Time Optimal Self-assembly for 2D and 3D Shapes: The Case of Squares and Cubes.
Résumé
We refine the current notion of time in self-assembly, and show constructions which are time- optimal, not only up to a constant. For this, we refine the notion of time-complexity of an assembly, to separate the influence of the concentrations from the intrinsic speed of the assembly. We give a time-optimal construction for the square. A formulation of tile-sets in terms of time allows us to build an optimal system for 3D-cubes.