, challenge is decide whether shape constructible. Previous work provides class shapes for which constructibility decided efficiently when move maximally into same direction induced global signal. this paper we consider single step model, i.e., model in particle moves one unit given direction. We restrict assembly process such at time actually added within workspace. prove deciding NP-complete three-dimensional shapes, maximum constructible approximated. The approximation algorithm applies 2D. further present linear-time algorithms not tree-shape 2D 3D Scaling yields constructibility; particular show 2-scaled copy every non-degenerate polyomino setting 3-scaled polycube