Time Optimal Self-assembly for 2D and 3D Shapes: The Case of Squares and Cubes

Self-assembling tile systems are a model for assembling DNAbased nano artefacts. In the currently known constructions, most of the effort is put on garanteeing the size of the output object, whereas the geometrical efficiency of the assembling of the shape itself is left aside. We propose in this paper a framework to obtain provably time efficient selfassembling tile systems. Our approach consists in studying how the flow of information has to circulate within the desired shape to guarantee an optimal time construction. We show how this study can yield an adequate ordering of the tiling process from which one can deduced a provably time efficient tile systems for that shape. We apply our framework to squares and cubes for which we obtain time optimal self-assembling tile systems.