Graduate Student Talk; Staged Self-AssemblyAssembly of Arbitrary Shapes with O(1) Glues

Abstract

Self-assembly is the process by which an organized structure can spontaneously form from simple parts. Adleman, Rothemund and Winfree suggested the two-dimensional tile assembly model. In this model a tile is an oriented unit square. Each edge has an associated bond type that interacts with a certain strength with matching sides of other tiles. A new tile can adsorb to a growing complex when the total interaction strength with its neighbors exceeds a certain parameter t.

We introduce staged self-assembly of tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. Staging allows us to break through the traditional lower bounds in the tile self-assembly by encoding the shape in the staging algorithm instead of tiles. All of our results are based on the practical assumption that only a constant number of glues, and thus only a constant number of tiles, can be engineered. We show how to assemble arbitrary shapes in staged assembly model.